Composite Systems Decisions (Decision Engineering)

Decision Engineering Series Editor Dr Rajkumar Roy Department of Enterprise Integration School of Industrial and Manu...

Author: Mark Sh. Levin

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Decision Engineering

Series Editor Dr Rajkumar Roy Department of Enterprise Integration School of Industrial and Manufacturing Science Cranﬁeld University Cranﬁeld Bedford MK43 0AL UK

Other titles published in this series Cost Engineering in Practice John McIlwraith IPA – Concepts and Applications in Engineering Jerzy Pokojski Strategic Decision Making Navneet Bhushan and Kanwal Rai Product Lifecycle Management John Stark From Product Description to Cost: A Practical Approach Volume 1: The Parametric Approach Pierre Foussier From Product Description to Cost: A Practical Approach Volume 2: Building a Speciﬁc Model Pierre Foussier Decision-Making in Engineering Design Yotaro Hatamura Intelligent Decision-making Support Systems: Foundations, Applications and Challenges Jatinder N.D. Gupta, Guisseppi A. Forgionne and Manuel Mora Publication due April 2006 Metaheuristics: A comprehensive guide to the design and implementation of effective optimisation strategies Christian Prins, Marc Sevaux and Kenneth Sörensen Publication due December 2006 Context-aware Emotion-based Multi-agent Systems Rajiv Khosla, Nadia Bianchi-Berthouse, Mel Seigel and Toyoaki Nishida Publication due July 2006

Mark Sh. Levin

Composite Systems Decisions With 126 Figures

123

Mark Sh. Levin, PhD Institute for Information Transmission Problems Russian Academy of Sciences 19 Bolshoj Karetny lane Moscow 127994 Russia

British Library Cataloguing in Publication Data Levin, M. Sh (Mark Shmuilovich), 1948Composite systems decisions. - (Decision engineering) 1. Systems engineering 2. Combinatorial optimization I. Title 620’.0011 ISBN-10: 184628001X Library of Congress Control Number: 2005935665 Decision Engineering Series ISSN 1619-5736 ISBN-10: 1-84628-001-X e-ISBN 1-84628-080-X ISBN-13: 978-1-84628-001-6

Printed on acid-free paper

© Springer-Verlag London Limited 2006 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a speciﬁc statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Printed in Germany 987654321 Springer Science+Business Media springer.com

The book is dedicated to colleagues

Preface

Traditional literacy consists of two phases: Phase 1. Basic literacy (i.e., to read, to write, to account). Phase 2. Computer literacy (e.g., to work with computers, to write computer programs). This book describes the research and educational direction called Design of composite systems decisions, which can be considered as an important part of the third phase of literacy. Let us consider the place and signiﬁcance of our direction (i.e., design of composite systems decisions). Design of composite systems decisions is a composite direction which implements combinatorial (modular) synthesis. This book focuses on composite decisions when a resultant decision consists of some interconnected parts (subdecisions, local decisions) and corresponds to a composite (composable, modular, decomposable) system. Our viewpoint is based on composition of the following: systems engineering and life-cycle engineering, computer science, applied mathematics and applied combinatorial optimization, and various application domains (e.g., engineering, management, computer science, and social science). The material can be considered as the continuation of the author’s monograph Combinatorial Engineering of Decomposable Systems (Kluwer, 1998) with the basic orientation to various application domains (engineering, information technology, management). The book consists of the four parts: Part I. Issues of Information Technology, including information, specialists, solving frameworks. Evidently, this part involves Decision-making Technology, including problem analysis, problem structuring, evaluation of alternatives, selection of the best alternatives, and analysis of the results, i.e., basic paradigm of decision making by H.A. Simon (e.g. [759, 762]). Note our direction extends traditional decision making paradigm by the special attention to generation (synthesis) of composite decisions on the basis of hierarchical combinatorial synthesis: (a) selection of the best local decisions and (b) composition of the local decisions into a resultant composite global decision. The eﬀorts are based on combinatorial engineering and hierarchical morphological multicriteria design, which were proposed in recent years by the author (e.g. [494, 497]).

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Preface

Part II. Systems Approaches (analysis, synthesis) and systems engineering are basic active generalized methodologies to describe/to model, to design, to redesign contemporary complex and multidisciplinary systems in engineering, management, social life, etc. Thus, we examine system modeling, analysis, synthesis and basic paradigms as a product life cycle and corresponding problems in life-cycle engineering (e.g., design/management of life cycle). The following basic system technological problems are examined: 1. hierarchical combinatorial system modeling; 2. system design as a combinatorial synthesis of composite systems; 3. revelation of system bottlenecks; 4. redesign/improvement of a system; 5. multistage design of systems, trajectory design; 6. system evaluation; and 7. system evolution for composite systems. Here, a special chapter is targeted to issues of system development/ evolution. Part III. Applied Systems Decisions illustrates the usage of the abovementioned design approaches to technological problems in many domains: synthesis of software, evaluation and redesign of buildings, planning of medical treatment, design of a multistage immunoassay technology, etc. The applications described can be used as a set of basic analogues for future extension and improvement. Part IV. Educational Issues is an additional crucial part of our direction and is targeted to three educational courses. The book is oriented to applied researchers, students, and practitioners in many domains. Concurrently, the material will be of interest to various scientists (e.g., mathematicians, computer scientists, economists, social engineers). The book can be used as a text for some courses (e.g., systems engineering, system design, life-cycle engineering, engineering design, combinatorial synthesis) at the level of undergraduate (a compressed version), graduate/PhD levels and for continuing education. Note, special student team research projects can be included into educational plans. The student teams above can involve students of diﬀerent professional domains. Further, the material will be useful for modular curriculum design. The draft version of the book was written in Israel (Beer Sheva, Tel Aviv) in 2000–2004, and the ﬁnal version was prepared in Moscow, Russia.

Moscow, June 2005

Mark Sh. Levin

Acknowledgments

First, I am grateful for the permission to use (to reprint) materials from my published articles: 1. IEEE, permission in respect of the following article (for Chapters 3 and 7): M.Sh. Levin, Modular System Synthesis: Example for Composite Packaged Software. IEEE Trans. on SMC, Part C, 35(4), 544–553, 2005. 2. Elsevier, permission in respect of the following articles (for Chapters 3, 11, and 12): M.Sh. Levin, System Synthesis with Morphological Clique Problem: Fusion of Subsystem Evaluation Decisions. Information Fusion, 2(3), 225–237, 2001. M.Sh. Levin, L. Sokolova, Hierarchical Combinatorial Planning of Medical Treatment, Computer Methods and Programs in Biomedicine, 73(1), 3–11, 2004. M.Sh. Levin, M. Firer, Hierarchical Morphological Design of Immunoassay Technology, Computers in Biology and Medicine, 35(3), 229–245, 2005. Second, I thank my colleagues (Moscow, 1970–1980) for their aid and collaboration in the multidisciplinary analysis and design of several applied engineering systems (a communication system, a control unit for a multiradar system, software systems, management information systems, decision support systems). The names of the above-mentioned colleagues are: Eng. Victor F. Brilliantov, Eng. Valentin P. Chuvilin, Eng. Vyacheslav Yu. Demyanenko, Dr Vladimir M. Kisler, Eng. Tatjana Kleimenova, Eng. V. Kurnosov, Dr Ruﬁna R. Naumova, Eng. Natalia Zalogina, Dr Yuri Zotov, Eng. Andrew Gilbershtein, Geologist Margarita S. Alferova-Temkina, Geologist Valery K. Burakov, Dr Vladimir Slavkin, Dr Alexander Rabinovish, Eng. Leonid Vainer, Eng. Alexander Berman, Technician Marina Kizim, Eng. Elena Vainer (Yazenko), Eng. Evgenia Chestnaya, Eng. Nina Sokolova (Martynova), and Technician Stas Bavrin.

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Acknowledgments

Third, I am grateful to my colleagues for the joint formal/informal R & D projects (Russia, Israel, Canada; 1981–2003): Dr Moshe A. Danieli (Ariel, Israel), Dr Boris J. Feldman (Ramat Gan, Israel), Dr Vladimir I. Fershter (Moscow, Russia), Dr Michael A. Firer (Ariel, Israel), Dr Oleg P. Kudinov (Moscow, Russia), Dr Yuri L. Levine (Vienna, Austria), Eng. David B. Magidson (Moscow, Russia), Researcher Andrew A. Michailov (Moscow, Russia), Dr Mark L. Nisnevich (Ariel, Israel), Dr Vladimir I. Poroskoon (Moscow, Russia), Prof Ivan Rival (Ottawa, Canada), Eng. Elena P. Samsonova (Moscow, Russia), Prof Suresh Sethi (Torono, Canada), Prof Jeﬀrey Sidney (Ottawa, Canada), Dr Ludmila V. Sokolova (Moscow, Russia), and Prof Chelliah Sriskandarajah (Toronto, Canada). Fourth, I acknowledge my scientiﬁc colleagues for many useful discussions on information technology, decision making, systems engineering, system modeling, and algorithm design and studies: Prof Fuad Aleskerov (Moscow, Russia), Prof Lev Bregman (Beer Sheva, Israel), Dr Pavel Chebotarev (Moscow, Russia), Prof Baruch Fischhoﬀ (Pittsburg, USA), Dr Jane M. Furems (Moscow, Russia), Dr Alex Kreinin (Toronto, Canada), Prof Boris G. Mirkin (London, UK), Prof Ali Ngom (Ottawa, Canada), Prof Michael Drahlin (Ariel, Israel), Prof Brian Prasad (Pasadena, USA), Prof Alexander Razborov (Moscow, Russia), Prof Yoram Reich (Tel-Aviv, Israel), Prof Ilya M. Sobol (Moscow, Russia), Prof Roman B. Statnikov (Moscow, Russia and Monterey, USA), Dr Vadim G. Timkovsky (Toronto, Canada), and Prof Alek Vainstein (Haifa, Israel). Fifth, I thank my relatives and friends for their attention and aid: Marina Bakhnov (Costa–Rica/USA), Valery Dikovsky (Israel), Jane M. Furems (Russia), Victor Gelman (USA), Rose Levin (Russia), Victor and Ira Levin (USA), Yuri and Natalia Levine (Austria), Esﬁr and George Leviten (USA), Jane and Michael Lozovsky (Russia), Ira Natapov (USA), Mark and Alla Neizvestny (Israel), Yuri and Ira Purinson (Israel), Alla and Valentin Rubenchik (Israel), and Boris and Luda Shmulyan (Israel). Sixth, I am grateful to Kate Brown (Springer, London, UK), Andrea Koehler (LE-TeX, Leipzig, Germany), and Sorina Moosdorf (LE-TeX, Leipzig, Germany) for their valuable work in editing my manuscript.

Contents

Part I Issues of Information Technology 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 General Problem-solving Framework . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 View from Artiﬁcial Intelligence Position . . . . . . . . . . . . . . . . . . . 7 1.4 Composite Systems and Problems . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5 Basic System Technological Problems . . . . . . . . . . . . . . . . . . . . . . 10 1.6 Information Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2

Components of Information Technology . . . . . . . . . . . . . . . . . . . . 2.1 Properties of Information Technology . . . . . . . . . . . . . . . . . . . . . . 2.2 Information and Hierarchical Structuring . . . . . . . . . . . . . . . . . . . 2.2.1 Schemes and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Approaches to Knowledge Acquisition . . . . . . . . . . . . . . . . 2.2.3 Some Hierarchical Information Systems . . . . . . . . . . . . . . 2.2.4 Our Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Decision-making Paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Decision-making Framework . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Towards Architecture of Decision Support Systems . . . . 2.3.3 Four-domain Decision Making . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Basic Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5 Multicriteria Ranking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Specialist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Role of the Specialist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Professional Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Solving Frameworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Search Spaces and Strategies . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Heuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Metaheuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.4 Algorithm Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13 13 13 13 15 16 17 18 18 18 20 20 22 22 22 23 23 23 25 26 26 28

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Part II System Approaches 3

Systems: Models, Analysis, and Synthesis . . . . . . . . . . . . . . . . . . 3.1 System, Frames, and Modularity . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 System and Structural Modeling . . . . . . . . . . . . . . . . . . . . 3.1.2 Two Basic Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Modular, Component-based Systems . . . . . . . . . . . . . . . . . 3.2 System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Principles of System Analysis . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Measurement Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 System Properties, Requirements, and Criteria . . . . . . . . 3.3 System Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Approaches to System Design/Synthesis . . . . . . . . . . . . . . 3.3.2 Hierarchical Morphological Approach . . . . . . . . . . . . . . . . 3.3.3 Towards Eﬃciency of Combinatorial Synthesis . . . . . . . . 3.3.4 Multistage Design/Planning: Example . . . . . . . . . . . . . . . 3.4 Multicriteria Evaluation of Composite Systems . . . . . . . . . . . . . . 3.4.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Traditional Approaches to Multicriteria Evaluation . . . . 3.4.3 Morphological Clique Problem for Evaluation . . . . . . . . . 3.4.4 Usage of Poset-like Scales for System Components . . . . . 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31 31 31 32 33 34 34 34 35 36 36 38 42 42 46 46 48 50 50 50

4

Issues of Systems Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Life-cycle Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Basic Stages of the Life Cycle . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Design/Management Problems and Life Cycle . . . . . . . . . 4.1.3 System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.5 System Redesign and Bottlenecks . . . . . . . . . . . . . . . . . . . 4.2 Maintenance of Composite Systems . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Multistage/Trajectory Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Morphological Scheme of Product . . . . . . . . . . . . . . . . . . . 4.3.3 Multistage Product Trajectory . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Design of Tree-like Trajectory . . . . . . . . . . . . . . . . . . . . . . . 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53 53 53 53 55 55 56 57 59 59 60 61 63 64

5

System Development and Evolution . . . . . . . . . . . . . . . . . . . . . . . 5.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Short Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Basic System Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Combinatorial Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Change Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Exchange Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Binary Relations over Change Operations . . . . . . . . . . . .

65 65 66 67 67 67 68 69

Contents

6

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5.4.4 Multicriteria Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Technological Evolution Problems . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Combinatorial Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 One-stage System Change . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.2 Multistage System Change . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.3 Auxiliary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Extended Cycle of System Evolution . . . . . . . . . . . . . . . . . . . . . . . 5.8 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69 69 70 70 70 71 71 71 74

Conﬁguration and Multi-product Systems . . . . . . . . . . . . . . . . . 6.1 Conﬁguration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Product Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Multi-product System: Common Modules . . . . . . . . . . . . . . . . . . . 6.3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Two-level Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 Structural Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.4 Complex Design Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75 75 76 77 77 77 84 86 91

Part III Applied Systems Decisions 7

Synthesis of Composite Packaged Software . . . . . . . . . . . . . . . . . 95 7.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 7.2 Approaches to Software Development . . . . . . . . . . . . . . . . . . . . . . 96 7.3 Criteria for Evaluation of Software . . . . . . . . . . . . . . . . . . . . . . . . . 97 7.4 Assessment of Interconnection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 7.5 Example of Modular Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 7.5.1 Model of Composite Applied Software . . . . . . . . . . . . . . . . 98 7.5.2 Hierarchy of Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 7.5.3 Comparison of Initial Alternatives for Components . . . . 99 7.5.4 Composing of Subsystem Alternatives . . . . . . . . . . . . . . . . 99 7.5.5 Composition and Analysis of System Alternatives . . . . . 100 7.5.6 Redundancy of Alternatives . . . . . . . . . . . . . . . . . . . . . . . . 102 7.6 Example of Multistage Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 7.6.1 Aggregation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7.6.2 Trajectory Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

8

Improvement of Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 8.1 Evaluation and Redesign of Buildings . . . . . . . . . . . . . . . . . . . . . . 107 8.2 Scheme for Improvement/Redesign . . . . . . . . . . . . . . . . . . . . . . . . 109 8.3 Structure of Building, Criteria, and Scales . . . . . . . . . . . . . . . . . . 110 8.4 Basic Set of Improvement Actions . . . . . . . . . . . . . . . . . . . . . . . . . 111 8.5 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 8.5.1 Evaluation Example: Integration Tables . . . . . . . . . . . . . . 113

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8.5.2 Evaluation Example: Morphological Design . . . . . . . . . . . 114 8.5.3 Improvement Actions and Criteria . . . . . . . . . . . . . . . . . . . 118 8.5.4 Improvement Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 8.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 9

Planning in Concrete Macrotechnology . . . . . . . . . . . . . . . . . . . . 123 9.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 9.2 Concrete Macrotechnology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 9.2.1 Basic Initial Information . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 9.2.2 Example for Normal Weight Concrete 300 . . . . . . . . . . . . 125 9.2.3 Example for System Improvement . . . . . . . . . . . . . . . . . . . 128 9.2.4 Example for Series–Parallel Production Process . . . . . . . 128 9.2.5 Example for Multistage Design . . . . . . . . . . . . . . . . . . . . . . 128 9.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

10 Transformation of a Specialist’s Proﬁle . . . . . . . . . . . . . . . . . . . . 131 10.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 10.2 Example of Retraining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 10.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 11 Planning of Medical Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 11.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 11.2 Medical Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 11.2.1 Structure of Medical Plan and Alternatives . . . . . . . . . . . 135 11.2.2 Criteria and Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 11.2.3 Compatibility of Local Decisions . . . . . . . . . . . . . . . . . . . . 137 11.2.4 Composite Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 11.3 Adaptation, Improvement, and Multistage Planning . . . . . . . . . 140 11.3.1 Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 11.3.2 Improvement of Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . 141 11.3.3 Multistage Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 11.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 11.4.1 Towards Medical Decision Support Systems . . . . . . . . . . . 142 11.4.2 Issues of Knowledge Acquisition . . . . . . . . . . . . . . . . . . . . . 142 11.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 12 Design of Immunoassay Technology . . . . . . . . . . . . . . . . . . . . . . . . 145 12.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 12.2 Immunoassay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 12.3 Structure of Immunoassay System . . . . . . . . . . . . . . . . . . . . . . . . . 146 12.4 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 12.4.1 Alternative Local Decisions . . . . . . . . . . . . . . . . . . . . . . . . . 147 12.4.2 Compatibility of Local Decisions . . . . . . . . . . . . . . . . . . . . 152 12.4.3 Design of Composite Decisions for Stages . . . . . . . . . . . . . 152 12.4.4 System Structure with Design Alternatives . . . . . . . . . . . 153 12.4.5 Compatibility for Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 12.4.6 Resultant Composite Decisions . . . . . . . . . . . . . . . . . . . . . . 154 12.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

Contents

xv

13 Common Part of Digraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 13.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 13.2 Common Part of Two Digraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 13.2.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 13.2.2 Basic Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 13.2.3 Ordinal Weights of Arcs and Comparison Binary Relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 13.3 Common Part of Several Digraphs . . . . . . . . . . . . . . . . . . . . . . . . . 165 13.3.1 Description of Arcs and Compatibility . . . . . . . . . . . . . . . 165 13.3.2 Solving Scheme and Algorithm . . . . . . . . . . . . . . . . . . . . . . 167 13.3.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 13.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 13.4 Additional Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 13.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 14 The Last Mile Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 14.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 14.2 Description of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 14.3 Alternatives, Criteria, and Compatibility . . . . . . . . . . . . . . . . . . . 173 14.4 Composite Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 14.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 15 Combinatorial Model of Political Administration . . . . . . . . . . 177 15.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 15.2 General Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 15.3 Schemes of Political Administration . . . . . . . . . . . . . . . . . . . . . . . . 178 15.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Part IV Educational Issues 16 General Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 16.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 16.2 Generalized Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 16.2.1 Trends in Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 16.2.2 Basic Design Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 16.2.3 Educational Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 16.2.4 Educational Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 16.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 16.3.1 Implementation of Program . . . . . . . . . . . . . . . . . . . . . . . . . 187 16.3.2 Towards Organizational Structure . . . . . . . . . . . . . . . . . . . 189 16.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 17 Design of Systems (Structural Approach) . . . . . . . . . . . . . . . . . . 193 17.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 17.2 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 17.3 Lectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 17.4 Laboratory Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

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17.5 Textbooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 17.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 18 Applied Combinatorial Optimization . . . . . . . . . . . . . . . . . . . . . . . 199 18.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 18.2 Goals and Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 18.3 Multi-layer Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 18.4 Lectures and Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 18.5 Textbooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 18.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

Part I

Issues of Information Technology

1 Introduction

1.1 Preliminaries Professor A.P. Ershov has deﬁned a skill in programming as the second literacy [235]. He has pointed out that in the centuries since the creation of printing machines, a majority of population have got the skill to read, to write, and to account, and this was the ﬁrst literacy. In the 1960s and 1970s, the number of people who could develop software and apply computers increased, and this was a stage of the second literacy [235]. Recently, a majority of the population have obtained skills in computer technologies. What will be next? In recent years we have seen many new software packages and information systems, computer networks and distributed computing, knowledge-based systems. What is crucial now? Let us examine the stratiﬁcation of contemporary computer technology as follows: (1) hardware, communication equipment; (2) software; (3) stratum of algorithms and interactive procedures (algorithm-ware); (4) mathematical models (model-ware); (5) information systems (data, knowledge); and (6) application problems. In my opinion, obtaining good decisions for applied problems is the main result of computer/information technologies. In 1970s and 1980s, theories concerning the analysis and design of eﬀective algorithms (e.g., complexity theory) were focused on bottlenecks in computer technology. Now there are bottlenecks at application stratum. Note, humans play primary roles not only as users, but also as sources of information (e.g., expert, specialist), researcher, decision maker. Thus we get the following: Stage 1. Description and modeling of applied situations. Stage 2. Generation, analysis, and selection of decisions. In my opinion, skills to implement these two stages above on the basis of modern computer/information technologies constitutes the third literacy (Table 1.1). In other words, this is a crucial step to the culture of thinking, planning of organization and creative activities, and implementation of the culture in today’s life.

4

Composite Systems Decisions

Table 1.1 Phases of literacy Phase

Elements

1st literacy ABC, words, (intermedia- numbers te centuries)

Operations

Combinations

Arithmetical operations, morphological operations, read and write

Words, sentences, schemes of accounting

2nd literacy ABC, elements Logical operations (1970–1980) of computer literacy

3rd literacy Concepts and (1990–) solving schemes for applications: (i) alternatives, criteria, estimates, etc. (ii) systems, architecture, components, life cycle, etc.

Basic problems of decision making (choice/ ranking, clustering); auxiliary problems (e.g., generation of criteria); composite problems (generation of alterna(tives, revelation of bottlenecks, design of composite decisions)

Schemes of computations and logical data processing, programs Frameworks (technological schemes): identiﬁcation of problems, accumulation of data, knowledge acquisition, information processing, decision making, system synthesis

Further, it is reasonable to point out the following tendencies: 1. Increase in some composite technologies that involve contemporary results from diﬀerent domains (e.g., engineering, biology, computer science, mathematics). 2. Acceleration in implementing innovations. 3. Time decreasing the macro-technological cycle (changing the generations of technologies, machine systems) from 12 to 2–3 years (sometimes to 6 months). 4. Increase in the intellectual level of activities. Now, decision making takes place at each workplace for each designer/worker/ clerk (e.g. [349]). Moreover one can see increase in an intelligent level of operations at each stage of the product life cycle (not only in R & D, but also in maintenance and utilization, etc.). Let us try to consider a scale for evaluating creativity. First, we examine the creative levels by G.S. Altshuller as the following ordinal scale [24]: Level 1. The use of a ﬁnished well-known object (product, technology, management decision, strategy, innovation, etc.). Level 2. Searching for and selection of an object. Level 3. Analysis and modiﬁcation of an initial well-known object.

1 Introduction

5

Level 4. Design of a new object. Level 5. Design of a new object system. Only levels 4 and 5 above are really creative ones, and level 3 has an intermediate character. Level 2 (search and selection) is the basic one in decision making. It is reasonable to consider levels 2 and 3 as quasi-intellectual or quasicreative ones. Note, experience in decision making may be an excellent basis for specialists with an intermediate creative level to solve problems at levels 2 and 3. Moreover, the right organization and support of teamwork allows to solve problems at levels 4 and 5 on the basis of a set of quasi-intellectual problems (when intellectual decisions are combinations of local quasi-intellectual solutions). Generally, two possible ways can be considered: Way 1. Searching for creative persons who can solve intellectual problems. This process involve searching for, selection, and training. This way is limited, because only a limited number of persons have the inclination for creative activities, and the process of the selection and training of creative persons also has some limitations. Way 2. Construction of global creative decisions based on local quasicreative solutions. This way is similar to the approach by C.E. Shannon: designing some reliable systems on the basis of non-reliable components. In our case, we are oriented towards composition of decisions at levels 4 and 5 on the basis of local decisions at levels 2 and 3. Finally, the signiﬁcance of the following has been increased: 1. Composite multidisciplinary products/systems and corresponding composite decisions. 2. Composite decision-making problems. 3. Composite decision-making procedures, including: 3.1. solving framework (algorithm schemes, macroheuristics, algorithm systems); 3.2. distributed group teams in decision-making processes which involve various domain experts; 3.3. special tools to compose local solutions from diﬀerent applied domains into a global resultant composite multidisciplinary decision. This book addresses engineering of composite (composable, modular) decisions for various composite (composable, modular) systems / products. A hierarchical morphological multicriteria design (HMMD) approach [497] is used as a basis to model a composite hierarchical decision and to design it.

1.2 General Problem-solving Framework Now let us examine design of decisions as a general problem-solving process: FROM applied problem(s) TO decision(s) Now it is reasonable to depict a basic decision cycle (and corresponding set of main concepts and worlds) as follows: 1. applied problem(s); 2. goal(s)

6

Composite Systems Decisions

(including requirements, criteria, constraints); 3. task(s) (including task hierarchies); 4. method(s) (including method and technique hierarchies, experts); and 5. decision(s). From the methodological viewpoint we can consider the same process for various applied domains (including engineering, computer science, management). The basic tendency consists in complexity of applied problems as follows: (1) multidisciplinarity; (2) uncertainty; (3) novelty of problems and nonexistence of specialists; (4) complex structure (e.g., multi-component problems); (5) very high cost of information resources; (6) a need for unique methods; and (7) a need for multistage monitoring of the decision-making process, including changes of external requirements. As a result, solving methods (e.g., mathematical methods as analytical methods; computing, simulation) are more and more transformed into the following: (i) some distributed organizational frameworks and/or (ii) problem solving computer environments. Finally, Figure 1.1 describes a general problem-solving cycle (on the basis problem-solving cycle of R.L. Ackoﬀ) [1]): (a) a world of applied problems and decisions (domain A); (b) a world of descriptions for problems as structures, frameworks, mathematical models (domain B); (c) a world of solving schemes (algorithms, design frameworks, environments) (domain C); and (d) a world of solving processes (domain D).

Domain B

Domain A

Structure of applied problem(s), framework, mathe- @ matical model(s) @

@

Domain C

@ @ R Solving scheme, design framework, algorithm, algorithm system, etc.

Applied problem(s)

6 6 6 Decision(s)

@

Solving process

Domain D

Figure 1.1 General problem-solving cycle Analogous, the design of decisions as a process is shown in Figure 1.2.

- Solving process Applied problems i P PP 1 6 PP Information Specialists: support experts, decision (data, knowledge) makers, etc.

1 Introduction

7

Decisions Methods: mathematical models, simulation, organizational procedures, experiments

Figure 1.2 Design of decisions: process and support

1.3 View from Artiﬁcial Intelligence Position Traditionally, problem-solving issues are under consideration in artiﬁcial intelligence (e.g. [111, 141, 414, 470, 557, 600, 603, 604, 610]). At the same time, the design processes (e.g., at early stages of conceptual design) are close to problem solving processes, e.g., such as exploring very large engineering design spaces [414]. Brown and Chandrasekaran classify conﬁguration and design tasks as follows [111]: 1. Routine tasks: well-deﬁned problems where solution approaches are known, but problems cannot be solved by simple straightforward algorithms. 2. Innovative tasks: the existing knowledge must be extended during the solving process. 3. Creative tasks: weakly deﬁned goals and solution procedures; new solution components need to be developed or introduced to ﬁnd a solution. Recently, the problems of exploring very large design spaces are also central ones in combinatorial chemistry (e.g., drug design, material engineering). Thus, design processes can be considered as problem solving and can be formulated as a search in a problem space (e.g. [603, 610]). In [414], an architecture for exploring very large design spaces is studied as follows: (i) design candidates are generated by combining components systematically from components libraries, (ii) a very large number of candidates are considered methodically and evaluated, and (iii) ﬁltering of resultant decisions is based on a dominance criterion. The main concepts of problem-solving processes are described in [142]: 1. Domain factual knowledge (DFK), including: objects, relations, properties, states, events, and processes, classes. 2. Problem-solving knowledge as conditions on the following: (sub)goals, state, problem instance data, DFK, and changes to state. 3. Problem state components: problem requirements (satisﬁed, unsatisﬁed); goal, subgoals; solution validation; solution(s), including solution parts and solution candidates. 4. Problem instance data: DFK terms. 5. Problem-solving goals.

8

Composite Systems Decisions

Figure 1.3 depicts the basic decision cycle and a problem-solving process. The decision cycle is as follows: goal(s) ⇒ tasks ⇒ method(s) ⇒ decision(s) ⇒ goal(s) . . . HH H H Hierarchy of decisions @ HH HHH @ @ H @ @ H H @ Hierarchy Hierarchy Q @ HHH @ Q of goals of Q @ H Q methods @ Q Hierarchy Q of Q tasks QQ

Figure 1.3 Interconnected hierarchies in problem solving

1.4 Composite Systems and Problems The majority of applied problems are complex composite ones. As a result, it is reasonable to apply special approaches as follows [491, 497]: 1. Dividing an initial problem into parts (decomposition, partitioning). 2. Choice of corresponding tools (e.g., techniques, experts, techniques of information presentation). 3. Aggregation (integration, fusion, synthesis) of results. 4. Planning the decision-making process (i.e., design of technological process of decision making, including the following stages: information accumulation, analysis of information, decomposition and parallelization of information processing, aggregation of results). As a result, the principles of system decomposability and a hierarchical approach to problem solving have to be applied [759]. Analogous ideas are the basic ones in the design and generation of solutions in engineering and management; for example: (a) morphological analysis [49, 409, 914]; (b) tables for the preparation of alternative decisions in management [385]; (c) analytic hierarchy process (AHP) [706]; (d) modular design and synthesis (e.g. [387, 464, 497, 576]); (e) component-based system design (e.g. [734]); (f) hierarchical design and planning [359, 453, 461, 721]; (g) organizational frameworks, environments for the hierarchical design [206, 497, 528]; (h) methods for system integration/synthesis (e.g. [497, 669]); and (j) special environments for supporting teamwork, including group decision making (e.g. [121, 467, 782]). Figures 1.4 and 1.5 depict a composite system and corresponding hierarchical solving process as selection and composition.

1 Introduction

9

zSystem x u re

of xLevel subsystems

...

u er

...

...

...

re

er

u re

...

of uLevel components re Level of

...

...

re alternatives

er

Figure 1.4 Composite system

Ranking of . . . alternatives

Ranking of alternatives

Ranking of . . . alternatives

Ranking of alternatives

? Composition of local composite alternatives

...

? Composition of local composite alternatives

? Ranking of alternatives

...

? Ranking of alternatives

? Composition of composite alternatives ? Ranking of alternatives and choice

Figure 1.5 Hierarchical selection and composition Our HMMD approach is targeted to synthesis of composite decisions. In this case, the following basic system problems exist (e.g. [491], [497]): (1) decomposition (partitioning, parallelization); (2) composition (integration, synthesis, aggregation). Possible approaches for these system problems above are depicted in Table 1.2.

10

Composite Systems Decisions

Table 1.2 Usage of decomposition and composition Function

Realization Decomposition 1. by criteria (e.g., in AHP of Saaty [706]) (parallelization) 2. by alternatives (or local decisions) (e.g., in HMMD [497]) 3. by elements of alternatives, e.g., methods of modular design and planning [49, 80, 206, 326, 337, 359, 453, 914] 4. by specialists, e.g., techniques DELPHY [532] 5. by techniques, e.g., morphology of methods in DSS COMBI PC [492, 497, 510] Composition (integration, synthesis, aggregation)

1. by results (e.g., computation of consensus) (e.g. [179]) 2. by alternatives/decisions, i.e., building of composite alternatives/decisions (methods of hierarchical design, e.g., HMMD [497])

1.5 Basic System Technological Problems Generally, it is possible to list the following basic system technological problems for complex composite systems: 1. Modeling of system (structural model, e.g., And–Or graphs, networks, Petri nets) (T1 ). 2. Hierarchical modular design (T2 ). 3. Revelation of bottlenecks (T3 ). 4. Redesign (improvement, upgrade, adaptation) (T4 ). 5. Multistage design (T5 ). 6. Evaluation of systems (comparison, diagnostics, etc.) (T6 ). 7. Modeling of system development/evolution process (ﬂow of system generations) and forecasting (T7 ). The problems above can be applied to systems, systems requirements, and standards. In the book, the problems above are examined on the basis of our HMMD approach to modular systems with various applied examples. Table 1.3 illustrates some applications of HMMD to the system technological problems above.

1 Introduction

11

Table 1.3 Applications and technological problems Applications

T1

1. 2. 3. 4. 5. 6. 7. 8. 9.

Information system User interface Building Design of team Concrete technology Medical treatment Educational programs Standards in multimedia Immunoassay technology

T2

T3

T4

T5

T6

T7

1.6 Information Support In recent years, the signiﬁcance of information support has increased. For example, decision support systems (DSSs) are integrated with management information systems (MIS) [274, 836]. Problem-solving processes are based on initial information from many information sources [435]. The generalized structure of an information support system is based on the main information functions and is as follows: I. Data: 1. keeping and maintenance of data; 2. basic information retrieval; 3. the design/redesign of composite queries; and 4. hierarchical multilevel retrieval with the selection, aggregation (synthesis, fusion, summarization), approximation of chosen data. II. Knowledge: 1. acquisition and maintenance of knowledge; 2. checking and correction/modiﬁcation of knowledge; 3. retrieval of knowledge; and 4. design of new knowledge systems (e.g., the design of some problem-solving strategies).

1.7 Summary This introductory chapter has brieﬂy described the contemporary trend to composite systems and composite systems decisions.

2 Components of Information Technology

2.1 Properties of Information Technology First, let us point out the basic properties of information technology: 1. Various kinds of sources: (a) statistical information; books, databases; (b) specialists, population. 2. Preservation of initial information and possibility for reprocessing. 3. Possibility for parallel/concurrent processing. 4. Possibility for usage of many processing methods. 5. Possibility to accumulate various results of information processing. 6. Very high ecological awareness. 7. High requirements for professional skills of specialists. 8. Unique role of humans. 9. High requirements for information presentation and human–computer interaction. 10. Integration of many domains (e.g., exact science, engineering, management and economics, psychology and cognitive science, education, art). 11. Wide range of users and professional domains (e.g., science, engineering, management and economics, education, art, private life).

2.2 Information and Hierarchical Structuring An integrated research direction of knowledge engineering and management is a key task [336, 372, 436, 558, 900]. This section addresses some issues of this direction, including the main problems, approaches, and applied systems. 2.2.1 Schemes and Methods In recent years, issues of skill /knowledge acquisition have played a central role in many domains (e.g., cognitive modeling, information technology, problem solving, knowledge-based systems, knowledge management, system design, engineering design, systems engineering, process systems engineering, team distributed design processes) [28–32, 50, 76, 97, 98, 102, 107, 182, 189, 263,

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327, 372, 395, 478, 485, 614, 617, 619, 677, 733, 825]. Let us point out some other important research directions which are close to the above-mentioned domain: (1) cognitive modeling of design processes [7, 30, 32]; (2) representation and study of design spaces [497, 555, 758]; (3) modeling of specialists and his/her behavior (e.g., mental models) [444, 698, 699, 807]; (4) relation between cognitive processes and operations research [439]; (5) models for representing experience in computers [447]; (6) usage of object-oriented structures to represent expert knowledge [159]; (7) visualization of knowledge and specialist experience [150]; (8) design of hybrid intelligent systems with combined representation of various knowledge kinds [563]; (9) organization and management of engineering information on complex products/systems and their reengineering [58, 151, 152, 495, 497, 619, 890]; (10) studying and developing the knowledge and skills of specialists [182, 189]; (11) acquiring engineering knowledge from design processes [395, 555]; (12) design and maintenance of engineering concept spaces [155, 414, 577], including concept lattices [865, 882]; (13) cognitive modeling for conceptual design [538]; (14) engineering history bases [813]; and (15) information modeling for evolution/development of products/systems [177, 178, 497, 505, 512, 513, 591, 626]. In addition, it is reasonable to point out the contemporary research direction on intellectual capital [228, 438, 543, 639, 795]. In my opinion, engineering skills are a crucial part of national and international intellectual capital. Figure 2.1 depicts the above-mentioned components. In this chapter, a hierarchical morphological framework is examined which is a useful organizational basis for systems engineering processes: to execute operations for the description, design, analysis and improvement of composite systems. In the case of composite systems or composite decisions, hierarchical structures are used for two goals (Figure 2.2): (a) hierarchy of the experts collaboration; (b) hierarchy of the resultant information description (for an engineering domain/system). J. Conklin [176] has pointed out that a hierarchical representation of information is more natural for users with an engineering background. Note, construction of a generalization space for domain knowledge is a contemporary approach in the ﬁeld of conceptual structuring [100, 101]. M. Minsky has pointed out the following architecture of representations [580]: (1) stories written in natural language; (2) story-like scripts; (3) transframes; (4) framearrays and picture-frames; (5) semantic nets; (6) K-lines; (7) neural nets; and (8) micronemes.

2 Components of Information Technology

15

Knowledge engineer@ @ (monitoring) @ @ @ HH @ Goal H @ knowledgeExpert(s) based system @ @ @ Additional @ Test tools support Knowledge information acquisition framework

Figure 2.1 Knowledge acquisition: components

System/domain

General expert(s)

. . . @@

Subsystem (subdomain) 1

@ Subsystem (subdomain) N

Subdomain expert(s)

Subdomain expert(s)

Figure 2.2 System hierarchy

2.2.2 Approaches to Knowledge Acquisition The following four basic interconnected cognitive acts are examined [609]: (a) action; (b) observation; (c) reasoning; and (d) evaluation. Thus, the above-mentioned four components form a fundamental for knowledge acquisition methods. Traditional methods of knowledge acquisition are described, for example, in [162, 360, 434, 484, 780]. Surveys on knowledge acquisition are contained in [97, 727]. In our opinion, knowledge acquisition techniques are connected with domains as follows: (i) problem domains; (ii) domain experts, including their properties (type of thinking, experience, etc.); (iii) methods for knowledge representation; and (iv) possible usage of the knowledge. Note that the knowledge life cycle involves stages as follows [87]: 1. creation; 2. mobilization; 3. diﬀusion; and 4. commoditization. The main kinds of system for knowledge acquisition are the following: 1. The knowledge acquisition activity matrix (a systems engineering conceptual framework) [695]; 2. KADS technology [731, 878];

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Composite Systems Decisions

3. Systems of conceptual knowledge and ontologies [250, 437, 780]: 3.1. CODE4: a uniﬁed system for managing conceptual knowledge [764]; 3.2. systems with a classiﬁcation model that gives a structure to a knowledge acquisition environment (e.g., STEPCLASS technique [278], M-Class model [562]); 3.3. construction of ontologies [329, 381, 618, 780, 784, 846]; 4. Knowledge acquisition techniques on the basis of ordinal classiﬁcations [278, 474]; 5. Knowledge acquisition with linguistic geometry method [798]; 6. Knowledge acquisition tools based on object-oriented approach (e.g., SOOKAT [638]); 7. Multistage knowledge acquisition (e.g., CAL Expert System [830]); 8. Systems for acquisition of various skills: 8.1. systems for the creating and maintenance of a skill catalogue on the basis of two kinds of initial information [617]: (a) skill-related discussion database, and (b) person-related electronic communications (e-mail database). 8.2. our approach based on hierarchies as morphological AND–OR trees [495, 497] (it is similar to ontological approach). 9. Other approaches: 9.1. systems based on prototypical knowledge (e.g., as prototype situations in system CENTAUR) [16]; 9.2. a system for representing and using real-world knowledge NETL [240]; 9.3. The knowledge acquisition and representation language KARL [251]. In addition, it is reasonable to point out the contemporary ontology design approaches to organization of knowledge as follows [381]: (a) inspirational approach; (b) inductive approach; (c) synthetic approach; and (d) collaborative approach. 2.2.3 Some Hierarchical Information Systems The main functional operations for the design, utilization, and maintenance of design information systems are the following [206, 492, 668]: (1) acquisition of new data and knowledge; (2) structuring, modeling; (3) representation; (4) learning; (5) access, control; (6) analysis, evaluation, correction; and (7) maintenance. Support information systems may be oriented to various components of a systems engineering (system design) process. Also, it is reasonable to list reference examples of some information systems: (1) information design model (EDM) for engineering design [227]; (2) distributed hypermedia system for managing knowledge in organizations (KMS) [18]; (3) hierarchical hypertext system (HHS) involving components of diﬀerent kinds and their attribute descriptions for various problem domains [490, 492]; (4) Designer’s Electronic Guidebook for mechanical engineering in Cambridge Engineering Centre [229];

2 Components of Information Technology

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(5) information model for cooperative product development SHARED [890]; (6) concept lattices and conceptual knowledge systems [856, 865, 882]; (7) system version spaces [178]; (8) systems as engineering concept spaces [155]; (9) special combinatorial design spaces [758]; (10) large design spaces [414]; (11) various kinds of ontology-based information systems [250, 616]; (12) information bases for evolution of products/systems [178, 497, 505, 512, 513, 626]; and (13) special engineering history bases [813]. Note, special logical studies of the hierarchical approach to modeling of knowledge are described in [238, 239, 346]. 2.2.4 Our Framework The basic contextual scale for information consists of four levels: (i) data, (ii) information, (iii) knowledge, and (iv) decision. Evidently, our main goal consists in the transformation of data, information, and knowledge into decisions. Here, structuring is the basic support operation [625, 867]. In our case, the decisions are based on a hierarchical morphological description (modeling) of some applied domains/systems. Figure 2.3 illustrates the structure of our decision environment for skills acquisition (on the basis of HMMD) [501]. Monitoring by @ @ knowledge engineer @ @ Applied domain/ /system

@ @ R

?

@ @ Domain expert: @ @ experience, motivation, 6 structural thinking, Hierarchical certain morphological goal, ﬂexibility approach including special support tools

Information: applied examples, analogues, requirements/ criteria ... engineering conceptual spaces

Figure 2.3 Structure of Environment In our case, support tools involve the following: (a) systems for multicriteria ranking, e.g., DSS COMBI PC [492, 497], and (b) a system for hierarchical design (DSS for hierarchical engineering design SED [492, 497]). Information

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Composite Systems Decisions

support is based on the following: (a) traditional scientiﬁc sources; (b) HHSs (requirements, criteria, situations, models, etc.) [490, 492]; (c) special systems as engineering concept spaces [155] and design spaces [414]; (d) system version spaces [178]; (e) Internet sources and tools; and (f) consulting of colleagues.

2.3 Decision-making Paradigm 2.3.1 Decision-making Framework The basic decision-making paradigm consists of several basic stages [274, 390, 701, 759, 762, 836]. The ﬁrst intellectual stage involves the following: analysis of a problem and its identiﬁcation, information search, including revealing the main resource constraints, etc. The second design stage includes a multicriteria description of the problem (generation of alternatives, speciﬁcation of criteria, and design of scales). The stage of choice is oriented to the evaluation of alternatives (accumulation of data on alternatives, acquisition of preference of specialists, information processing), selection of the best alternatives, and analysis of results including sensitivity analysis. And the ﬁnal stage is an implementation of the decision (i.e., the best alternative(s)). Clearly, special tools are required to support all the stages above. DSSs are oriented to these objectives [274, 497, 781, 836]. Now let us point out a set of main components of decision-making technology [74, 274, 836]: (1) alternatives, (2) criteria (and corresponding scales), (3) data (estimates of alternatives upon criteria, and expert preferences), (4) techniques (multicriteria choice, selection, etc.), (5) specialists (experts for the decision-making process, domain experts for the evaluation process, decision maker), and (6) resultant decisions. Each component above maybe speciﬁed apriori or formed in the solving process. For example, alternatives may be speciﬁed or may be generated (corrected) as a result of solving procedures. Table 2.1 contains basic stages of the traditional decision-making paradigm of H.A. Simon [274, 390, 759, 762, 836]. Note, the concept of decision-aiding methodology as an extension of decision making was suggested in [701, 832, 833]. 2.3.2 Towards Architecture of Decision Support Systems A systemic view of decision support is described in [37]. The basic components of decision support procedures are the following: initial information base of models and methods, knowledge base, base of typical situations, and analysis and learning of user. A discussion of the design and use of DSSs is contained in [708], including the following: (a) generic technological components, (b) system requirement analysis and speciﬁcation, (c) the use of alternative analytical methods, and (d) evaluation of such systems. The following technological way is examined: (1) user needs, (2) system requirements, (3) hardware and software allocation of the requirements, and (4) development of suitable hardware and software architectures.

2 Components of Information Technology

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Table 2.1 Stages of decision making and information support Stages of decision making

Concepts, roles

Basic processes of information support

1. Problem identiﬁcation

Problem types Resources Bottlenecks Objectives Constraints

Search and selection of analogous problems Search and/or selection of objectives, design of objective spaces

2. Structuring Criteria Scales

Search and/or composing of criteria Choice/design of scales

3. Generation Alternatives Experts of alternatives

Search and choice of analogous alternatives Composing of composite alternatives

4. Evaluation Techniques of assessment of alternatives Estimates Experts

Search of data choice for alternatives Selection of experts Forming of expert groups

5. Choice (selection, ranking)

Techniques Search and choice of techniques Experts Search and selection of experts Decision makers

6. Analysis

Search and choice of techniques Techniques Search and selection of experts Experts Decision makers

The basic structure of a DSS involves the following parts [274, 426, 489, 497, 505, 648, 724, 781, 827, 836]: user interface, database, knowledge base, model base, HELPER. In addition, contemporary DSSs include tools for standard decision-making problems, and their combinations. In recent years, DSSs have been developed as integrated environments which are oriented to several stages of the decision-making process. The list of components for modern DSSs is as follows: 1. Models (multicriteria techniques, processing of interval estimates and fuzzy descriptions of alternatives, on-line design of problem-solving schemes, statistical data processing, knowledge bases, procedures of the result analysis. 2. Support of preliminary stages of decision making (preliminary data processing, procedures for identiﬁcation and structuring of problems). 3. Tools for human–computer interaction (graphical user interfaces, training subsystems, expert procedures, support of group/distributed work). 4. Information support (e.g., communication with databases, hypermedia systems). Modern DSSs are based on the above-mentioned structure, and involve libraries of techniques, artiﬁcial intelligence components, procedures for the analysis of results, hyper-information subsystems, and special procedures for

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Composite Systems Decisions

problem identiﬁcation and structuring [274, 435, 492]. In addition, visualization of multiattribute information (e.g., by 2D and 3D graphics) is applied for user interfaces [408, 545, 566, 857]. Finally, important tendencies are the following: 1. support of group work [121, 467]; 2. knowledge-based subsystems (e.g., production subsystems, neural networks) with orientation to some auxiliary problems as follows: selection of techniques [808, 836, 876]; 3. subsystems for scheduling and model management [594]; 4. graphical interfaces [497, 827]; 5. hypermedia information components [274, 435, 490]; 6. subsystems for intellectual problems (generation of composite alternatives, design of criterion hierarchies, forming of specialist groups, generation of composite models) [497, 706]. 2.3.3 Four-domain Decision Making Generally, decision-making processes are based on a four-domain (four spaces) framework as follows (Figure 2.4): (i) a domain of alternatives, (ii) a domain of criteria and attributes, (iii) a domain of solving methods (algorithm, interactive procedures and their combinations), and (iv) a structural domain of the resultant decisions. Each above-mentioned domain can be modeled on the basis of some structures and hierarchies (from simple structures to complicated ones). Note, a closely integrated investigation is described in [827], including a multidimensional visual and interactive support environment for multicriteria decision making.

Space of BB B criteria/ B attribute

Space of =⇒ alternatives =⇒

⇓ ⇓

Solving process

B

=⇒ =⇒

⇑ ⇑

@ @ Space of decisions @ @

Space of methods (e.g., strategies, algorithms, rules)

Figure 2.4 Four-domain decision-making framework

2.3.4 Basic Structures Figures 2.5, 2.6, 2.7, and 2.8 illustrate some basic structures for the parts of the decision-making framework considered (alternatives, criteria/attributes,

2 Components of Information Technology

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decisions, and methods). The following simple structures are examined: (a) a single element, (b) a set of elements, (c) a chain of elements (e.g., series structure, linear order), (d) a tree-like structure over elements, (e) a parallel– series structure, (f) partitioning of an element set (a set of clusters), (h) a multi-layer hierarchy of elements, and (f) the general case of a digraph. Note, the kind of element structure is a crucial from the viewpoint of complexity issues. For example, many combinatorial problems are polynomial ones on simple structures (e.g., at the level of parallel–series graphs, interval graphs). This is based on the property of decomposability.

HH H

AA A

(a) Set of alternatives

(b) Clusters of alternatives

HH

AA

Q AAQQ A Q

A

(c) Hierarchy of composite alternatives

Figure 2.5 Structures of alternative space

?

(a) The best alternative

? ? ? ? ? ... ... ? ? ? (b) Linear ordering (c) Stratiﬁcation of alternatives of alternatives

@ R @ @ @ R ? ? ? ? ... ? ? ? HHH j ?HH H j? (d) Poset of alternatives

Figure 2.6 Basic structures for decision space

@ I @ @ R @ @ R @

(a) Independent (b) Criteria under dependence criteria

HH HH H H HH HH Q AA AAQQ AA A A Q A

(c) Hierarchy of criteria/ attributes

Figure 2.7 Structures of criteria/attributes

22

??HH DBK DBK DBK DAH ?H @HH H H@ H H@ H @H H Composite Systems Decisions

...

(a) The only one method

(b) Library of methods

A A ?. . . AAU AAU A A A ? AA U AA U AAU

solving strategies

basic modules algorithms/ procedures

(c) Three-layer (modular) structure

Figure 2.8 Structures of solving method space 2.3.5 Multicriteria Ranking The following approaches/methods are basic ones for multicriteria ranking alternative ones: (1) utility function techniques [261, 427]; (2) AHP [84, 706]; (3) outranking techniques (e.g., methods ELECTRE, Promethee) [104, 700, 701]; (4) interactive techniques of multicriteria analysis [446, 449]; (5) knowledge bases and neural networks [521, 869]; (6) a special approach on the basis of a technological viewpoint (as multiagent systems, generation of a solving strategy on the basis of libraries of algorithms and procedures) [492, 497, 510]; (7) hybrid techniques [245, 350].

2.4 Specialist 2.4.1 Role of the Specialist In previous sections we have considered types of specialist in a problem-solving process (e.g., in decision-making): (1) decision maker (main person, who is responsible for all results); (2) domain expert (initial data accumulation, generation of alternatives, assessment of alternatives and preference relations); (3) specialist for organizational support of decision-making technology; (4) knowledge engineer (organization of a cycle knowledge acquisition, knowledge veriﬁcation, knowledge modiﬁcation, maintenance, and utilization). It is reasonable to emphasize the unique role of the specialist in organizational support of decision-making technology. In this kind of technology, an object under analysis and transformation is a very diﬃcult multi-factor decision problem (e.g., engineering, organizational, social–economical, ecological, political). Note here that the contemporary viewpoint is targeted to intellectual capital [880].

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23

2.4.2 Professional Levels The classiﬁcation of specialists is a crucial issue. Traditional classes of specialists are the following: (a) novice (beginner), (b) professional (competent), and (c) expert. P.J. Denning suggested a prospective seven-level classiﬁcation of specialists [207]: 1. Novice (beginner): (a) common situations are unfamiliar; (b) practice in simple situations. 2. Advanced beginner (rookie): (a) problem solving and practice with rules and strategies; (b) need supervising for more complex tasks. 3. Professional (competent): (a) practice in many standard situations; (b) advanced problem solving; (c) extensive practice in both common and exceptional situations; (d) apprenticeship to more advanced professionals and teams; (e) membership in professional networks. 4. Proﬁcient professional (star): (a) deals with complex situations eﬀortlessly; (b) individual performance is a benchmark for others; (c) considerable experience and practice across a wide range of situations over years of work; (d) apprenticeship to experts; (e) coaching; (f) putting self into wide range of situations; (g) membership and contribution to professional networks. 5. Expert (virtuoso): (a) appears to solve diﬃcult, complex problem effortlessly; (b) enormous breadth and depth of knowledge; (c) routinely forms and leads high-performance teams; (d) admired by others as a benchmark of team performance; (e) performance standards are beyond those of most practitioners; (f) apprenticeship to masters; (g) advanced coaching, development of breadth; (h) teaches others; (i) years or decades of practice. 6. Master: (a) capacity for long-range strategic thinking and actions; (b) sees historical drifts and shifting clearings; (c) has studied with many diﬀerent teachers and has developed own distinctive style; (d) has produced innovations in the standard practices of others; (e) altered the course of history in the ﬁeld, and knows how to do this again; (f) teaches others to be experts and masters; (g) learning continues by working with other masters as teachers; (h) creates and leads professional networks; (i) teaches others. 7. Legend: (a) work has widely accepted impact; (b) same as for master with emphasis on public appearance.

2.5 Solving Frameworks Now, the selection/design of algorithms and planning the solving processes are central and the most important research directions. For example, intelligent technologies are considered as searching for algorithms for dynamical optimization problems (including ﬂexible execution strategies, e.g., any-time algorithms) [454, 910]. The basic trend is targeted to problem-solving environments [685]. 2.5.1 Search Spaces and Strategies State-space search is the basic approach to problem solving and design [760, 903] on the basis of the following components: (1) goals, (2) state spaces, and

24

Composite Systems Decisions

(3) operations for various design domains and design problems. The search methodology can be considered as fundamental in several domains, e.g., mathematics, computer science, operations research and its signiﬁcance is increased [430]. Here, the key problems are the following: (i) design of search space; (ii) design of a search strategy in the search space. Let us list the basic search strategies as follows: 1. Constraint-based space-decreasing methods [850] (Figure 2.9). 2. Gradient-like methods. Figure 2.10 depicts a search space and an improvement search strategy (e.g., local optimization, greedy algorithms, k-exchange technique). 3. Grid-based methods (e.g., design method of parameter space investigation (PSI) suggested by I.M. Sobol and R.B. Statnikov [768, 787] (Figure 2.11). 4. Region-approximation-based methods (e.g., spanning tree-based algorithms, ellipsoid method). 5. Decomposition-based methods: dynamic programming approach as series multistage design of solution parts, step-by-step. 6. Parallel methods (Figure 2.12). 7. Random methods (e.g., random walks). 8. Partitioning–synthesis methods on the basis of HMMD (Figure 2.13). 9. Hybrid strategies. In this book, the partitioning–synthesis method is the basic one used: (a) partitioning the initial search space into subspaces; (b) search for the best local decision for each subspace; and (c) combination (composition, synthesis) of the local decisions into the global resultant decision.

BI

I B AI A A Constraint 1 Constraint 2 HH HH @ @ HH @ @ HH @ @ HH @ Resultant HH@ @ @ H @ @ HH @ decisions @ @ @ Figure 2.9 Constraint-based strategy

Resultant

-6

- decisions

Initial point

Figure 2.10 Improvement strategy

2 Components of Information Technology

25

Figure 2.11 Grid-based strategy

Resultant decisions

6

-

6

6

@ I @ 6 Initial points

6

Figure 2.12 Parallel strategy

H Y HH

HH

A

*

HH Part A HH

Part B

Part C

-

Composite decision

B

@ @ @ @ @ @ @ @

C

?? Figure 2.13 Partitioning–synthesis strategy

2.5.2 Heuristics In recent decades, the signiﬁcance of heuristic approaches has increased. The situation is based on the fact that the majority of real applied problems are very complicated and require composite heuristic solving schemes which can be considered as hierarchical multi-stage algorithm systems. Thus, it is reasonable to examine a systems engineering approach to the design of algorithm systems. The list of traditional well-known heuristic approaches involves the following [42, 61, 67, 127, 281, 306–308, 312, 377, 379, 424, 473, 537, 569, 643, 675, 679, 844]: 1. Lagrangian relaxation; 2. greedy algorithms; 3. tabu search; 4. simulated annealing; 5. artiﬁcial neural networks; 6. approximation solving

26

Composite Systems Decisions

schemes; 7. genetic algorithms and evolutionary computing; 8. constraint satisfaction approach; and 9. probabilistic approaches. In my opinion, a basic trend in the ﬁeld of heuristics design is the following: FROM algorithms (e.g. [61]) TO algorithm frameworks (e.g. [602]). A three-stage algorithm framework is described for a sports timetabling problem by C.L. Nemhauser and M.A. Trick [602]. Multi-stage algorithm systems have been proposed, for example, in [307, 308]. Moreover, the heuristic algorithm systems can be considered as speciﬁc problem-solving environments which have been studied in recent years [215, 280, 685]. Here, the structure of the systems, the kinds and the basic algorithm frameworks are proposed which can be considered as a step to the design of algorithm systems. 2.5.3 Metaheuristics Many real-work problems require a complex solving approach, such as metaheuristics [127, 306] and hyper-heuristics [430]. The basic materials and surveys on metaheuristics are contained in the following sources: [61, 66, 67, 140– 142, 172, 280, 281, 440, 497, 643, 675, 679, 684, 761, 863, 911]. The list of main metaheuristic kinds involves the following: 1. ant colony optimization; 2. tabu search; 3. simulated annealing; 4. genetic/evolutionary computing including evolutionary multiobjective optimization; 5. GRASP; 6. memetric algorithms; 7. neural networks; 8. variable neighborhood search; 9. reactive search; 10. scatter search; 11. anytime algorithms; and 12. hybrid methods. 2.5.4 Algorithm Systems Here, let us consider structures of algorithm systems [498]. The essence of the contemporary novelty in this ﬁeld is based on the following: eﬀectiveness of simple algorithmic schemes is limited and it is reasonable to build more complex multi-level, hierarchical solving frameworks which involve series–parallel and adaptive solving process. The structure of the algorithm system can be analyzed as follows: 1. Control unit (planning, adaptation): (a) selection of corresponding basic algorithms, and (b) design of composite solving strategy. 2. Level of execution: (a) analysis of an initial problem, (b) execution of a solving process, and (c) analysis of results. 3. Level of bases/repositories: (a) problems and examples, (b) algorithms and procedures, and (c) solving strategies. Here, let us examine the basic kinds of algorithm systems structures. First, let us point out the main parameters of the algorithm systems: 1. Kind of algorithm base: (a) one-algorithm framework; (b) algorithm set with parallel execution of the algorithms; and (c) complex multistage algorithm framework (e.g., series, series–parallel).

2 Components of Information Technology

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2. Feedback: (a) without feedback; (b) with feedback of two types as follows: (i) analysis of resultant solution; and/or (ii) analysis of intermediate results. 3. Kind of algorithm framework (scheme, composite strategy) synthesis: (a) ﬁxed algorithm framework (algorithm strategy); (b) ﬂexible design of algorithm framework (e.g., selection of standard algorithm strategies, synthesis of new algorithm frameworks). Thus, the following functional operations have to be examined: (1) analysis of problem data (input), (2) solving process, (3) analysis of results, (4) modiﬁcation/selection of algorithm, (5) selection/synthesis of an algorithm set, (6) aggregation of results, and (7) selection/synthesis of an algorithm scheme. Clearly, the simplest solving scheme involves the initial data, the solving process, the result, and the analysis of the result. Figures 2.14, 2.15, 2.16, and 2.17 depict possible more complicated situations (e.g., parametric modiﬁcation/selection of algorithm, selection/design of algorithm scheme). Analysis of results Initial ? data Analysis (input) - of problem

? Modiﬁcation - of algorithm

6

Solution(s) (output) -

Solving - process (algorithm)

Figure 2.14 Simple one-algorithm framework Analysis of results Initial ? data Analysis (input) - of problem

Repository of problems

? Modiﬁcation - and selection of algorithm

6 Solving - process (algorithm)

Solution(s) (output) -

Base of algorithms

Figure 2.15 One-algorithm framework with algorithm base Note, it is possible to add into the multi-algorithm framework at Figure 2.15 a block for aggregation of results which were obtained on the basis of diﬀerent algorithms.

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Composite Systems Decisions

Analysis of results Initial ? data Analysis (input) - of problem

Repository of problems

? Modiﬁcation - and selection of algorithms

6

Solution(s) (output) -

Solving - process (algorithms)

Base of algorithms

Figure 2.16 Multi-algorithm framework with algorithm base

Initial ? data Analysis (input) - of problem

Repository of problems

? Design of - algorithm scheme

Base of algorithms

Analysis of results 6 Solving - process (scheme)

Base of algorithm schemes

Solution(s) (output) -

Methods for scheme synthesis

Figure 2.17 Multi-algorithm scheme framework

2.6 Summary We have examined some components of information technology: (a) information, (b) knowledge acquisition/management, (c) decision-making framework, (d) specialists, and (e) solving strategies. A successful design for complex composite decisions is based on background and experience in the components above.

Part II

System Approaches

3 Systems: Models, Analysis, and Synthesis

3.1 System, Frames, and Modularity 3.1.1 System and Structural Modeling A system is often deﬁned as a set of interconnected elements (e.g. [339, 340, 355, 497, 849]). Generally, all buildable systems are state machines (Turing machines [837]). On the other hand, there exist the following uncertain situations when it is necessary to examine other system models: 1. early stages of the system life cycles (e.g., requirements engineering, conceptual design); 2. complex-large scale systems for which complexity issues of corresponding state machine are very hard; 3. some non-intent system usage situations. In these cases, various other models (including some aggregated system models) can be used, including special kinds of state machines at high-level system abstraction (e.g., functional spaces and construction on their basis). The more important modeling approach is based on graphs [79, 339, 353– 355, 579, 622, 687, 886]. Graph-like system models are very useful from various viewpoints, including the following: (a) simple for domain experts, (b) simple for computer modeling, transformation/processing, visualization. Here, it is reasonable to point out the following structural models and approaches: 1. Various kinds of hierarchies (e.g. [339, 340, 394, 849]). 2. Petri nets [304, 649, 650]. 3. And–Or trees and some advanced models of such type (e.g., state charts, grammars) [345, 356–358, 384]. 4. Morphological trees with design alternatives as a modiﬁcation of And– Or tree [497]. 5. Ontologies (e.g. [471, 616]). This approach is mainly used for information systems (e.g., in medicine and engineering databases). Some problems here are more important than others; for example: (a) design and identiﬁcation, (b) comparing, (c) merging, (d) aligning, (e) maintaining, (f) translating between diﬀerent formalism [471, 616]. 6. Sign graphs (e.g., for social systems) [687].

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7. A special multidisciplinary combinatorial approach for various engineering systems on the basis of combinatorial representations as follows [744]: (1) ﬂow graph representation (FGR) (for static systems), (2) potential graph representation (PGR) (for mechanisms), (3) resistance graph representation (RGR) (for electrical, dynamical, hydraulic systems), and (4) line graph representation (LGR) (for planetary gear systems). 8. Version modeling and conﬁguration management on the basis of four special version models (mainly, for electronic and software systems) (e.g. [177, 178, 246, 247, 425, 574]). 9. Special recent research directions mereology and mereotopology and their extensions (e.g., region-connection calculus) are oriented to studying parts, wholes, and part–whole relations [40, 297, 523, 766, 854]. This leads to modeling of spatio-temporal objects and their relations (e.g., in image sequences). Special methodologies for structural modeling were suggested in [289, 290, 485, 867]. In addition, it is reasonable to point out the following main issues connected with system modeling [147, 337–341, 344, 565, 571, 633, 849]: (a) system architecture/structure (including multidisciplinarity); (b) control; (c) dynamics/behavior; (d) uncertainty and its modeling; (e) human factors; (f) life cycle; and (h) development and evolution (micro-evolution processes, macroevolution processes). 3.1.2 Two Basic Frames Here, we brieﬂy consider a system, its parts, and internal and external interconnection (Figure 3.1). This frame is a basis for the ﬁrst steps of examining all kinds of systems. Another basic system frame consists of the system and a control unit (Figure 3.2). From the viewpoint of system complexity, it is necessary to list four levels of system kinds (classiﬁcation of A. Shenhar) [749]: Level 1. Arrays (network of systems, e.g., network of radars). Level 2. System (multiple functions; radar, defense system). Level 3. Assembly (one function, e.g., TV). Level 4. Component.

Neighbor system(s) -

Subsystem @ @ R

@ @ @ External @ @ @ @ requirements @@ @ @ @ @ @ @ @

System

@ @ R @ . . . Subsystem @ R @

Figure 3.1 System and its interconnection

3 Systems: Models, Analysis, and Synthesis

33

Control unit Input 6

? System

Output -

6 Feedback

Figure 3.2 System with control unit 3.1.3 Modular, Component-based Systems The trend to modular systems and component-based systems can be considered as basic to all engineering domains (e.g. [56, 85, 234, 348, 387, 391, 419, 497, 750, 901, 902]). Interestingly, modularity is the main fundamental in nature too. Multi-year eﬀorts in the modular description of mechanical systems were realized by I.I. Artobolevsky in Russia (Artobolevsky’s encyclopedia) as a vocabulary of basic mechanical system components (e.g. [41]). The main recent component-based approaches to systems have been described in [186, 284, 615]. The main goals of modularity are the following (e.g. [56, 377, 387, 637, 714]): 1. Management of complexity. 2. Parallel work. 3. Accommodation of future uncertainty. 4. Variety of resultant modular systems. 5. Flexibility, adaptability, reconﬁgurability of resultant modular systems. As result, the following can be obtained: 1. simple design process and simple all phases of life cycle; 2. short life cycle of product, long life cycle of product modules; 3. reconﬁgurable systems (e.g., manufacturing systems): long life cycle for system generations; 4. simple design and support of product families (airplanes, cars, etc.); 5. simple design and support of diﬀerent products (on the basis of module libraries for reuse). Dividing a system into its parts is based on two approaches: (i) decomposition, to get a chain of series system parts (e.g., series process, as in manufacturing, in dynamic programming); and (ii) partitioning, to get a parallel process (i.e., parallel system parts). The basic approaches for partitioning/decomposing some complex systems are as follows: A. Content analysis and engineering experience as follows (divide and conquer): (a) by system functions (basic functions, auxiliary functions), and (b) by system parts (physical partitioning).

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Composite Systems Decisions

B. Cluster analysis (clustering, i.e., step-by-step integration of very small system parts/modules on the basis of module parameters and module interconnection). Descriptions of clustering methods are contained in [12, 27, 315, 361, 399, 400, 406, 583, 851]. A special well-known modular R & D direction consists in application of axiomatic design and design structure matrix [331]. In some researches, a modular approach to complex systems is based on special simulation models [237].

3.2 System Analysis 3.2.1 Principles of System Analysis The main principles of system analysis are as follows: 1. Study of product/system life cycle (e.g., creation, R & D, manufacturing, marketing, utilization, recycling). 2. System development. 3. Interconnection of a system with environment (nature, community, other systems). 4. Interconnection among system parts/components (e.g., functions, information, energy, dynamics). 5. Taking into account system changes (e.g., data, external requirements, interconnection) 6. Analysis of main system properties (parameters). 7. Integration of system approaches for studies: decomposition, composition, hierarchical approach. 8. Analysis of main contradictions (engineering, economics, organization, etc.). 9. Integration of approaches to system studies: (e.g., experiments, mathematical modeling, heuristics). 10. Interaction among specialists of diﬀerent professional domains, of diﬀerent levels (e.g., engineering, management, computer science, mathematics, social science). Using the above-mentioned principles leads to successful results. 3.2.2 Measurement Issues Issues of measurement of system parameters are often basic ones. Here, the list of basic problems involves the following: (a) selection/design of measurement scales; (b) selection/design of a measurement method; and (c) selection/design of data/information processing frameworks and methods used (including methods for information integration/fusion). The basic kinds of scales are as follows: 1. Quantitative scales.

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2. Qualitative scales: 2.1 nominal scales, 2.2 ordinal scales, and 2.3 posetlike scales. 3. Composite scales (e.g., multicriteria/multiparameter spaces, lattices). It is reasonable to point out some basic measurement problems: 1. One object: 1.1 evaluation upon a nominal scale; 1.2 evaluation upon an ordinal scale; 1.3 evaluation upon a poset-like scale; 1.4 evaluation upon a quantitative scale; and 1.5 evaluation upon a composite scale (e.g., parameter vector). 2. Set of objects: 2.1 classiﬁcation (clustering) of objects, i.e., evaluation on the basis of a nominal scale; 2.2 ordering of objects, i.e., evaluation on the basis of an ordinal scale; 2.3 design of a poset on the object set, i.e., evaluation on the basis of a poset-like scale; 2.4 evaluation upon a quantitative scale; and 2.5 evaluation upon a composite scale (e.g., parameter vector). 3. A composite object: 3.1 evaluation upon a nominal scale; 3.2 evaluation upon an ordinal scale; 3.3 evaluation upon a poset-like scale; 3.4 evaluation upon a quantitative scale; and 3.5 evaluation upon a composite scale (e.g., parameter vector). The main measurement problems for composite systems are the following: (1) system components measurement, (2) system measurement (as a wholeness) with an orientation to a quantitative scale (or an ordinal scale), and (3) aggregation/integration/fusion of system components estimates into a resultant system estimate [497, 503, 783]. 3.2.3 System Properties, Requirements, and Criteria In recent years, the signiﬁcance of generating system properties and criteria (as requirements engineering) has increased (e.g. [255, 366, 775, 906]). The design of a criteria system (a set of criteria, a hierarchy of criteria, a criteria space) is the crucial ﬁrst phase of the system analysis and system synthesis. It is reasonable to point out the following hierarchy of main system properties [565]: Level 1. stability including reliability; Level 2. controlability; Level 3. adaptability and visiability; Level 4. self-organization. At the same time, it is reasonable to depict several common levels as follows: 1. Bottom level: product and its properties. 2. Level of engineering and technology: life-cycle engineering, connection with other products/systems, etc. 3. Economical level: markets, global economics, social networks of diﬀerent kinds. 4. Ecology: global policy, ecology. The above-mentioned levels are basic ones for the framework of system requirements and further to criteria spaces. Note, a special hypertext system is described in [490] which contains criteria sets for various systems.

36

Composite Systems Decisions

3.3 System Synthesis The signiﬁcance of system integration/synthesis is increasing. This situation is based on the following reasons: 1. System complexity is increasing. The systems have multi-level hierarchical structure and multidisciplinary nature. 2. The design process is usually realized under uncertainty. 3. The possible complex systems decisions do not exist. 4. Modular design approach is more widely used. 5. Application of product families and product platform. As a result, selection processes only (i.e., selection of the best system decision) cannot be applied. System integration/synthesis methods are studied in many domains (and often based on diﬀerent traditions): (1) design of complex products (e.g., mechanical engineering, electrical engineering, aerospace engineering) [34, 137, 737, 738, 744, 810, 858]; (2) design of product families, product platforms [200, 213, 218, 219, 373, 378, 405, 433, 445, 553, 568, 723, 831, 841]; (3) synthesis of conﬁgurations for computers, networks, etc. [287, 309, 415, 417, 554, 556, 817, 892]; (4) integration in information systems, in information and knowledge engineering (e.g. [497, 697, 772]); (5) team design in personnel management (e.g. [464, 497]); (6) integration techniques of sharing and collaboration among work-groups (e.g. [659]); (7) strategic (multistage) design and/or planning (e.g. [84, 497]); (8) ﬁnancial planning (to construct multi-period ﬁnancial planning strategies for ﬁrms and organizations) (e.g. [904]); (9) evolutionary synthesis in biology (e.g. [77, 78]). This section describes the following: (i) main approaches to system synthesis; (ii) our morphological approach HMMD; and (iii) examples. 3.3.1 Approaches to System Design/Synthesis J.R. Dixon has described the following design ﬂow as a basic one [209]: 1. Inventory (generation of design decisions). 2. Evaluation, engineering analysis/computing (e.g., computing some basic engineering system parameters as eﬃciency, reliability, productivity, performance). 3. Decision making as the selection of the best design decisions. Evidently, it is necessary to take into account basic external requirements (e.g., market, government). Clearly, each level of the above-mentioned design ﬂow can contain the same three stages (inventory, evaluation, decision making). The second crucial viewpoint is based on the main levels of a real hierarchical design ﬂow and corresponding roles: 1. System: general designer/manager. 2. Subsystems: general designer for subsystems.

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37

3. System parts/components: medium-level designers. 4. System elements: detail designers. The third viewpoint is based on case histories in system design (e.g. [654]). Finally, the fourth viewpoint consists of experience and knowledge of additional support specialists (e.g., scientiﬁc studies of some additional issues, information support). In recent decades, the majority of applied problems are very complicated and require some special composite eﬀorts, including the following: I. System approaches to design and planning. II. Knowledge of domain experts (engineering and design skills of specialists) as a basis of the approaches, including corresponding cycle of knowledge technology/engineering (knowledge acquisition, modeling, testing, correction, and utilization). III. Hybrid methods which involve, for example, traditional optimization techniques, multicriteria decision-making technology, and artiﬁcial intelligence approaches. In recent years, the signiﬁcance of approaches for complex systems design has increased. The following methods can be listed as being the main ones: 1. Formal methods for design (e.g. [103, 119, 210, 294, 464, 804–806]). 2. Synthesis ﬁnite automata approach [826]. 3. Optimization on the basis of complex non-linear mixed integer programming (e.g., design/synthesis in chemical engineering, in process systems engineering) (e.g. [6, 267, 326]). 4. Non-linear multicriteria (multiobjective) optimization (e.g. [572, 787, 793, 844]) including evolutionary design (e.g. [77, 636]) and evolutionary multiobjective optimization techniques (e.g. [168, 169, 202, 272, 911]). 5. Multidisciplinary optimization in aerospace and structural engineering (e.g. [22, 788]). 6. Decision-based design (usage of decision theory and multicriteria decision making in design) (e.g. [737, 738, 757, 786]). 7. PSI for the design of various complex systems and ﬁnancial planning [768, 787, 788]. 8. Various methods of global optimization (e.g. [6, 268, 269]). 9. Hierarchical system design (e.g. [96, 359, 453, 528, 803, 899]), modular system design (e.g. [80, 387]) and morphological analysis (e.g. [49, 409, 914]), including design on the basis of And–Or trees (e.g. [384, 599, 667]) and our HMMD [497]. Here, it is reasonable to point out the contemporary approach to modular design (mainly for software systems) as component-based system design [23, 35, 109, 370, 402, 615, 646, 691, 861]. 10. Grammatical design [113, 686, 799] and design on the basis of grammar description for composable systems, as in software engineering (e.g. [282, 283, 746]). 11. Special artiﬁcial intelligence approaches on the basis of expert systems (knowledge-based systems), e.g., R1/MICON [333, 556, 809] for computer engineering, VLSI design, (e.g. [103, 295]). 12. Case-based reasoning methods in design (e.g. [540]).

38

Composite Systems Decisions

13. Evolutionary synthesis (e.g. [77, 78]). Here, it is reasonable to point out multiobjective evolutionary optimization again (e.g. [803, 822, 911]). Evolutionary optimization approaches can provide creative design, such as combining components into a novel, creative way [682]. 14. Hybrid methods (e.g. [809]). At the same time, it is reasonable to point out some speciﬁc design problems which are important for complex composite systems [497]: 1. Basic system design: 1.1. Design of a system as a wholeness. 1.2. Synthesis or integration of a composite system. 1.3. Multistage planning as the design of a multistage (series, parallel–series) composite strategy. 2. System improvement, reengineering (revelation of system bottlenecks, generation of improvement actions, scheduling of the actions). 3. Strategic system design (under uncertainty): 3.1. One-stage strategic system design. 3.2. Multistage system design. From this viewpoint, some of the above-mentioned system design methods are oriented only to the design problem 1.1, and it can be very diﬃcult to apply them for other design problems. Mainly, methods of artiﬁcial intelligence (AI), hybrid methods (including HMMD) can be considered as basic ones for the more complicated and/or multistage design/planning problems above. In my opinion, many important system properties (e.g., reliability, adaptability, ﬂexibility) are based on special system redesign (reengineering) and strategic design problems which can be implemented as the above-mentioned complex design problems. 3.3.2 Hierarchical Morphological Approach The hierarchical combinatorial synthesis is based on a design morphology which corresponds to an initial hierarchical knowledge structure (design alternatives, their interconnection, etc.). The design morphology is a speciﬁc new hierarchical representation for domain knowledge. The synthesis approach consists of the following two main phases: 1. Design of the basic design morphology, including assessment of its design alternatives and their interconnection. 2. Bottom-up selection and synthesis of the design alternatives to obtain a resultant system (composite solution as a target system, a parallel–series strategy). Our hierarchical morphological approach is based on a partitioning– synthesis strategy (Figure 2.13). HMMD [494, 497] is close to multistage evolutionary optimization methods (e.g. [15, 169, 312]). We use our experience in hierarchical approaches to system modeling and organization of information on problem domains [490, 492]. The assumptions of HMMD are as follows: 1. the system has a tree-like structure (an organic hierarchy [175]); 2. a system excellence is a composite estimate which integrates components’ (subsystems, parts) qualities and qualities of interconnection (IC) or compatibility among

3 Systems: Models, Analysis, and Synthesis

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subsystems; 3. monotone criteria for the system and its components are used; 4. quality of system components and IC are evaluated on the basis of coordinated ordinal scales. The following designations are used: (a) design alternatives (DAs) for leaf nodes of the model; (b) priorities of DAs (r = 1, ..., k; 1 corresponds to the best one); and (c) ordinal compatibility (IC) for DAs (w = 0, ..., l, l corresponds to the best one). A basic version of HMMD involves the following phases: Stage 1. Design of a tree-like system model. Stage 2. Generation of DAs for leaf nodes of the model. Stage 3. Hierarchical selection and composition of DAs into composite DAs for the corresponding higher level of system hierarchy. Stage 4. Analysis and improvement of composite DAs (decisions). Figures 3.3 and 3.4 1 depict a hierarchical system and corresponding requirements. Figure 3.3 illustrates our hierarchical scheme, which is based on generation of alternative decisions for leaf nodes of the system model, evaluation and ranking of the alternatives, composition of composite decisions, their evaluation and ranking, etc. An illustration of the requirements for the system and its components is shown in Figure 3.4. Composition and evaluation of composite decisions

6 @ I @ ...

Composition and evaluation of ... composite decisions ... @ I @ Ranking of Ranking of alternatives alternatives ... 6 6 Generation of alternatives

Generation of alternatives

Figure 3.3 Bottom-up hierarchical framework

1

Copyright IEEE. Reprinted, with permission, from M.Sh. Levin, Modular System Synthesis: Example for Composite Packaged Software. IEEE Transactions on Systems, Man, and Cybernetics, Part C, 35(4), 544–553, 2005.

40

Composite Systems Decisions

Requirements (criteria) ⇒ NS = A B ⇒ A for S A A A Requirements Requirements A B (criteria) ⇒ K AK ⇐ (criteria) for A ⇒ A A ⇐ for B A A A Requirements Requirements A (criteria) ⇒ H AH⇐ (criteria) D ⇐ for D for C ⇒ C Figure 3.4 Hierarchy of requirements Now let us consider our formulation for the composition problem (morphological clique problem) [497]. Let G = ({A(j), j = 1, ..., m}, {{E(j), j = 1, ..., m} ∪ Ec }) be a morphological graph, where A(j) is a set of vertices (design alternatives DAs) in morphological class j, | A(i)&A(j) |= 0, E(j) is a set of arcs inside the morphological class j (partial order), Ec is a set of arcs (compatibility, interconnection IC) between DAs of diﬀerent morphological classes (symmetric binary relation). We will use priorities besides use of E(j). The problem is: Find a composition or a morphological scheme ( morphological clique) S = S(1) ... S(j) ... S(m) (where S(j) is a selected decision alternative for the jth component) of DAs (one representative from each morphological class Aj ) with non-zero IC. In the basic version of a morphological clique problem, the following vector for excellence of system S is used: N (S) = (w(S); n(S)), where w(S) is the minimal value of pairwise compatibility in S, n(S) = (n(1), ..., n(r), ..., n(k)), where n(r) is the number of components of the rth quality in S. Thus we search for composite decisions which are nondominated by N (S). A basic solving scheme consists of the following: (1) building of admissible morphological schemes, and (2) revelation of Pareto-eﬀective composite decisions by N . The usage of HMMD for many combinatorial problems is based on the following evident morphological macroheuristic [497]: Stage 1. Partitioning an initial problem into subproblems. Stage 2. Generation of local decisions (DAs) for subproblems. Stage 3. Assessment of interconnectivity of DAs for diﬀerent subproblems. Stage 4. Composing the best composite decision(s) of the problem at the higher hierarchical level. The solving scheme of the composition problem is based on the following two stages: (1) construction of feasible morphological schemes and (2) selection of Pareto-eﬀective solutions by N . This problem is NP-hard in general [442]. It is reasonable to use an enumerative algorithm starting from the maximal

3 Systems: Models, Analysis, and Synthesis

41

value of w and from the best DAs in each morphological class or an algorithm on the basis of dynamic programming. Figure 3.5 illustrates the decomposable system S = X Y Z. Here, examples of the composite system are: S1 = X1 Y4 Z3 ; S2 = X1 Y1 Z2 ; and S3 = X2 Y2 Z2 . For the composite decision in Figure 3.5, we get N (S1 ) = (1; 0, 2, 1), N (S2 ) = (3; 1, 1, 1), and N (S3 ) = (2; 3, 0, 0).

N S =X Y Z S1 = X1 Y4 Z3 S2 = X1 Y1 Z2 S3 = X2 Y2 Z2 Y Z AX A A (2) (3) X Y 1 1 HA AHZ1 (1) HA HAX2 (1) AHY2 (1) AHZ2 (1) AHX3 (1) HAY3 (2) AHZ3 (2) AHY4 (3)

1

3 2

Z3 Z2 Z1 2

X1

X2 X3

3 3 3 Y2 Y3 Y1 Y4 3

2

Figure 3.5 Example of composition problem (priorities of DAs are shown in parentheses) S3 - < 3, 0, 0 > Ideal point < 2, 1, 0 >

< 2, 0, 1 >

< 1, 2, 0 >

S2 - < 1, 1, 1 >

< 0, 3, 0 >

< 1, 0, 2 >

< 0, 2, 1 >

< 0, 1, 2 >

@ I @ S1

worst < 0, 0, 3 > The point Figure 3.6 Position (histogram) presentation of the lattice of system quality for N = (w; n(1), n(2), n(3)), w =const, m = 3, l = 3

DIdeal 1 HA Improvement point S D K S N (S3 ) S S S S S S S S S S S S N (S2 ) S S K S S N (S1) I w=3 w=2 w=1 Figure 3.7 Discrete space of system excellence for N (S)

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Composite Systems Decisions

Thus, N (S2 ) and N (S3 ) are Pareto-eﬀective points and N (S2 ) N (S1 ), N (S3 ) N (S1 ). Figure 3.6 depicts an example of the discrete space of system excellence (system quality) for a ﬁxed level of compatibility (for n(S)). Figure 3.7 depicts the integrated discrete space of system excellence (for N (S)) and examples of decisions. Note that the space consists of three ordered lattices; each of them corresponds to the lattice from Figure 3.6. 3.3.3 Towards Eﬃciency of Combinatorial Synthesis The combinatorial synthesis problem is NP-hard. We examine the following basic solving schemes: 1. directed heuristic algorithm [497] and 2. dynamic programming approach [503]. Note some special cases of the morphological clique problem are more simple from the viewpoint of complexity (e.g., approximate solvable cases [497]). In the future, it is reasonable to conduct special studies: (a) application of some other search strategies, e.g., a bidirectional search procedure [136]; (b) an additional complexity analysis of special cases of the morphological clique problem. At the same time we can point out special useful properties above of our basic combinatorial problem: (i) the problem is based on ordinal information and it is very useful for a domain specialist; (ii) the problem (and the solving process) can be divided into parts and the specialist has his access to each problem part and at each stage of the solving process. Thus, from the viewpoint of an extended complexity (while taking into account human factors), the morphological clique problem is suﬃciently easy and useful. 3.3.4 Multistage Design/Planning: Example Let us consider multistage planning processes on the basis of an example for planning a user interface [504]. Here, the following basic components of the examined system are considered: (i) operations of data processing, (ii) operations of knowledge acquisition or transformation, and (iii) training of user and data/knowledge representation. The design framework consists of the following stages: 1. Forming a basic hierarchical morphological space of operations (HMSO). 2. Analysis of an initial situation (user, task) and adaptation of an HMSO (design of a working version of an HMSO) as follows: (a) selection or identiﬁcation of appropriate operations on the basis of constraints; (b) parallelization of operations on the basis of parameterization of techniques, and use of diﬀerent experts; and (c) training the user. 3. Design of a composite solving strategy, including the following two phases: (a) selection of operations (multicriteria ranking); (b) synthesis on the basis of steps as follows: composing a series strategy or constructing an operation chain (morphological clique).

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There exist the following sources of user interface adaptation: (a) user; (b) task; and (c) intermediate results of problem solving (information for feedback). Note studies of the user modeling and adaptation are considered in detail in [203, 444]. In the main, the following techniques have been applied for the model selection, and sequencing (synthesis of series strategies): (a) artiﬁcial intelligence techniques (e.g. [214, 244, 525]); (b) linear programming problems (e.g. [594]); (c) integer programming problems, such as searching for an optimal path to a required output [325]; and (d) nonlinear integer programming for the modular design with redundancy, i.e., with parallel fragments [80]. Here, we examine conceptual design, and combinatorial models for the selection, modiﬁcation, and composing of the solving strategies and their elements. The generation of an HMSO is based on conceptual analysis and design [288, 695]. Our example is based on the examination of a system for knowledge acquisition and use. We examine an HMSO as follows: 1. Prototyping P : 1.1 Problem identiﬁcation I. 1.2 Selection/generation of terminology T . 1.3 Knowledge acquisition V . 2. Design of work version D. 2.1 Enhancement of problem description (type, terminology) E. 2.2 Acquisition of additional knowledge W . 3. Utilization U . Generally, an HMSO is based on the following kinds of operations: (1) knowledge acquisition (interaction); (2) data/knowledge processing (computation); (3) data/knowledge representation (interaction); and (4) training of user (interaction). The following criteria for the evaluation of DAs are used [325, 497, 606]: required computer resources; required human resources; quality of ranking (robustness, etc.) possibility for data representation; possibility for an analysis of intermediate data; and usability (easy to learn, understanding, acceptability, habits, etc.). In our example, we apply representation elements or DAs for leaf nodes as follows: command language (X1 ); menu (X2 ); icons (X3 ); and graphic/ animation (X4 ). In addition, we consider the following parallel aggregate (parallel combined) DAs: X5 = X1 &X2 ; X6 = X3 &X4 ; and X7 = X2 &X3 &X4 Here, the index corresponds to the number of DAs, and instead of X we use a certain notation of the leaf (e.g., T1 , E3 ). Our working HMSO obtained is presented in Figure 3.8. Thus, the problem is: to select DAs (kinds of alternative representation elements: {X1 , ..., X7 } for each leaf node (tree-like system model, Figure 3.8) to compose a series combination (a series solving strategy) of the DAs.

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Composite Systems Decisions

N Strategy

S =P DU S1 = P1 D1 U5 = ((I1 &I2 ) T2 (V3 &V4 )) (E4 W4 ) (U1 &U2 ) S2 = P1 D1 U2 = ((I1 &I2 ) T2 (V3 )&V4 )) (E4 W4 ) U2 S3 = P2 D1 U5 = (I3 (T1 &T2 ) V4 ) (E4 W4 ) (U1 &U2 )

Prototyping

Design

K PP ==II T T V V (1) 1

5

2

Utilization

K DD ==EE W W (1) U K UU

6

1

4

= (3) 2 = (2) U4 = (1) U5 = U1 &U2 (1) U7 = U2 &U3 &U4 (1)

4

P2 = I7 T2 V3 (1)

H

H

I T Problem Generation identiﬁof terminology cation I1 (4) T1 (2) I2 (1) T2 (3) I3 (2) T5 = T1 &T2 (1) I4 (3) I5 = I1 &I2 (1) I6 = I3 &I4 (2) I7 = I2 &I3 &I4 (1)

H

H

1

H

V E W Knowledge Enhan- Knowledge acquisition cement acquisition V1 (4) E1 (4) W1 (4) V2 (3) E2 (3) W2 (3) V3 (2) E4 (1) W3 (2) V4 (2) W4 (1) V5 = V1 &V2 (3) W5 = W1 &W2 (3) V6 = V3 &V4 (1) W6 = W3 &W4 (1) V7 = V2 &V3 &V4 (1) W7 = W2 &W3 &W4 (1)

Figure 3.8 Design morphology

Let us construct a series solving strategy on the basis of the morphological clique problem. Priorities of DAs (r = 1, ..., 4), obtained by expert judgment, are presented in parentheses in Figure 3.8. Table 3.1 contains the basic compatibility for basic DAs. As a result, we obtain the compatibility presented in Tables 3.2 and 3.3. Table 3.1 Compatibility X1 X2 X3 X4 X5 X6 X7 X1 X2 X3 X4 X5 X6 X7

1 2 3 4 1 4 5

2 4 4 5 3 4 4

3 5 2 5 4 3 4

4 5 5 1 4 3 2

1 3 4 4 3 4 3

4 4 3 3 4 2 2

5 4 4 2 3 2 1

3 Systems: Models, Analysis, and Synthesis

45

Table 3.2 Compatibility T1 T2 T3 V1 V2 V3 V4 V5 V6 V7 I1 I2 I3 I4 I5 I6 I7 T1 T2 T3

1 2 3 4 1 4 5

2 4 4 5 3 4 4

1 3 4 4 3 4 3

1 2 3 4 1 4 5 1 2 1

2 4 4 5 3 4 4 2 4 3

3 5 2 5 4 3 4 3 5 4

4 5 5 1 4 3 2 4 5 4

1 3 4 4 3 4 3 1 3 3

4 4 3 3 4 2 2 4 4 4

5 4 4 2 3 2 1 5 4 3

Table 3.3 Compatibility W1 W2 W3 W4 W5 W6 W7 E1 E2 E3

1 2 3

2 4 4

3 5 2

4 5 5

1 3 4

4 4 3

5 4 4

Thus, we get the following composite DAs: (a) P1 = I5 T2 V6 , N (P1 ) = (4; 2, 0, 1, 0); (b) P2 = I3 T5 V4 , N (P2 ) = (4; 1, 2, 0, 0); and (c) D1 = E4 W4 , N (D1 ) = (5; 2, 0, 0, 0). Table 3.4 contains the compatibility for the higher level of system hierarchy. Table 3.4 Compatibility D1 U1 U2 U4 U5 U7 P1 P2 D1

4 3

2 2 4

4 4 5

4 3 1

3 4 4

3 3 2

Now we combine composite Pareto-eﬀective (by N ) DAs: (i) S1 = P1 D1 U5 = ((I1 &I2 ) T2 (V3 &V4 )) (E4 W4 ) (U1 &U2 ), N (S1 ) = (3; 3, 0, 0, 0); (ii) S2 = P1 D1 U2 = ((I1 &I2 ) T2 (V3 &V4 )) (E4 W4 ) U2 , N (S2 ) = (4; 2, 1, 0, 0); (iii) S3 = P2 D1 U5 = (I3 (T1 &T2 ) V4 ) (E4 W4 ) (U1 &U2 ), N (S3 ) = (3; 3, 0, 0, 0). Figure 3.9 illustrates two above-mentioned Pareto-eﬀective points for S. Let us point out a couple of bottlenecks and improvement actions for composite DAs:

46

Composite Systems Decisions

(a) (P1 , U5 ) (compatibility 3 ⇒ 4) for S1 , new N = (4; 3, 0, 0, 0) (ideal point) and (b) U2 (priority 2 ⇒ 1) for S2 , new N = (4; 3, 0, 0). The resultant series planning strategies for S are depicted in Figure 3.10.

HD A Ideal point S

S

S

K D

S

S

S

KS D

S

S

S S

S S

S

...

S

S

S S

w=3

w=4

w=5

Figure 3.9 Space of system excellence and Pareto-eﬀective points S1

- I1 - I2

- - T 2 - - V 3 - - E4 - V4 -

- W4

- - U1 - U2 -

S2

- I1 - I2

- - T 2 - - V 3 - - E4 - V4 -

- W4

- U2 -

- E4

- W4

- - U1 - U2 -

S3

- I3

- T1 - - V 4 - T2 -

Figure 3.10 Series planning strategies

3.4 Multicriteria Evaluation of Composite Systems 3.4.1 Preliminaries This section addresses 2 speciﬁc evaluation issues: integration of ordinal evaluation decisions for subsystems into a global system evaluation decision. Note, 2

Reprinted from M.Sh. Levin, System Synthesis with Morphological Clique Problem: Fusion of Subsystem Evaluation Decisions. Information Fusion, 2(3), 225237, 2001. (with minor amendments); with permission from Elsevier.

3 Systems: Models, Analysis, and Synthesis

47

modeling a multi-attribute space for complex systems is examined in the following domains: 1. Multicriteria analysis and decision making (e.g. [427, 706, 793]). 2. Theory of system design (e.g. [103, 294, 464, 788]). 3. PSI method for the design of complex systems [768, 787, 788]. In recent years, the importance of modular system design (including engineering of system life cycle and system evaluation issues) has increased; for example: (a) modular system architecture, system modeling (e.g. [56, 693, 716]); (b) evaluation of products and systems (e.g. [86, 503, 626, 660, 683, 696, 873, 913]); (c) modular system design (e.g. [56, 119, 321, 387, 552]); and (d) modular design of product/system life cycles (e.g. [464, 552, 588, 709, 794]). Thus, we focus on issues of aggregation/integration of estimates for subsystems. The issues of integration (aggregation, fusion) of structured information are examined in several domains; for example: (i) decision making (e.g. [179, 859, 860]); (ii) information fusion (e.g. [92, 194, 195, 534]). Our basic attempt is oriented to building some special spaces for the above-mentioned situations. We examine hierarchical (tree-like) models for composite systems. The following main evaluation approaches can be considered (resultant scale/space for system excellence is pointed out in parentheses): I. Traditional Approaches: 1. Multicriteria description of the system (vector space). 2. Multi-attribute utility analysis (quantitative scale). 3. AHP (quantitative scale). 4. Integration tables for ordinal information (ordinal scale). 5. Pareto-like approaches (ordinal scale). 6. Usage of special expert systems (ordinal scale). II. Morphological Approaches: 1. Basic morphological clique problem (discrete spaces of system excellence). 2. Generalization of morphological clique problem on the basis of poset-like scales (four basic versions) for system components (several extended modiﬁed lattices of system excellence). Here, well-known data envelopment analysis (DEA) is not considered (e.g. [148, 181, 739]). Our generalization of the basic morphological clique problem is examined, including asymmetric compatibility and poset-like scales for evaluation of system parts. The poset-like scales for evaluation system components and composite systems correspond to real engineering practice (e.g., conceptual design). A dynamic programming solving scheme for the morphological clique problem is described brieﬂy. Numerical examples illustrate the approach, several versions of the scales for evaluation of system components, some discrete spaces for evaluation of a composite system, and the solving processes.

48

Composite Systems Decisions

3.4.2 Traditional Approaches to Multicriteria Evaluation Here some basic traditional approach to multicriteria evaluation of complex systems are brieﬂy described. Special approaches to software evaluation on the basis of multicriteria methodology and expert systems (including an analysis of situations, usage of software proﬁles, etc.) are described in [91, 592, 785, 862]. The traditional approach to evaluate a complex system is based on a multiparameter (multi-attribute, multi-criterion) vector-like description of the system. As a result, we get a point in a multidimensional (multiparameter) space. After that, many approaches can be used to map the point above (i.e., a vector system description) into a quantitative or ordinal scale of system quality (quality metric, eﬀectiveness, productivity, performance, excellence). Multi-attribute utility analysis consists in mapping the vector system description into a quantitative scale on the basis of a utility function Figure 3.11). Let a system be described by the parameter vector p1 , ..., pn . Then we can consider the following function: fu = F (p1 , ..., pn ), where F aggregates parameters into a resultant quality of the system (e.g. [261, n427]). A basic example of the utility function is an additive function: fu = j=1 αi pi , where αi is a weight of parameter i. Thus, we get a quantitative scale for system excellence (a metric). This approach is used in many engineering (e.g., metrics in software engineering) and economical (e.g., indexes) domains.

0

DH

D

DK

A

- f u

Figure 3.11 Illustration for utility function A special approach to integrate the system parameters has been proposed by T.L. Saaty as hierarchical aggregation of weighted parameters: analytic hierarchy process (the AHP) (e.g. [84, 706]). Here, we brieﬂy describe a hierarchical procedure (integration tables) for integration of ordinal estimates that was proposed in [305]. In this case, parts/components of a system are evaluated upon ordinal scales and integration of the scales for composite system parts/components is based on integration tables that are obtained from experts. The integration tables correspond to monotone functions of algebraic logic (or multiple-valued logic) which have been studied in mathematical logic (e.g. [740]) and in decision-making procedures (e.g., in DSS COMBI PC [497]). Note, similar techniques are applied in technical diagnosis for electronic systems. The approach is illustrated in Figure 3.12 and Figure 3.13. An evaluation example is the following (ordinal estimates are shown in parentheses): (i) initial estimates: A(3), C(2), D(1); (ii) intermediate estimate: B(1); and (iii) resultant estimate: S(2). The usage of Pareto-like approaches provides generation of an ordinal scale for system excellence on the basis of some layers in a multiparameter space, e.g., as follows (Figure 3.14): (a) ideal point; (b) Pareto-eﬀective points; and (c) points which are close to Pareto-eﬀective points; etc. This method is the basic one in multicriteria analysis.

3 Systems: Models, Analysis, and Synthesis

System S = A B = A (C D)

z

x

xB

u

A

C

u D

Figure 3.12 Example of system structure Scale 1 1 1 2 2 2 3 3

1 2 3 4

for S 2 2 2 3 3 3 3 4

1 2 B 3 @ I 4 @ Scale for B 1 2 3 4 1 1 2 3 A 2 2 3 3 3 3 4 4 1 2 3 4 C 1 1 2 Scale 2 Scale for C 3 for A 3 4

1 2D 3 6

Scale for D

Figure 3.13 Example: integration of scales Criterion 1 6

Ideal point

u uh h u Pareto-eﬀective e upoints er e r hher he Criterion 2

Figure 3.14 Illustration for Pareto-approach

49

50

Composite Systems Decisions

3.4.3 Morphological Clique Problem for Evaluation In [516] the morphological clique problem (and HMMD) was used for evaluation of a composite system (a building). In this case, a hypothetical design is conducted and the resultant discrete space of system excellence (system quality) is divided in the several layers on the basis of the Pareto approach (Figure 3.15). As a result, an ordinal scale of system quality is obtained. Ideal point

S

S

A H

A H

S

A

S

S

N3 S

S

A

S

N2

S

S S

wo = 1

D K

S

S

A

S S

A

wo = 2

S

A H

S S

N1 A

A

wo = 3

Figure 3.15 Basic discrete space of system excellence (w = 1, 2, 3)

3.4.4 Usage of Poset-like Scales for System Components In [503], usage of three kinds of simple poset-like scales for assessment of system components (or DAs in HMMD) is examined (Figure 3.16). In this case, there is a change of the above-mentioned basic discrete space of system excellence (Figure 3.17) into an extended version of the space, e.g., as is depicted in Figure 3.18.

3.5 Summary In this chapter, the following issues for composite systems have been considered brieﬂy: (i) modeling, (ii) analysis, (iii) synthesis, and (iv) evaluation for composite systems. For issues (i) and (iv), the trend from a whole system to a composite system requires various graph-like models, special scales for assessment of system components, and special algorithms for integration / aggregation /fusion of estimates for system parts into resultant estimates for the system. In addition, two methods (integration tables and HMMD) are described for issue (iv). Approaches to issue (ii) are traditional ones (i.e., structural modeling, system analysis). For system synthesis (issue (iii)), HMMD is applied.

3 Systems: Models, Analysis, and Synthesis

51

Evidently, other approaches can be used for the systems issues above as well (e.g., various methods for system design, AI techniques for system assessment/evaluation and design, fuzzy approaches). The issues considered are basic ones for contemporary engineering directions as follows: (a) design of special engineering databases [777] and engineering concept spaces as special kinds of engineering history bases (e.g. [155]); (b) investigation of system development/evolution; and (c) design of system family and platforms. In addition, let us point out the following. From the generalized viewpoint, it is reasonable to consider three systemic levels: 1. systems (products, processes, technologies), 2. requirements of the systems, and 3. standards. It is often crucial to consider the system approaches, methods, and problems for levels 2 and 3 (i.e., for requirements and standards).

Case 1: basic ordinal scale A H 1 A H

2

A H

3

Case 3: several ideal points 1’

H

A A

A

H 2 AA A H

3

1”

Case 2: several intermediate points A H 1 A A AA 2” 2’ H A A AA H 3

Case 4: cases 2 and 3 A 1” 1’ H @ @ H @A 2” 2’ A A AA H 3

Figure 3.16 Basic simple element scales

52

Composite Systems Decisions

1, 1, 1

1, 1, 2

1, 2, 2

2, 2, 2

A

AA

A

AA

1, 1, 3

1, 2, 3

2, 2, 3

1, 3, 3

2, 3, 3

3, 3, 3

Figure 3.17 Discrete space of system excellence: case 1

Ideal points

N (S1 )

C

C

C

C

C C

C

C C

wo = 1

C

C

C

C

wo = 2

C

C C

C

C C

C NC (S3 ) C N (S2 ) C C C C C wo = 4 wo = 3

C

C C

wo = 5

Figure 3.18 Discrete space of system excellence (w = 1, 2, 3, 4, 5)

4 Issues of Systems Engineering

4.1 Life-cycle Engineering 4.1.1 Basic Stages of the Life Cycle The life cycle of a product/system consists of the following basic stages: (1) creation, (2) R & D, (3) manufacturing, (4) testing, (5) marketing, (6) transportation, (7) utilization and maintenance, and (8) recycling/reusing. Contemporary integrated engineering/management disciplines (including special software tools and corresponding educational courses) are considered as follows: design/planning of life cycle, life-cycle management, life-cycle engineering, and support/maintenance of life cycle. The above-mentioned disciplines are based on the integrated examination of all or several stages of the product/system life cycle. Examples of the integrated approach are the following (e.g. [164, 254, 514, 549, 852]): (i) integration of design and manufacturing systems; (ii) integration of design, manufacturing, and inspection (testing) systems; (iii) integration of design, process control, and process operability: (iv) integration of design, manufacturing, and transportation systems; and (v) integration of design, material selection, and manufacturing systems. The integrated approach is very useful from the following basic viewpoints: (a) complexity of the product/systems, (b) complexity of the life-cycle stages and their interconnection, (c) complexity of a chains of life product cycles, and (d) integration of various products/systems into product families/platforms. Evidently, product life cycle can be examined as a complex multistage system and it is possible to use corresponding multistage design methods (e.g. [497]) in which a composite decision consists of components corresponding to life-cycle stages. This book contains a set of real-world applications of this integrated approach to various applied domains. 4.1.2 Design/Management Problems and Life Cycle In recent decades, engineering of product life cycle has became a crucial direction in engineering and management. Many researchers have studied product

54

Composite Systems Decisions

life-cycle issues on the basis of various methodological approaches, e.g., systems engineering [89, 368, 552, 709, 794], concurrent engineering ([463], [658]), enterprise engineering environments [114, 128, 824], product life cycle design and management [71, 254, 549, 588, 620], decision trees (e.g. [180]); and system integration [119, 321, 464, 497]. A traditional approach consists in hierarchical decision making for system design [359, 460, 461, 464, 497, 605]. Contemporary approaches involve integration of hard (e.g., CAD/CAM, FMS, CIM) and soft (e.g., TQM, JIT, concurrent engineering) technologies [13]. As a result, expert engineering/design/management knowledge plays central roles at several hierarchical levels: (a) expert knowledge for detail design/management at each stage of the life cycle; (b) expert knowledge for top-level integration (e.g., issues of functionality, information, resource, and organization). Here, a combinatorial framework for engineering of product life cycle on the basis of a hierarchical (tree-like) description is considered. The result corresponds to a composite technological strategy. In fact, three concepts are used: (i) an integrated intelligent design and manufacturing system, (ii) an integrated product and process design, and (iii) a modular approach (e.g. [56, 59, 300, 387, 423, 464, 526, 608, 693, 716, 834]). The hierarchical morphological description of the composite process with ordinal information is a special kind of design knowledge on a composite system. HMMD is used as a basic information model and design method [497]. Our list of basic management/design problems is as follows [497]: Problem 1. Design of composite system. Initial information: requirements and information. Goal: composite system decision. Problem 2. Improvement/transformation of a composite system. Initial information: composite system decision. Goal: bottlenecks, improvement actions, new improved composite system decision. Problem 3. Strategic design under uncertainty. Initial information: requirements and information under uncertainty. Goal: composite system decision. Problem 4. Multistage planning of a system (design of a system trajectory). Initial information: requirements and information. Goal: sequence of composite system decisions (for each stage). Problem 3 can be based on the following: 1. Probabilistic description of DAs and/or IC. In this case, we can examine probabilistic estimates as additional elements of initial vector estimates. 2. Fuzzy description of DAs and/or IC. Approaches to solving the cases above are described in [497]. Problem 4 requires using HMMD at two levels: (1) design of a system for each stage; and (2) coordination of the design decisions at each stage (top-level design of a composite system trajectory). Some problems of the product trajectory design are described in [497, 793] and in this book.

4 Issues of Systems Engineering

55

4.1.3 System Requirements In recent decades, a special signiﬁcant engineering direction was established: requirements engineering (e.g. [198, 255, 536, 689, 877, 898]). This is targeted to the following basic kinds of requirements: 1. business requirements; 2. user requirements; 3. high-level or system requirements; 4. functional requirements (things the system must do); 5. non-functional requirements (properties the system must have); 6. design requirements/design constraints; 7. manufacturing constraints; 8. performance requirements; 9. interface requirements (with other systems); 10. aesthetic requirements; 11. qualiﬁcation requirements; 12. logistics requirements; 13. environmental requirements; 14. system, subsystem and component requirements; and 15. reuse requirements. Here, the basic idea consists in organization of special projects (requirements engineering processes) to generate requirements speciﬁcations. The projects above can be based on the following information sources: (i) information from users, (ii) previous experience (e.g., design, manufacturing), (iii) description of analogous systems, and (iv) various use cases. A list of basic approaches/methods is the following: 1. system analysis; 2. discovering; 3. acquisition of domain experts knowledge, skills, experience; 4. structuring and integration of information; 5. modeling and representation of information; 6. dynamical modeling/simulation; 7. prototyping; 8. analysis of dynamics (e.g., basic system trends); 9. accumulation of testing results and information on system/product life cycles; 10. scenarios (including conceptual maps, graph models); and 11. strategic planning and forecasting. 4.1.4 System Design A recent study on design methods is contained in [153]. Design methods in engineering design (mainly for mechanical engineering) are described in [222]. Many issues of machine design (CAD) in mechanical engineering are described in [363]: design decisions, plans, design of product/system, selection of materials, planning the manufacturing process, etc. Contemporary design approaches are based on the following three trends: 1. Usage of an extended set of various design methods. 2. Examination of the design process while taking into account the system life cycle, including the following: 2.1. taking into account all stages of life cycle, i.e., manufacturing, utilization and maintenance. 2.2. early stages of the design process, e.g., conceptual design [870]. 3. Usage of new kinds of design environment, including distributed collaborative environments based on the Internet and Web technologies (e.g. [524, 870]). A comparison project is described in [52] in which 11 high-level system design methods were used for the same several design (benchmark) problems, including the following: (1) state transition diagrams; (2) algorithmic state machine (ASM) notation; (3) model-based system engineering; (4) Graphical Description Language; (5) RDD-100; (6) structured analysis (using entity relationship diagrams, data ﬂow diagrams, state transition diagram with

56

Composite Systems Decisions

Ward–Mellor notation); (7) functional decomposition; (8) object-oriented analysis (OOA) with Shlaer–Mellor notation; (9) OOA and object-oriented design (OOD) with Booch notation; (10) an operational evaluation modeling (OpEM)-directed graph; and (11) IDEF0 (Integration Deﬁnition of Function Modeling). In the article above, additional design methods for future investigations have also been pointed out [52]: (1) CORE, (2) colored Petri nets, (3) Slate, (4) fuzzy-neural systems, (5) SilverRun, (6) the Objectory, (7) VHDL, and (8) Sim Factory. Our description of the system design/synthesis methods is contained in Chapter 3. 4.1.5 System Redesign and Bottlenecks Issues and problems of reengineering, improvement, change, redesign, and upgrade became to be the most crucial (e.g. [211, 212, 328, 497, 694]). One can see this tendency in all domains, e.g., in large urban environments, and in network-like systems (transportation systems, communication systems, computer networks, distributed information systems). It is necessary to point out a special system trend exists: From

system improvement To

on-line system adaptation.

Now this situation (e.g., on-line system reconﬁguration) is very important in the ﬁeld of algorithms and software in communication and computer systems [560, 561]. The redesign/improvement process is based on the following phases: Phase 1. Generating new system system requirements as a result of changing an external environment. Phase 2. Revelation of system bottlenecks. Phase 3. Design of the improvement/adaptation plan. Phase 4. Implementation of the improvement plan. Here, phase 1 corresponds to a special kind (often on-line) of requirements engineering. Phase 2 consists of a special kind of system design [497, 504, 516]. Phase 2 (revelation of system bottlenecks) can be based on the following four approaches: 1. Engineering analysis (expert judgment). 2. Traditional methodological approach: 2.1. design of system structure (a structural multi-component model); 2.2. assessment of reliability for system components; and 2.3. selection of the most non-reliable system component (Pareto approach from Japanese system of quality management). 3. Multicriteria approach: 3.1. design of system structure (a structural multi-component model); 3.2. multicriteria assessment of system components from the viewpoint of basic system properties as reliability, safety, performance, etc.; and

4 Issues of Systems Engineering

57

3.3. multicriteria ranking of the system components to reveal the most important parts. 4. Revelation of the most prospective system design version from the viewpoint of improvement of its components or component compatibility: 4.1. multi-version design of a composite (modular) system on the basis of HMMD to get a set of composite design alternatives (system versions); 4.2. dividing the set of obtained system versions into system quality layers: (1) ideal decision(s); (2) Pareto-eﬀective decisions; (3) near Pareto-eﬀective decisions; (4) other decisions; 4.3. analysis of the decisions (i.e., system versions) from layers 2 and 3 above from the viewpoint of their possible improvement (by components, by component compatibility); and 4.4. revelation of the best decisions on the basis of an optimization problem as follows: maximization of the following ratio: resultant improvement of the system quality layer to additional resource for the improvement above either upon the scale of a component or upon the scale of components’ compatibility. As a result, we get a set of possible improvement actions (a space of improvements). Here, the analysis of the total vector estimate [497] of N (S ) = the composite system decision is used for system version S : (w(S ); n1 (S ), n2 (S ), ...). On the other hand, it is also possible to apply other gradient-like approaches. In the main, the usage of HMMD in real-world examples involves the revelation of bottlenecks on the basis of the above-mentioned approach 4.

4.2 Maintenance of Composite Systems In this subsection, we describe basic parts of the maintenance processes [183, 187, 344, 519, 632, 715, 887]. The following objects can be examined under maintenance procedures: (i) system and/or system part (component, unit); (ii) system state(s); and (iii) system function or function cluster (as a group of interrelated functions). The basic types of system characteristics are as follows: (a) reliability (stability, etc.), (b) safety, (c) viability, survivability (d) robustness, and (e) performance. Figure 4.1 depicts a framework for the maintenance procedures. Maintenance procedures can be targeted to the following: (1) whole system; (2) multi-component (modular) system, e.g., one-layer modular system,

58

Composite Systems Decisions

hierarchical or multi-layer system, multi-layer modular system with complex module interrelation (including interrelation between diﬀerent layers and branches); (3) developing systems, e.g., a system trajectory on the basis of upgrade of system components, system structure, interconnection between components); and (4) external environment. Objects: systems/parts, system states, system functions. System type: whole system modular system developing systems external environment. System characteristics: reliability (stability), safety, viability% survivability, robustness, performance.

Kind of maintenance: basic maintenance, preventive maintenance, self-maintenance. @ @ R ?

KE

@ I @

Maintenance problems: analysis/evaluation, prediction, operational management, information modeling, strategy planning.

Figure 4.1 Framework for the maintenance procedures

A generalized maintenance scheme involves the following parts: 1. General system installation. 2. Maintenance of personnel: 2.1. training of personnel; 2.2. regular testing and retraining of personnel. 3. Maintenance of the system: 3.1 planning/scheduling of maintenance operations; 3.2. execution of inspection procedures as system diagnosis/ evaluation to reveal some bottlenecks/faults (including planning and execution of the inspection); 3.3. change of the system on the basis of two kinds of activity: (i) repair and/or (ii) system components/modules replacement. 4. Analysis of the system, accumulation of data, prediction. The basic maintenance problems are: (a) system analysis/evaluation (systems, its part, etc.); (b) system prediction; (c) operational management/ preventive maintenance: (testing, evaluation, accumulation of additional information, repair/replacement); (d) design of information model for system and each part (object); (e) design/planning of maintenance strategy: selection of object under maintenance, selection of operation (i.e., inspection, repair, re-

4 Issues of Systems Engineering

59

placement), assignment of time for the operation(s), and execution of the operation(s). A brief survey of the maintenance organization follows. Four areas of key life-cycle maintenance (repair and prevention) management decisions are considered in [130]: (1) component replacement; (2) capital equipment replacement; (3) inspection procedures; and (4) resource requirements. Selection tools and techniques for model-based diagnosis is described in [144]: (a) the predictors; (b) the candidate generators; and (c) the diagnosis strategists. A description of development for the intelligent maintenance optimization systems over past years is contained in [443]. An intelligent probing approach for diagnosis of network-like systems is described in [106]: (i) planning phase (i.e., selection of a probe set), and (ii) diagnosis phase. A special basic attention is targeted to analysis and maintenance of system faults [156]. A diagnostic information fusion system for the diagnosis of complex multicomponent products/systems (on the basis of various information sources and a set of information processing frameworks) is suggested in [310]. Preventive maintenance for a system and the system components is examined in [715]. Statistical modeling for preventive maintenance is described in [298] and [299]. Now let us point out the following viewpoint: majority of the maintenance procedures can be realized on the basis of multicriteria decision making procedures, combinatorial optimization problems, and design of composite decisions.

4.3 Multistage/Trajectory Design 4.3.1 Preliminaries In recent years, the importance multistage product/system design, process systems engineering, and life-cycle engineering has increased [120, 327, 464, 497, 514] and multicriteria approaches to the design problems have been described [169, 342, 768, 787, 793]. Multicriteria approaches to the design of the optimal system trajectories (for the design or planning of products/systems) have been considered in [497, 793]. A very interesting and useful problem as the design of optimal reconﬁguration strategy has been suggested in [479]: (a) a modular system is examined, (b) system usage is oriented to a multistage mission with diﬀerent system requirements at the mission stages, (c) the designed strategy is based on system reconﬁguration (i.e., selection and interconnection of system units), and (d) possible system faults are taken into account. Note, similar problems for system trajectories are considered in the interesting ﬁeld of system evolution (e.g. [623, 626, 671, 712]). This section is based on [512, 514] and focuses on the following: (a) hierarchical morphological modeling of a composite high-tech product and generation of the product alternatives; and (b) design of a multistage product strategy (trajectory) for several series time intervals.

60

Composite Systems Decisions

A morphology for a diagnosis system is considered as a basis to generate a set of product versions (product family). The K-stage time period is analyzed. The problem is: Find the best product version (or a version combination) for each time stage while taking into account requirements (criteria) at each stage and compatibility between product versions at diﬀerent stages. Thus, a product trajectory can be found. A basic criteria set is used (cost of the version, required additional research, possible proﬁt, possible extension of market, knowledge/experience of users, etc.) with special criteria weights for each time stage. Note, it is possible to use a special criteria system for each time stage too. The solving procedure consists of two parts: (a) multicriteria ranking (selection of Pareto-eﬀective local decisions) of product versions at each stage; (b) composing selected product versions into parallel–series product trajectories. Further, the investigation is based on multicriteria decision making and combinatorial morphological models (e.g., HMMD) [497]. In fact, modular design is applied (e.g. [387, 464, 497]). 4.3.2 Morphological Scheme of Product A morphological scheme of a diagnosis system is presented in Tables 4.1 and 4.2. Table 4.1 Structure of diagnosis system and versions: part 1 A. Functions 1. Structural modeling (a) simple (b) special subsystem 2. Integration of data (a) simple (b) with stratiﬁcation functions 3. Forecasting (a) simple (b) multistage (c) multialternative 4. Actions (a) simple (b) multistage (c) multialternative 5. Specialist space (a) simple (b) multistages

V1

V2

V3

V4

V5

@

$

&

#

V6

V7

o

%

@

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@

@

$

&

#

o

%

$

& &

# #

o o

% %

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4 Issues of Systems Engineering

61

System versions are generated as follows: Stage 1. Versions V1 (prototype), V2 , V3 , and V4 . Stage 2. Versions V2 , V3 , V4 , V5 , and V6 . Stage 3. Versions V3 , V4 , V5 , V6 , and V7 . It is the intent to examine some aggregated situations when several versions will be promoted into the market (e.g., version 3 and version 5). Note, it can be reasonable to consider special system versions with a support (consulting) service of users as follows: V1 , V2 , V3 , V4 , V5 , V6 , and V7 . Table 4.2 Structure of diagnosis system and versions: part 2 B. Support tools 1. Graph modeling (a) simple (b) special subsystem 2. Decision making (a) simple (b) special subsystem 3. Knowledge engineering (a) simple (b) special subsystem 4. Allocation of data (a) ﬁxed (b) simple (c) special subsystem 5. Database (a) ﬁles (b) special subsystem 6. Export/import of data (a) none (b) special subsystem 7. Visualization (a) very simple (b) some support (c) special subsystem

V1

V2

V3

V4

V5

V6

@

$

&

#

o

V7

% @

@

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$ %

4.3.3 Multistage Product Trajectory Here, we examine three-stage product trajectory. Criteria and their weights are contained in Table 4.3.

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Composite Systems Decisions

Table 4.3 Criteria and their weights for marketing issues (part M ) Stage 1 Stage 2

Criteria 1. 2. 3. 4. 5. 6. 7.

Cost of version Volume of required academic research Knowledge/experience of practitioners Required new algorithms&procedures Required additional software packages Possible proﬁt Volume of possible market and its extension 8. Possible competition 9. Usability of product 10. Reliability of product

Stage 3

−4 −2 1 −1 −1 2 4

−2 1 2 2 1 3 5

−4 2 3 2 2 4 5

−2 2 2

−3 3 2

−3 4 3

Estimates of DAs and resultant priorities for stages 1, 2, and 3 are presented in Tables 4.4, 4.5, and 4.6 respectively. Table 4.7 contains the compatibility. Table 4.4 Estimates and priorities (stage 1) DAs V1 V2 V3 V4

Criteria 1

2

3

4

5

6

7

8

9

10

1 2 3 4

0 1 2 4

4 4 4 5

1 2 2 3

0 0 1 1

1 2 3 5

2 2 2 3

1 1 1 2

1 2 3 4

5 5 5 4

Total priority 2 2 2 1

Table 4.5 Estimates and priorities (stage 2) DAs V2 V3 V4 V5 V6 V4 &V6

Criteria 1

2

3

4

5

6

7

8

9

10

2 3 4 5 7 11

1 2 4 6 8 8

4 4 5 6 6 6

2 2 3 5 7 7

0 1 1 3 5 5

2 3 5 6 8 9

2 2 3 4 5 6

1 1 2 4 5 4

2 3 4 5 7 7

5 5 5 4 3 2

Total priority 4 3 3 2 1 1

As a result, we obtain the following best composite decision (i.e., threestage product trajectory): S1 = V4 V6 (V3 &V5 &V7 ), N (S1 ) = (7; 3, 0, 0, 0). Note trajectory S2 = V4 (V4 &V6 ) (V3 &V5 &V7 ), (N (S2 ) = (5; 3, 0, 0, 0)) can be improved by increasing the interconnection between V4 and V4 &V6

4 Issues of Systems Engineering

63

(5 ⇒ 7). Evidently, prototype version V1 is required as a preliminary version too. Figure 4.2 depicts some resultant three-stage trajectories. Table 4.6 Estimates and priorities (stage 3) DAs

Criteria

V3 V4 V5 V6 V4 &V6 V7 V3 &V7 V5 &V7 V3 &V5 &V7

1

2

3

4

5

6

7

8

9

10

3 4 5 7 7 9 9 9 10

2 4 6 8 8 10 10 10 10

4 5 6 6 6 8 8 8 9

2 3 5 7 7 9 9 9 10

1 1 3 5 5 7 7 7 8

3 5 6 8 8 10 13 16 19

2 3 4 5 5 7 8 9 10

1 2 4 5 5 8 8 7 6

3 4 5 7 7 9 9 9 10

5 5 4 3 3 2 2 2 2

Total priority 4 4 4 4 3 3 2 2 1

Table 4.7 Compatibility V1 V2 V3 V4 V5 V6 V7 V4 &V6 V1 V2 V3 V4 V5 V6 V7 V4 &V6 V3 &V7 V5 &V7 V3 &V5 &V7

7 7 7 7 7 7 7 7 7 7 7

6 7 7 7 7 7 7 7 7 7 7

5 6 7 7 7 7 7 7 7 7 7

4 5 6 7 7 7 7 7 7 7 7

3 4 5 6 7 7 7 7 7 7 7

2 3 4 5 6 7 7 7 7 7 7

1 2 3 4 5 6 7 7 7 7 7

2 3 4 5 6 7 7 7 7 7 7

4.3.4 Design of Tree-like Trajectory Here, we consider a more complicated situation when a decision process has a tree-like structure (a tree-like structure of possible decision situations). Clearly, for each node of the decision tree it is reasonable to use our hierarchical design approach and to get a design morphological hierarchy including composite decisions. In the next phase, the composite decisions obtained have to be integrated on the basis of the initial decision tree. The scheme is as follows: Stage 1. Design of a basic decision tree. Stage 2. Design for each tree node a design morphological hierarchy, including composite decisions. Stage 3. Coordination of the composite decisions for the tree nodes to get tree-like trajectories.

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The tree-like trajectories described can be applied in many important domains, e.g.: (a) strategies for product design (while taking into account changes in markets, etc.); (b) special kind of multistage medical treatment; and (c) multistage strategies for environmental systems. V3 V4 V5 V2 V6 V3 V4 &V6 V4 H V7 V1 HH V V3 &V7 V2 5 H H H V6 V5 &V7 V3 H H H H V &V V3 &V5 &V7 V4 4 6 0 Stage 1 Stage 2 Stage 3 Figure 4.2 Illustration for multistage product trajectory

T -

4.4 Summary In this chapter, some basic problems of system engineering have been considered: (1) design/management problems in life-cycle engineering, (2) generation of systems requirements, (3) organization of system maintenance, and (4) multistage/trajectory design. The ﬁrst three problems are only described in brief. Generally, our design of composite decisions on the basis of HMMD can be applied for the above-mentioned problems. Finally, the fourth problem (design of multistage trajectory) can be considered as the most prospective direction for future theoretical and applied researches.

5 System Development and Evolution

5.1 Preliminaries Recently, the signiﬁcance of system changes has increased. Moreover, many specialists now need certain skills in the analysis, understanding, and evaluation of the system development and evolution processes. P.J. Denning described [207] that only master and legend can see historical drifts and have the capacity for long-range strategic thinking and actions. At the same time, such an ability increasingly required for specialists at the levels of professionals too. In general, several diﬀerent kinds of evolution for long-life products (software packages) are described in [186]: 1. Evolution of system requirements, functional and non-functional. 2. Evolution of technology related to diﬀerent domains. 3. Evolution of technology used in software products. 4. Evolution of technology used for the product development. 5. Evolution of society. 6. Business changes. 7. Organizational changes. This chapter involves a brief survey and our combinatorial approach to development/evolution of engineering composite systems [497, 505, 513]: 1. Study of existing combinatorial approaches to the representation of system evolution/development for composite systems of various kinds. 2. Design of new structural (combinatorial) representations of composite (decomposable, composable) systems (e.g., chains, tree models, And–Or tree models, tree model with morphology of alternatives, network models). 3. Combinatorial representation of basic change operations for composite systems. 4. Formulation and analysis of some basic combinatorial optimization problems for system changes. 5. Analysis of some interesting applications (computer science, engineering, management, biology, social science). 6. Analysis of some special problems: (i) representation of system evolution history for certain kinds of composite systems; (ii) revelation of system evolution trends (forecasting) for certain kinds of composite systems; (iii)

66

Composite Systems Decisions

multistage system design/planning; and (iv) analysis of evolution processes for system requirements. Here, our research is oriented to an extension of hierarchical combinatorial approach (i.e., HMMD). We examine the description, synthesis, and transformation (including multistage changes) of composite (composable, decomposable) systems for the representation, analysis, design/planning, and forecasting of system evolution processes. HMMD involves a basic combinatorial model (morphological clique problem) for the design and redesign of composite systems. Here, a special composite system for changes is considered as follows: (i) change of system parts, (ii) change of interconnection among system parts, and (iii) change of system model (structure). These three actions lead to (a) new special combinatorial operations and (b) special problems for the representation of development/evolution.

5.2 Short Survey Some basic rules for development of technical systems were proposed by G.S. Altshuller [24]. The origin of modular evolution has been described in [533]. M.M. Lehman and J.F. Ramil suggested special laws for evolution of software systems [480]: 1. Continuing change, 1974. 2. Increasing complexity, 1974. 3. Self-regulation, 1974. 4. Conservation of organizational stability, 1978. 5. Conservation of familiarity, 1978. 6. Continuing growth, 1991. 7. Declining quality, 1996. 8. Feedback system, 1996. An engineering analysis for invention and evolution of many products is described in [277]. A morphological approach for technological forecasting has been ﬁrstly used in [49]. Emergent evolution is studied in [591]. Scanning the technology is examined in [279]. Some examples of system evolution are described in [648]. Interesting attempts to apply modern techniques of multicriteria decision making for a multistage design of technological systems are contained in [63] and [120]. Operations technology and system evolution were considered in [702]. Patterns of some technological systems (e.g., for transportation systems) are described in [712]. An extended approach to system development/evolution as emergent synthesis has been described in [840]. Note, traditional investigations in system evolution are mainly oriented to the following: 1. some ﬁelds of modern computations (evolutionary programming, evolutionary computing, etc.) [270, 312, 379]; 2. evolutionary design methodology [122, 468]; 3. version modeling in VLSI design [425]; 4. four model versions in software engineering [178, 246, 247];

5 System Development and Evolution

67

5. the eight basic laws above for software evolution [480]; 6. the Shakun model for evolutionary system design (ESD) [742]; 7. three-dimensional model for system design evolution (design, redesign, reusing) [823]; 8. examination of technological paradigms and technological trajectories on the basis of technical changes [216]; 9. product evolution from the viewpoint of redesign methodology [623, 626, 895]; 10. approaches to reconﬁgurable manufacturing in machine-building (e.g., [564]); 11. process information as engineering history bases [813]; 12. software evolution and evolutionary design of software [671, 796]; 13. combinatorial modeling of system evolution (e.g. [505]). Technological evolution and improvement trajectories are important components of economics and strategic management (e.g. [36, 191]).

5.3 Basic System Models We examine the following basic combinatorial models for composite systems: 1. chain; 2. tree; 3. morphological tree (our system model, when for each leaf node we have some design alternatives DAs, is similar to an And–Or tree; Figure 5.4a and b illustrates this kind of system models); 4. network; and 5. morphological network (here, DAs are examined for each network node as in morphological tree).

5.4 Combinatorial Operations 5.4.1 Change Operations The following system change operations are examined: I. Operations for design alternatives of system parts DAs. 1.1. Change/improvement of DA O1 : Ai ⇒ Ai . 1.2. Deletion of DA O2 : A− i . 1.3. Addition of DA O3 : A+ i . 1.4. Aggregation of DAs O4 : {Ai } ⇒ Aa = A1 &A2 &.... 1.5. Standardization of DAs O5 : {Ai } ⇒ As or {Asj }. II. Operations for subsystems (system parts, components). 2.1. Change/improvement of a system part O6 . 2.2. Deletion of a system part O7 . 2.3. Addition of a system part O8 . 2.4. Aggregation of system parts O9 . III. Operations for the system conﬁguration (O10 ). As a result, a phase of the system evolution can be considered as a set of the above-mentioned operations. For each operation, a set of attributes has to be examined (e.g., required resources, proﬁt). Thus, one-stage or multistage

68

Composite Systems Decisions

optimization problems for system transformation can be studied (while taking into account some general external system evolution requirements/laws). In addition, it is reasonable to point out a co-evolution process [539] that is based on changes of external system requirements (e.g., markets, customers, new external system environment). 5.4.2 Exchange Operations Exchange operations for chain-like systems are basic ones in scheduling (algorithm design) [281] and in genome studies (e.g., mutations) [285]. Figure 5.1. depicts three types of exchange operation for elements. Analogous versions of the operations exist for blocks as block exchange (a series sequence of elements). Rotation of a block can be examined too (Figure 5.2). K-exchange operations are illustrated in Figure 5.3 for a 3-exchange case) [502]. Similar types of exchange operation can be examined for other kinds of combinatorial system models (e.g., for m-dimensional arrays, trees, morphological tree). Evidently, operations considered are similar to mutation operations in biology and evolutionary computing. EO1 :

?? a b

EO2 :

? a

EO3 :

? a

? b ? b

Figure 5.1 Modiﬁcations of exchange operations @ a ... b@ ?

?

?

?

b ... a @ @ Figure 5.2 Chain: rotation of a block ... a

b

c ...

-

. c b a .

R @ ? ? @ . a c b . . b a c. . b c a . . c a b . Figure 5.3 Illustration for a 3-exchange operation

5 System Development and Evolution

69

5.4.3 Binary Relations over Change Operations There are three kinds of binary relations over the change operations set: (1) equivalence Re ; (2) complementarity (compatibility) Rc ; and (3) precedence Rp . These relations have to be used as structural constraints. In chapter 8, a numerical example of the relations is described for the redesign of buildings [516]. 5.4.4 Multicriteria Description Clearly, it is reasonable to describe the above-mentioned change operations on the basis of their two main properties: 1. eﬀectiveness (proﬁt) and 2. required resources. As a result, we obtain a multicriteria description and components of the description can be used in optimization problems for system changes as elements of the objective function(s) and constraints. Some examples of system evolution/changes are contained in [497, 516].

5.5 Technological Evolution Problems We consider the following basic research problems: Problem 1. Combinatorial (structural) representation of composite systems and their evolution (including alternatives for system changes as system evolution operations: local operations for system elements/components and global operations for the system or its parts). Problem 2. Structural visualization of system evolution processes. Problem 3. Representation of system evolution processes as a special evolution network or system macro-evolution (a set of interconnected evolution trajectories). Problem 4. An analysis of proximity for system versions (including vector-like proximity; proximity as a substructure). Problem 5. Optimal system transformation (maximization of a resultant proﬁt, minimization of resources which are required for the evolution operations; taking into account constraints for evolution operations and their relations, etc.). Problem 6. An analysis of system evolution processes (revelation of bottlenecks, clustering of system versions, etc.). Problem 7. An analysis of dynamics for requirements to system evolution processes, including revelation of future system requirements. Problem 8. System forecasting. Problem 9. Multistage evolution optimization problems (e.g., on the basis of multistage HMMD). Problem 10. Study of special graphs and graph approaches for system modeling (e.g., graph dynamics) and the above-mentioned evolution networks.

70

Composite Systems Decisions

5.6 Combinatorial Problems 5.6.1 One-stage System Change First, the list of basic supporting procedures is as follows: 1. Selection of operations (change items). 2. Selection of the change items (i.e., operations) while taking into account some resource constraints. 3. Deﬁnition of parameter values for the items. 4. Integration/synthesis of the items into a composite system change. 5. Multicriteria ranking of the items while taking into account their attributes. 6. Ordering/scheduling the items. Let us brieﬂy point out some combinatorial models for the one-stage system change: 1. Knapsack problem for selection of the items while taking into account their utility and some resource constraints [281]. 2. Multiple-choice problem (a modiﬁcation of the knapsack problem when the item set is divided into groups and only one item is selected from each group). 3. Multicriteria ranking for ordering the items while taking into account their estimates upon criteria. The problem is the basic one in multiple criteria decision making [427]. 4. The morphological clique problem [497]. 5. Scheduling the change operations can be based on well-known scheduling problems. Scheduling problems are described in [281]. 6. For some complicated situations it may be reasonable to examine mixed integer programming models [326]. Here, our eﬀorts are oriented not only to select the best operations while taking into account their utilities and resource constraints, but to deﬁne some continuous parameter values for the operations. Figures 5.4a and b illustrate a system change on the basis of morphological clique problem (HMMD): S a ⇒ S b . S b = A B D+

N

Sa = A B C−

N

A

N K AA A KA

B 1 − 2 3

N AB KB

− 1 2

C

D AC AC

A

1 2

N KA K AA AH

B 1 3 + 4

N K BB AH

2 + 3

D

HD AH D HA D HA D

1 2 3

(a) (b) a Figure 5.4 Initial system S and changed system S b

5.6.2 Multistage System Change The multistage design approach (or trajectory design) on the basis of morphological clique problem can be used here [497]. Figure 5.5 illustrates a threestage evolution process as a two-level hierarchy on the basis of a morphological

5 System Development and Evolution

71

clique problem (HMMD). The evolution process consists of the following: 1. structuring of stages; 2. composition of composite changes (a set of interconnected evolution operations) for each stage (bottom hierarchical level); and 3. composition of multistage evolution trajectory (up-level of the hierarchy).

N AH

AH

Initial state

@ @ Changes @

...

@ @ Changes @

AH

Goal state

...

@ @ Changes @

Figure 5.5 Illustration of multistage evolution 5.6.3 Auxiliary Problems It is reasonable to point out some auxiliary problems for system models as follows: 1. approximation (e.g., searching for a spanning tree); 2. computing a proximity (similarity) between some systems; 3. mapping of systems; and 4. design of some submodels or supermodels (as substructures or superstructures) for system models.

5.7 Extended Cycle of System Evolution The extended cycle of system evolution processes involves changes of system requirements/speciﬁcations. Clearly, an external system environment is changed (e.g., markets, customers), and this trend leads to new system generations. In [539], this process is described as a system co-evolution process that contains the following: (a) searching for design solutions; (b) exploration of the design solutions; and (c) revision of the system speciﬁcation. Generally, this process may be examined as a game between design process and changed external system environment.

5.8 Applications Evidently, examination of development/evolution processes is very prospective for many applied domains, e.g., engineering systems: (a) software systems on the basis of intelligent DSSs; (b) algorithm systems for combinatorial optimization problems (algorithms, algorithm schemes/frameworks, hierarchical algorithm systems); (c) measurement systems; (d) manufacturing systems in machinebuilding; and (e) technological processes in biochemistry, etc. Some examples of one-stage and multistage system evolution are described in [497–499, 503, 504, 516].

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Composite Systems Decisions

A six generations example of old advice and systems for signal processing is as follows (list of generations and corresponding functions) [513]: 1. Frequency measurement (device S1 ): (1) analysis of frequency spectrum in a wide range. 2. Frequency spectrum (analyzer S2 ): (1) analysis of frequency spectrum in a wide range and (2) possibility to change (scan) frequencies. 3. Simple devices for analysis and signal processing (S3 ): (1) analysis of frequency spectrum in a wide range, (2) possibility to change (scan) frequencies, and (3) frequency spectrum processing (ﬁltering, etc.). 4. Simple system for analysis and signal processing (S4 ): (1) analysis of frequency spectrum in a wide range, (2) possibility to change (scan) frequencies, (3) frequency spectrum processing (ﬁltering, etc.), and (4) usage of signal and spectrum analysis results in applied problems. 5. Simple system for digital analysis and signal processing (with computer) (S5 ): (1) analysis of frequency spectrum in a wide range, (2) possibility to change (scan) frequencies, (3) frequency spectrum digital processing (ﬁltering, etc.), and (4) usage of signal and spectrum analysis results in applied problems. 6. System for digital analysis and signal processing (with special computer(s)) (S6 ): (1) analysis of frequency spectrum in a wide range, (2) possibility to change (scan) frequencies, (3) frequency spectrum processing (ﬁltering, etc.), and (4) usage of signal and spectrum analysis results in applied problems. The structures of system generations examined are as follows: Generation 1: 1. Device S1 . 1.1 Input part A: A1 (conductor). 1.2 Resonance part B: B1 (mechanical contour), B2 (electric contour), B3 (multi-resonance system). 1.3 Visualization part C: C1 (reed subsystem), C2 (read subsystem and scale). Generation 2: 1. Spectrum analyzer S2 . 1.1 Input part A: A2 (cable or waveguide). 1.2 Heterodyne part B : 1.2.1 Heterodyne D: 1.2.1.1 Generator G: G1 (tuned circuit), G2 (klystron). 1.2.1.2 Multiplier H: H1 (nonlinear element – diode). 1.2.2 Resonator E: E1 (electric contour), E2 (cavity resonator), E3 (mechanical resonator). 1.2.3 Detector F : F1 (diode). 1.3 Visualization part C: C3 (visualization device), C4 (monitor). Generation 3: 1. Simple device for analysis and signal processing S3 . 1.1 Input part A: A2 (cable or waveguide). 1.2 Heterodyne part B :

5 System Development and Evolution

73

1.2.1 Heterodyne D: 1.2.1.1 Generator G: G1 (tuned circuit), G2 (klystron). 1.2.1.2 Multiplier H: H1 (nonlinear element – diode). 1.2.2 Resonator E: E1 (electric contour), E2 (cavity resonator), E3 (mechanical resonator). 1.2.3 Detector F : F1 (diode). 1.3 Processing part I: I1 (correlation analysis), I2 (detection of signal in noise). 1.4 Visualization part C: C3 (visualization device), C4 (monitor). Generation 4: 1. System for analysis and signal processing S4 . 1.1 Input part A: A2 (cable or waveguide). 1.2 Magistral (interface) part M : M1 (magistral 1), M2 (magistral 2), M3 (magistral 3), M4 (magistral 4). 1.3 Processing part (analog) I . 1.4 Visualization part C: C4 (monitor). Generation 5: 1. System for digital analysis and signal processing with computer S5 . 1.1 Input part A: A2 (cable or waveguide). 1.2 Magistral (interface) part M : M5 (standard magistral). 1.3 Processing part (digital) as computer I . 1.4 Visualization part C: C4 (monitor). Generation 6: 1. System for digital analysis and signal processing with special computer S6 . 1.1 Input part A: A2 (cable or waveguide). 1.2 Magistral (interface) part M : M5 (standard magistral). 1.3 Processing part (digital) as computer (with special processor) I . 1.3.1 Computer J: J1 (basic computer). 1.3.2 Special computer K: K1 (one-processor computer), K2 (multiple-processor computer). 1.4 Visualization part C: C5 (special monitor as work station), C6 (multiple-monitor subsystem). It is possible to reveal evolution phases for the above-mentioned generations as follows: Phase 1. S1 ⇒ S2 : O1 : A1 → A2 , O1 : {C1 , C2 } → {C3 , C4 }, O6 : B → B . Phase 2. S2 ⇒ S3 : O2 : C3 , O8 : I. Phase 3. S3 ⇒ S4 : O8 : M , O9 : {B , I} → I . Phase 4. S4 ⇒ S5 : O5 : {M1 , ...} → M5 , O6 : I → I . Phase 5. S5 ⇒ S6 : O3 : C5 , C6 , O6 : I → I . Figure 5.6 illustrates a chain-like macro-evolution process for the example above of signal processing [513].

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Composite Systems Decisions

System for

N digital signal processing + Computer System for 1 analog signal S N PP ... q P processing + Magistral (interface part) Device for 1 analog signal S N PP ... q P processing + Processing part Spectrum 1 analysis S N PP ... q P + Heterodyne device part + Visualization Frequency 1 N measurement PP ... q P device S S5

4

3

2

1

Figure 5.6 Macro-evolution process

5.9 Summary Our combinatorial approach to modeling system development/evolution is described in this chapter. It is reasonable to list the following issues: 1. A special engineering experience is now accumulated in the design and utilization of many engineering systems (manufacturing, aerospace, computers, measurement, etc.). Usually, the experience is based on several (e.g., four or ﬁve) series generations of the systems. Thus, we face the problems of system improvement and ways to the next system generations. 2. The description of system evolution/development leads to the following: (a) special engineering spaces [155, 765, 816] and (b) modeling as graphdynamics [17, 664]. 3. The usage of combinatorial models for the analysis, representation, design, transformation, and forecasting of composite systems can be very useful for non-engineering domains (e.g., biology, organizational science). 4. It is reasonable to point out the signiﬁcance of the above-mentioned problems for contemporary educational processes [499]. Thus, it is possible to examine a special combinatorial ABC for evolution/development of composite systems. 5. The combinatorial representations of system evolution processes can be considered as useful frameworks for acquisition of expert knowledge.

6 Conﬁguration and Multi-product Systems

6.1 Conﬁguration Conﬁguration can be deﬁned as the following parts of a system [49, 193, 352, 497, 573, 707, 771, 914]: 1. System components and DAs (instances or system component types) for each system component. 2. System architecture. 3. Interaction of the system components (and corresponding DAs). Evidently, this viewpoint is the same for many kinds of systems: products, processes, manufacturing systems, etc. Clearly, our composite system involves the following: (a) system hierarchical model (i.e., a system architecture), (b) design alternatives for each system component (DAs), and (c) interconnections between DAs. This approach corresponds to the above-mentioned deﬁnition of conﬁguration. System conﬁguration can be considered for products, for complex systems (including product families), and for processes [110, 138, 157, 174, 264, 296, 316, 352, 416, 445, 541, 556, 707, 726, 801, 879]. A signiﬁcant problem consists in system conﬁguration analysis and requires special conﬁguration analysis tools. Conﬁguration management has been studied many years [177, 178, 246, 247, 425, 574]. Mainly, this direction is oriented to software systems and is based on four models of system versions for software conﬁguration management [178, 246, 247]: (1) check-out/check-in model (component versions are transferred individually between repository and workspace); (2) composition model (version selection and combination of a composite product: product ﬁrst); (3) long transaction model (version ﬁrst); and (4) change set model (a conﬁguration is described in terms of change sets). In recent decades, the basic trend in technological processes consists in reconﬁgurable systems: (a) reconﬁgurable manufacturing systems (e.g. [371, 564, 839, 897]), including reconﬁguring intelligent holonic systems [265]; (b) self-reconﬁguring robot systems (e.g., [595, 704]); (c) reconﬁgurable computing systems (e.g. [95, 174, 479]).

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Composite Systems Decisions

An optimal reconﬁguration strategy for a degradable multimodule computing system is investigated in [479], including (i) time of the system reconﬁguration and (ii) target system conﬁguration.

6.2 Product Family The basic issues in contemporary modular design are the following (e.g. [137, 213, 380, 388, 445, 568, 751]): (a) modeling of products, product platforms, product variants, product families, and product portfolios; (b) product platform development; (c) architectural issues of product family; (d) knowledge management in platform product development; and (e) product platform customization measurement of the various properties. It is reasonable to point out an important recent trend [433, 445, 722]: From

portfolio thinking

To

platform thinking.

M.S. Sawhney has described the following kinds of platforms [722]: 1. product platform, 2. brand platform, 3. business process platform, 4. customer platform (target markets), and 5. global platform (i.e., geographical markets). Platform thinking provides the following [722]: (1) speed; (2) coherence; (3) referenceability; and (4) option value. The basic methodological chain consists in the following [213, 465, 568, 717, 718, 720]: building blocks (modules) =⇒ product platforms =⇒ product families. In [200], an integrated approach is described for the concurrent design of the following: (i) product family and (ii) its assembly system. Data-miningbased methodology for the design of product families is described in [10]. Generally, three problems can be examined: (1) design of a product set as the basic design (i.e., orientation to several composite decisions); (2) special design of multi-product systems with selection of basic elements (with common parts) for the systems; and (3) redesign of product sets (e.g. [497, 752]). In the case of common modules of several products (problem 2 above), it is reasonable to examine the following two axes for analysis of our design process: 1. design of: (i) a product; (ii) a multi-product system (product family); and (iii) common module set for a multi-product system. 2. design of a trajectory for: (i) a product; (ii) a multi-product system; (iii) a common module set for a multi-product system. Commonality measurements involve two parts [173, 404]: (i) the component part commonality and (ii) the process commonality. Some versions of the models with component commonality have been described in, for example, in [55, 291, 292, 581]. Note, that the problem can be approximately solved on the basis of the following combinatorial optimization problems: (i) covering problem, (ii) minimal Steiner tree problem. Recent references are the following:

6 Conﬁguration and Multi-product Systems

77

(i) product platform systems [213, 218, 219, 316, 317, 455, 553, 567, 568, 624, 690, 720, 763, 897]; and (ii) modular architecture [8, 192, 387, 464, 465, 497, 550, 719, 792, 901].

6.3 Multi-product System: Common Modules 6.3.1 Preliminaries In this section, combinatorial synthesis of multi-product systems is examined on the basis of morphological approach [49, 409, 497, 914]. We consider a composite (modular) product as a set of interconnected parts/modules [497]. A multi-product system is examined as a set of the modular products with some common module(s). The design of the multi-product system can be based on the following two solving strategies: 1. A traditional (basic) strategy: (i) independent design of each product; (ii) design of the multi-product system as integration of the products (i.e., by the selection the certain common module). 2. Design of the multi-product system under constraints of modularity (i.e., concurrent design of all system products). Here, an extension of HMMD is described. The following design problems are considered: (a) a composite system/product; (b) two-level hierarchical systems: (i) two product with a common module, with a set of common modules; (ii) several products with a common module, with a set of common modules); and (c) multi-level hierarchical systems. In addition, allocation of modularity into several product is described too. 6.3.2 Two-level Hierarchy Two Products Here step-by-step, we consider the following two situations: (a) two product system with one common module; (b) two product system with several common modules. These design problems are reduced to our basic morphological clique problem. First, let us examine the most simple case for two-product system with one common module (Figure 6.1, an example, priorities of DAs are shown in parentheses). Structural descriptions of the corresponding design are depicted in Figure 6.2 and Figure 6.3 (an example).

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Composite Systems Decisions

KDS = P P = X Y Z B C K P = Z B C

KP =X Y Z

P1 = Z1 B3 C3 P2 = Z1 B1 C2

P1 = X1 Y4 Z3 P2 = X1 Y1 Z2 Y Z AX A A HAX1 (3) HAY1 (3) AHZ1 (1) HAX2 (1) HAY2 (1) AHZ2 (1) HAX3 (1) HAY3 (2) AHZ3 (2) HAY4 (3) AHZ4 (3)

B

A C HAB1 (3) AHB2 (1) HAB3 (2)

A AHC1 (1) AHC2 (1) AHC3 (2)

Figure 6.1 Two-product system with one common module

IHX

L

HH B Y HH Z P P B I H H HH C H HHL I

Figure 6.2 Graph of two-product system with common module B1 B

X X 1 X2

Z

B2

X3

Z2

Z1

B3

Y1

Z3

C1

Y2

Z4

C2

Y3

C3

Y4

C

Y Figure 6.3 Composition of two-product system with common module An evident (basic) design strategy (Figures 6.4 and 6.5) consists of the following two series steps: 1. design of each product; 2. selection of the

6 Conﬁguration and Multi-product Systems

79

best common module. The compatibility estimates for products P and P are contained in Tables 6.1 and 6.2. Table 6.1 Compatibility of DAs (P ) Y1 Y2 Y3 Y4 Z1 Z2 Z3 Z4 X1 X2 X3 Y1 Y2 Y3 Y4

2 2 2

1 3 2

1 3 1

2 2 2

1 1 3 1 3 1 1

1 0 0 2 1 1 2

2 2 1 2 3 2 2

2 2 2 2 2 2 2

Table 6.2 Compatibility of DAs (P ) B1 B2 B3 C4 C1 C2 Z1 Z2 Z3 Z4 B1 B2 B3

2 1 3 2

0 3 2 2

1 1 3 2

0 0 3 2 2 3 1

1 3 1 2 2 2 1

2 1 3 2 2 2 2

The resultant composite solutions are (Figure 6.5): (a) P = X3 Y2 Z1 , N (P ) = (2; 3, 0, 0); (b) P = Z2 B2 C2 , N (P ) = (2; 3, 0, 0). As a result, we can analyze the common module for a two-product system and get two admissible solutions as follows (Figure 6.5): (i) S 1 = X3 Y2 Z3 B2 C2 , N (S 1 ) = (1; 4, 1, 0); (ii) S 2 = X3 Y2 Z4 B2 C2 , N (S 2 ) = (2; 4, 0, 1). On the other hand, it is reasonable to consider another (direct) design strategy on the basis of the analysis of a ﬁve-component system: {X, Y, Z, B, C}. This strategy can lead to the better result (Figure 6.6): S = X2 Y2 Z3 B2 C1 , N (S) = (2; 4, 1, 0), N (S) N (S 1 ) and N (S) N (S 2 ). Generally, the following simple lemma is right: Lemma 6.1. N (S) N (S) ∀S, ∀S, where S is a solution of the direct strategy, S is a solution of the basic strategy. Proof. A search space of the basic strategy is a subspace of a search space of the direct strategy.

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Composite Systems Decisions

Coordination (selection) of common module for system part Z 6

6

Design of product P

Design of product P

Figure 6.4 Basic design strategy

Z Z X Y ZZ B C I @ @ Z Z B 1

3

2

2

2

3

2

4

X3 Y2

2

2

1

Product P N (P ) = (2; 3, 0, 0)

C2

Product P N (P ) = (2; 3, 0, 0)

Figure 6.5 Example for basic strategy

S The ideal S

S

S

S

S

S

N (S S)S 1

w=1

S

S N (S) S S 2 N (S ) w=2

point S S S S S

w=3

Figure 6.6 Discrete space of system excellence for N (S 1 ), N (S 2 ), N (S)

Two products with a set of common modules are now examined. Figure 6.7 illustrates a two-product system with two common modules (an example,

6 Conﬁguration and Multi-product Systems

81

priorities of DAs are shown in parentheses). Figure 6.8 depicts the general system graph and Figure 6.9 depicts an example of the composition process for a resultant system: P = X1 Y2 Z3 , P = Y2 Z3 B1 C2 ; common modules Y2 and Z3 .

KDS = P P = X Y Z B C K P = Y Z B C

KP =X Y Z

P1 = Y1 Z1 B3 C3 P2 = Y2 Z1 B1 C2

P1 = X1 Y4 Z3 P2 = X1 Y1 Z2

Y Z AX A A X Y (3) (3) 1 1 HA HA AHZ1 (1) HAX2 (1) HAY2 (1) AHZ2 (1) HAX3 (1) HAY3 (2) AHZ3 (2) HAY4 (3) AHZ4 (3)

B

C A A B (3) 1 HA AHC1 (1) AHB2 (1) AHC2 (1) HAB3 (2) AHC3 (2)

Figure 6.7 Two-product system with two common modules

P

L B I

@ B Y@ P @ I X H @ HH @C HH Z HB @L I

Figure 6.8 Graph of two-product system with two common modules

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Composite Systems Decisions

Y

1 Y Y2

B1 B

X

Y3

B2

X1

Y4

B3

Z1

C1

Z

C2

X2 X3

2 Z3

C3 C

Z4 Z Figure 6.9 Composition of two-product system with two common modules

D K S = P P P = U V X Y Z B C KP =X Y Z

K P = U V P1 P2

= U1 V3 = U2 V1

A A HAU1 (2) HAV1 (2) HAU2 (1) HAV2 (1) HAV3 (3) U

V

P 1 = X 1 Y4 Z 3 P2 = X1 Y1 Z2 @

@

A @Y A HAX1 (3) HAY1 (3) HAX2 (1) AHY2 (1) AHX3 (1) HAY3 (2) AHY4 (3) X

Z

A HAZ1 (1) HAZ2 (1) HAZ3 (2) HAZ4 (3)

K P = Z B C

P1 = Z1 B3 C3 P2 = Z1 B1 C2

B

C A A HAB1 (3) HAC1 (1) AHB2 (1) HAC2 (1) HAB3 (2) HAC3 (2)

Figure 6.10 Three-product system with one common module

Several Products Here, the design of a multiple product systems is examined. Also, the design process is reduced to our basic HMMD framework. Now we examine a three-product system with one common module (Figure 6.10, an example, priorities of DAs are shown in parentheses). Structural descriptions of the corresponding design are depicted in Figure 6.11 and Figure 6.12 (an example). The design strategy is based on the three-product system (with a common module).

L L EIB L L I I

6 Conﬁguration and Multi-product Systems

P

P

AA UA

83

V

B A P Y A HH A HH HH C A A X A Z A A A

Figure 6.11 Graph of three-product system with common module

X X 1

U U 1 U2

Z1 Z

X2

Z2

X3

Z3

@ @

V1 V2 V3 V

Z4

B1 B

Y

B2

Y1

B3

Y2

Y3

C1

Y4

C2 C3 C

Figure 6.12 Composition of three-product system with common module In the case of several common modules, two basic situations exist as follows: (a) the same set of common modules (Figures 6.13, 6.14, 6.15, and 6.16); (b) diﬀerent common modules (Figures 6.17, 6.18, 6.19, and 6.20). In Figures 6.13 and 6.17 priorities of DAs are shown in parentheses. The solving strategy is about the same one (as in previous sections).

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Composite Systems Decisions

KDS = P P P = U V X Y Z B P1 P2

K P = Y Z B

KP =X Y Z

K P = U V = U1 V3 = U2 V1

P1 = Y2 Z1 B3 P2 = Y1 Z1 B1

P 1 = X 1 Y4 Z 3 P 2 = X 1 Y1 Z 2 @

U

A HAU1 (2) HAU2 (1)

V

A HAV1 (2) AHV2 (1) HAV3 (3)

@ @Y @Z @A @A A X Y (3) (3) HA 1 HA 1 AHZ1 (1) X Y (1) (1) HA 2 HA 2 AHZ2 (1) Y X (1) (2) 3 3 HA HA AHZ3 (2) HAY4 (3) AHZ4 (3) X

B

A HAB1 (3) HAB2 (1) HAB3 (2)

Figure 6.13 Three-product system with two common modules

X L P

B O

@PPP P PP P @ @B IB I PPPE Z @ Y @ @ @ @ P @I V U I

Figure 6.14 Graph of three-product system with two common modules

6.3.3 Structural Models Here, we consider structural models the composite systems with common modules. The basic model of a composite system while taking into account interconnection of system parts corresponds to our morphological clique or a clique (at simplest level) [497]. In the case of a multi-product system, the simplest structural model leads to a simple solving scheme. Figures 6.21 and 6.22 depict some basic examples of the structural models. Concurrently, the models can be useful for system analysis. In the general case, the models do not correspond to planar graphs. In fact, each product corresponds to a morphological clique (or clique for a generalized structural model) and the cliques have product parts (i.e., common vertices as common modules) or subcliques (in the case of several common modules). Now it is reasonable to consider a classiﬁcation formulae for a multiproduct system as follows: < l|n|k|t >, where n is the number of products, l

6 Conﬁguration and Multi-product Systems

85

is the number of hierarchical levels, k is the number of common modules, t is the type of commonality (symbol corresponds to the situation with the same set of common modules in products). Thus, we get the following descriptions for our examples: (a) < 3|2|1| > (Figure 6.1), (b) < 3|2|2| > (Figure 6.7), (c) < 3|3|1| > (Figure 6.10), (d) < 3|3|2| > (Figure 6.13), (e) < 3|3|3| > (Figure 6.17), and (f ) < 4|2|2| > (Figure 6.23). X1

B1

X2

B2

X3 X

Y1

B

Z1

Z2

Y2

@ @

B3

Z

Y @ @

Y3

Z3

Y4

Z4 V1

U1

V2

U2

V3 V

U

Figure 6.15 Composition of three-product system with two common modules

X

Y Z B

P U

V

P

P

Figure 6.16 Structural intersection of products

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Composite Systems Decisions

KDS = P P P = U V X Y Z H C K P = U V X Y P1 P2

= U1 V3 X1 Y2 = U2 V1 X1 Y2

KP =X Y Z H P1 = X1 Y4 Z3 H1 P2 = X1 Y1 Z2 H1

K P = Y Z C

P1 = Y1 Z4 C3 P2 = Y1 Z1 C2

@

U

A HAU1 (2) HAU2 (1)

V

@ @ X @Y H Z @A @A A A A X Y Z (3) (3) (1) V (2) HAH1 (3) HA 1 HA 1 AH 1 HA 1 X Y Z (1) (1) (1) (1) V AHH2 (1) HA 2 HA 2 AH 2 AH 2 Y Z X (1) (2) (2) V (3) 3 3 3 3 HAH3 (2) HA HA AH HA HAY4 (3) AHZ4 (3)

C

A AHC1 (1) AHC2 (1) AHC3 (2)

Figure 6.17 Three-product system with diﬀerence in common module set

P IV A A C A O A A Y U AB I E I A A P A A A A A A A A I B AE IB Z A X A A A A A AB I H P Figure 6.18 Graph of three-product system with diﬀerence in common module set

6.3.4 Complex Design Problems Multi-level Hierarchy In the case of a multi-level hierarchical system, the design situation is more complicated. At the same time, it is possible to use a series bottom-up design framework that involves at each hierarchical level one of the design problems

6 Conﬁguration and Multi-product Systems

87

considered in previous section. Figure 6.13 illustrates a two-product system with possible modularity at diﬀerent levels of system hierarchy. In our case, we start at the bottom level of the system hierarchy and examine (level by level) corresponding design synthesis problems while taking into account the modularity: Phase 1. The design of the two-product system consisting of products P 1 and P 2 , (i.e., we consider the following composite system: X, Y, U, V ). Phase 2. The design of the two-product systems consisting of products S and S (i.e., the system examined is: A, B, C, P 1 , C, D, P 2 , E).

V V V V 3 2 1

C1 C2 C3

@ @ @

U

Y

@ @

@Y

U1

@ U2 @ @

C

Y1 2

Y3

@ @

Y4

@ X X X X 3 2 1

Z Z 1

2

Z Z3 Z4

H1 H2 H

H3

Figure 6.19 Composition of three-product system with diﬀerent common modules

P

P

U

C

V

P X Y H Z

Figure 6.20 Structural intersection of products

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Composite Systems Decisions

P2 P1 H H H@ AH @ @ AA@ HH A H H @ @ H H @ @ HA HA (a) Two products/one module P1

P2

A@ A@ @ @ H H A A A AH AAH H A A H @ @A, @ @A, (b) Two products/two modules Figure 6.21 Structural models

P4 P3 P2 P1 H H H H AH @ AH @ AH @ AH @ @ @ @ @ A H A H A H A H H H H H @ @ H @ H @ H H HA @ @ HA HA @ @ HA (a) Chain-like model A @ A@ 3 A H A A H 2 A H A @ A@A, @ @ H @ 4 A @ A H A H 1 A A @ A@ @ 6 A @A,H @ A @ HH AA 5 A @ @ ,H A@ @A @ A @ H A A H 7 A @ @A, (b) Tree-like model

Figure 6.22 Structural models

6 Conﬁguration and Multi-product Systems

E IB S

B I S

A B

I

H A1 A HAA2 A H A3

I H B1 A A H B2 H B3 A A H B4

89

= S S

B I S

= A B C P1 C

= C D P2 E

C D

IP 2 = Y U V I I IP 1 = X Y I

HAC1 HAD1 A H C1 HAC2 A H D2 A H C2 Y U V HAC3 HAD3 X Y A H C3 A A A A A

A H D4

HAY1 HAU1 A H V1 HAX1 HAY1 HAY2 A H U2 A H V2 HAX2 HAY2 A H Y3 HAU3 A H V3 A H X3 HAY3 A H Y4 HAY4

E

I

HAE1 HAE2

Figure 6.23 Two-product multilevel system

Allocation of Commonality Figure 6.24 illustrates allocation of three kinds of modularity (M1 , M3 , M3 ) into three products P1 , P2 , and P3 . This problem corresponds to a multi-target multi-track assignment (e.g. [68, 88, 503]). First, the problem of one-kind modularity allocation can be described. In the case of two products, we get the well-known basic assignment problem or matching for two sets. In the case of several sets (i.e., several products), the problem is more complicated and corresponds to multi-target multi-sensor assignment problem for the only one common target (e.g. [68]). But real situations require the investigation of several kinds of modularity. The following framework can be considered: Phase 1. Extraction of the most important modularity kinds. This preliminary design stage is oriented to the extraction of the possible modularity kinds (e.g., through a selection of the most important modularity kinds from a set of initial kinds). Phase 2. Revelation of the possible candidates for each kind of modularity (in each product). Phase 3. Allocation of modularity kinds. Phase 4. Analysis of the results (and feedback to previous phases if it is reasonable). Figure 6.25 illustrates phase 3 above. Now let us consider the corresponding optimization problem. The traditional way consists of the formulation of a one-objective integer programming model. Our designation is as follows: P = {P1 , ..., Pi , ..., Pn } is the set of products, M = {M1 , ..., Mj , ..., Mk } is the set of possible common modules, C j = {cji1 , ..., cjil , ..., cjili } is the set of candidates for the change into common module Mj in parts/components

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Composite Systems Decisions

of product Pi (here li corresponds to the number of candidates in product Mj ), s(cjil ) is the cost of the change for product part/component cjil into common module Mj , e(cjil ) is the proﬁt (eﬀectiveness) of the change for product part/component cjil into common module Mj . The model is: li n k

max

e(cji,l ) xi,j,l

i=1 j=1 l=1 li n k

s.t.

s(cjil ) xi,j,l ≤ S

i=1 j=1 l=1 li k

s(cjil ) xi,j,l ≤ Si ; i = 1, ..., n

j=1 l=1 li k

xi,j,l ≤ 1; xi,j,l ∈ {0, 1}; i = 1, ..., n

j=1 l=1

where S is the total resource constraint for the changes and Si is the total resource constraint for the changes in product Pi . In the real situation, the problem has to be formulated as a multi-objective one, because it is necessary to examine a multi-attribute description of the required resources and a multicriteria description of the resultant eﬀectiveness. On the other hand, it is reasonable here to use a morphological clique problem oriented to allocation [497], or allocation on binary relations [500]. M1

M2

M3

@ @

@ @

P

m1

m2

m1

@

m2

A A

m3

m2

P3

AA

P2

@ @

1

Figure 6.24 Allocation of modularity M1 , M2 , M3

m3

6 Conﬁguration and Multi-product Systems

91

Product P 1

M1

Product P 2

M2

M3

Product P 3

Candidate for M3 Candidate for M2 Candidate for M1

Candidate for M2

Figure 6.25 Allocation of modularity as multi-assignment

6.4 Summary In this chapter we have discussed system conﬁgurations (deﬁnition, design and management problems), product families and platforms, including a methodological chain as modules–product platforms–product families, kinds of product platforms, etc. The ﬁnal part of the chapter describes application of our HMMD to several design problems for selection of common modules in multiproduct systems. It is reasonable to point out the following two research directions: 1. Design of special tools for modeling, visualization, and analysis of the objects considered: system conﬁgurations, product platforms, product families, (including multi-product systems with common modules). 2. Design of special repositories for accumulation of real examples of system conﬁgurations, product platforms, product families.

Part III

Applied Systems Decisions

7 Synthesis of Composite Packaged Software

7.1 Preliminaries This chapter 1 describes the usage of HMMD [494, 497] for system synthesis (integration) as a combinatorial hierarchical selection and composition design of a complex software package consisting of multiple components [508]. Our approach is illustrated here on the basis of a numerical example: synthesis of composite packaged software. We consider the following problems: integration of the system, improvement of obtained design decisions, and multistage design. Several perspectives of software development processes are presented in (e.g. [69, 70]). Computer aided support environments (CASE) are often used for software development (e.g. [774]). These integrated environments are deﬁned as collections of special software and hardware tools including program composition techniques for automatic software generation. However, in this case, components are, in the main, operators or program parts. Further, it is reasonable to examine three system levels of software engineering as follows: 1. Bottom-level coding (coding software blocks; coding complex software). 2. Intermediate-level modular design (modular design of composite software, modular design of user interfaces). 3. High-level design (joint design of a system consisting of software and hardware components; strategic planning of product life cycle). In our opinion, the signiﬁcance of levels 2 and 3 increases [43, 70, 80, 529, 646, 647, 669]. Contemporary software development is often based on combining many software systems and packages. For example, we face this situation when modular programming is used for software development (i.e., modular system architecture) [80, 529, 607, 646, 647]. Many modern software packages have standard interfaces for the connection with other software packages. Thus a system developer can combine selected packaged software components into a target composition. It is reasonable to point out the possibility for the 1

Copyright IEEE. Reprinted, with permission, from M.Sh. Levin, Modular System Synthesis: Example for Composite Packaged Software. IEEE Transactions on Systems, Man, and Cybernetics, Part C, 35(4), 544–553, 2005 (with minor amendments).

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Composite Systems Decisions

end user to integrate his/her software environment on the basis of standard components too. Moreover, this process is an integration of systems, including both software and hardware components [669]. Special new CASE tools are developed for coordinating the complex projects [885]. Issues of interconnectibility of software components are crucial ones in the design of hybrid systems [369, 529, 809], concurrent engineering environments (e.g. [674]), and design research projects (e.g. [206, 593]). Note that the combinatorial approach is very important for the design of a composite applied software environment on the basis of well-known software packages. In recent years, the multicriteria selection problem has been played a central role in design processes [120, 236, 409, 460, 487]. Various approaches have been used for software selection, for example: (a) criteria like cost/beneﬁt [14, 64, 755]; (b) empirical models [323]; (c) mathematical models [754]; (d) optimization knapsack-type models for reliability of modular software systems [44, 80]; and (e) multicriteria methodology [475] including Analytic Hierarchy Process AHP [64, 242, 730]. Note also the selection and implementation of packaged software for small business are analyzed in [401]. The signiﬁcance of software quality, including both product and process quality, is pointed out in [69]. The chapter involves a brief description of software development and several numerical design examples.

7.2 Approaches to Software Development Various well-known software development approaches have been used including: structured and system approaches, the Jackson approach to software development (JSD), object-oriented programming, component-based software development, and soft systems methodology [70, 83, 109, 129, 205, 646, 723, 734, 773, 888, 899]. Many papers are oriented to the systematic comparison of software design methods [132, 396, 778]. Typical phases in the complete software engineering life cycle are described in [70]. Software development process control is investigated in [43]. Some papers included speciﬁc paradigm for software development, e.g., stages of software storming [412]; steps of an iterative design for DSSs [781]; a knowledge-based approach to automate a software design method for concurrent systems is described in [578]; and phases of expert system development [367]. Note a survey on automating software development is contained in [578]. In [688], factors of implementing issues for system development methodology on the basis of an analysis of 61 companies are examined. A review of concepts for system development methods is contained in [396]. Aspects of software adaptability are described in [243]. A social analysis of software development paradigms on the basis of three approaches (traditional, iterative, and component-based) is described in [691]. Planning and management of software evolution processes are examined in (e.g. [146, 149, 480]). The main concepts of software development are based on the following two approaches: (i) hierarchical design (e.g. [21, 108, 129, 888, 899, 909]); and

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97

(ii) prototyping (e.g. [116]). Here the ﬁrst approach is applied. Here we assume the use of modular programming when module versions are developed and assessed independently, and there are some independently evaluated interfaces between module versions (design alternatives DAs) for diﬀerent software functions. Note version models for software conﬁguration management are examined many years (e.g. [178]), including several types of basic models. Here our approach corresponds to the composition model.

7.3 Criteria for Evaluation of Software Many authors have investigated criteria for the evaluation of software [43, 86, 93, 118, 242, 257, 527, 656, 676, 729, 836, 853, 899, 907, 909]. The evaluating concepts for software quality include the following (e.g. [93, 678]): (1) quality objectives; (2) quality factors; (3) criteria; (4) evaluation process; (5) measures; and (6) aggregation measures. Speciﬁc levels for evaluation are proposed in [676]: objectives, factors, and subfactors. A structured methodology for software evaluation on the basis of AHP is used in [476]. In this approach, some organizational aspects are taken into account and the following levels are investigated: manager, personnel, programs, and modules. Software quality engineering which involves quality measures for all design stages (requirements; design; coding; testing; and maintenance) is considered in [133]. DSSs and their key characteristics are described in [781]. The number of known software metrics exceeds 200 (e.g. [252, 913]). In [656], software quality is examined as minimization of the number of faults or defects that exist during and even after software development. Metrics for in-process tracking and measurement have been examined in [420]. In our case, it is necessary to design a special hierarchical criteria space. Note a similar approach is the basic one in requirements engineering [21].

7.4 Assessment of Interconnection A measure of interconnection (compatibility) among modules in a program structure (coupling) depends on the interfaces between modules [663]. Software systems contain several types of interrelation among components, including: data, control, and sequencing [736]. Evaluation processes of the interconnection can be based on the following factors [529, 669, 736, 909]: (1) interface between software components; (2) data format; and (3) common elements (i.e., program modules, element of interfaces). In [529], three levels of the hierarchy for hybrid systems are considered as follows: (a) loose coupling (communication via data ﬁles and parameters passing); (b) tight coupling (direct communication); and (c) fully integrated. An ordinal scale (0, ..., 9) for modules coupling is introduced in [909] (p. 114). Our speciﬁcation of IC weights in HMMD is based on the following two approaches: (a) expert judgment and (b) multicriteria ranking the basic estimates of IC parameters above.

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Composite Systems Decisions

7.5 Example of Modular Design 7.5.1 Model of Composite Applied Software Our example has a hypothetical character. We propose an integration of a composite IBM PC software environment for the end user consisting of several well-known packages. The following tree-like structure of composite software is analyzed (Figure 7.1): 1. Subsystem A = M P : Data Base Management System DBMS (M ) + Integrated Software IP (P ). 2. Subsystem B = D H L: Decision Support System DSS (D) + Hypertext System HS (H) + Language for Artiﬁcial Intelligence LAI (L). It is reasonable to point out the following sources to describe examined speciﬁc software packages: (a) DBMSs (M ) (e.g. [631, 651, 652, 836]); (b) IPs (P ) (e.g. [642, 836, 907]); (c) DSSs (D) (e.g. [118, 313, 492, 836]); (d) HSs (H) (e.g. [18, 176, 492]); and (e) LAI (L) (e.g. [170, 481]). 7.5.2 Hierarchy of Criteria Criteria and estimates of software are taken mainly from several journals (PC World, Microcomputers, InfoWorld, Expert Systems Users, etc.). We use the following criteria: 1. DBMSs: (1) tools of development (0 corresponds to No, 1 corresponds to Yes, and 2 corresponds to Excellent; further ordinal scale are similar); (2) speed (0, 1, 2); (3) report development (0, 1, 2); (4) adaptability of interface (0, 1); (5) cost (USD); and (6) query building environment (0, 1, 2). 2. IPs: (1) graphics (0, 1, 2); (2) easy of use report (0, 1, 2); (3) database (0, 1); (4) telecommunication (0, 1, 2); (5) text processor (0, 1, 2); (6) adaptability of interface (0, 1); and (7) cost (USD). 3. DSSs: (1) user interface (1, 2); (2) dialog support (0, 1, 2); (3) training subsystem (0, 1); (4) models (0, 1, 2); (5) AI components (0, 1); (6) previous experience of use (0, 1); and (7) cost (USD). 4. HSs: (1) browsing (0, 1); (2) graphics (0, 1); (3) multiple windows mode (0, 1); (4) AI components (0, 1); (5) cost (USD); (6) previous experience (0, 1); and (7) range of use (0, 1, 2). 5. LAIs: (1) cost (USD); (2) previous experience of use (0, 1, 2); (3) range of users (0, 1); and (4) quality of service (0, 1, 2). Table 7.1 contains aggregative criteria for the subsystems (the ﬁrst index corresponds to the component, negative monotony is shown in parentheses).

7 Synthesis of Composite Packaged Software

NS

S =AB = A5 B4 S2 = A4 B3 S3 = A1 B1 S4 = A4 B2 S5 = A2 B2 1

= (M1 P4 ) (D3 H5 L2 ) = (M3 P4 ) (D5 H5 L3 ) = (M3 P1 ) (D1 H1 L2 ) = (M3 P4 ) (D2 H1 L2 ) = (M4 P1 ) (D2 H1 L2 )

Subsystem A = M P

KAA

1

2

A3 A4 A5 A6

HM

= M3 P1 (1) = M4 P1 (1) = M5 P3 (1) = M3 P4 (2) = M2 P4 (3) = M6 P4 (3)

H

99

Subsystem B = D H L B1 = D1 H1 L2 (1) B2 = D2 H1 L2 (1) B3 = D5 H5 L3 (2) B4 = D3 H5 L2 (3)

K

H

H

H

P D H L Hypertext Package DBMS Integrated DSS M1 (1) Package D1 (1) H1 (1) for AI P1 (1) L1 (1) M2 (1) D2 (2) H2 (1) M3 (1) P2 (2) D3 (2) H3 (1) L2 (1) M4 (2) P3 (2) D4 (3) H4 (2) L3 (2) M5 (2) P4 (2) D5 (4) H5 (2) L4 (2) M6 (3) P5 (2) D6 (4) H6 (2) L5 (3) M7 (3) P6 (3) H7 (2) L6 (3) M8 (4) P7 (3) H8 (3) L7 = L2 &L3 (1) M9 (4) Figure 7.1. Structure of system (priorities of DAs are shown in parentheses)

7.5.3 Comparison of Initial Alternatives for Components At this stage, the following operations for terminal vertices of the system model are executed: (1) generation of DAs for each leaf vertex; (2) assessment of DAs upon criteria; and (3) ranking the DAs upon criteria estimates. DAs for terminal vertices, and their estimates are shown in Tables 7.2, 7.3, 7.4, 7.5, and 7.6. Computed resultant ordinal priorities of DAs are presented in Figure 7.1. 7.5.4 Composing of Subsystem Alternatives Now let us examine the next hierarchical level and execute the following actions: (1) speciﬁcation of compatibility between DAs; (2) composition oﬀ composite DAs; (3) assessment of DAs upon criteria; and (4) ranking the DAs. Compatibility estimates of DAs are presented in Tables 7.7 and 7.8. DAs of subsystems A and B are shown in Table 7.9. Figure 7.2 depicts a concentric presentation of composite DAs B1 and B3 .

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Table 7.1 Aggregative criteria Criteria Fa1 Cost (−1) Fa2 Graphics Fa3 Ease of use Fa4 Telecommunication Fa5 Adaptability of interface Fa6 Text processor Fa7 Report development Fa8 Speed Fa9 Environment for query building Fb1 Cost (−1) Fb2 Range of use Fb3 AI components Fb4 Experience of use Fb5 Dialogue support

Table 7.2 Estimates of DAs DAs

Fm5 + Fp7 min(Fm3 , Fp1 ) max(Fm1 , Fp2 ) min(Fm2 , Fp4 ) min(Fm4 , Fp6 ) max(Fm3 , Fp5 ) max(Fm3 , Fp2 ) max(Fm2 , Fp3 ) Fm6 Fd7 + Fh5 + Fl1 min(Fh7 , Fl3 ) max(Fd5 , Fh4 ) Fd6 + Fh6 + Fl2 Fd2

Table 7.3 Estimates of DAs

Criteria 1 2 3 4

M1 M2 M3 M4 M5 M6 M7 M8 M9

Speciﬁcation

2 2 1 1 1 1 1 0 0

2 2 1 1 1 1 1 0 0

2 2 1 1 1 1 1 0 0

2 2 1 1 1 1 1 0 0

5

6

482 490 486 237 502 451 333 240 180

3 3 2 2 3 0 0 0 0

DAs

Criteria 1 2 3 4 5 6

P1 P2 P3 P4 P5 P6 P7

2 2 2 1 2 1 0

2 2 2 1 0 2 2

1 1 3 1 1 0 1

3 0 1 1 1 1 0

1 2 2 1 1 0 0

1 0 0 1 1 0 0

7 506 94 438 477 510 130 87

7.5.5 Composition and Analysis of System Alternatives Compatibility estimates between DAs of the subsystems are shown in Table 7.10. Table 7.11 contains composite DAs for the target system. This allows to assess the composite DAs of the target system whit respect to the criteria, and to compare. Further, one may analyze some bottlenecks and improvement actions (Table 7.12). In our example, all improvement actions correspond to the improvement of Pareto-eﬀective points. Note that the improvement of interconnection (A1 , B1 ) or (A2 , B2 ) from 2 to 5 allows to get the following two ideal decisions: A1 B1 and A2 B2 . Results of this analysis can be applied as initial information for redesign. Figure 7.3 depicts the discrete space of system excellence and Pareto-eﬀective decisions.

7 Synthesis of Composite Packaged Software

Table 7.4 Estimates of DAs DAs

Criteria 1

DAs

2 3 4

L1 1700 L2 3000 L3 2500 L4 5000 L5 2850 L6 13570 L7 = L2 &L3 5500

1 1 2 0 1 0 2

2 2 1 1 1 1 2

DAs

D1 D2 D3 D4 D5 D6

1 1 1 1 1 0 0 1

1 1 1 1 0 0 0 1

1 1 1 1 1 1 0 1

350 600 300 500 700 100 100 470

1 1 1 1 0 0

1 1 0 0 0 1

2 1 1 2 1 1

0 0 1 0 0 0

0 1 1 1 0 0 1 1

M1 M2 M3 M4 M5 M6 M7 M8 M9

2 2 1 0 1 1 1 1

0 0 2 3 0 0 0 0 0

0 0 2 0 0 0 0 0 2

2 1 1 0 4 0 0 0 1

3 1 3 0 0 5 0 0 0

0 0 0 0 0 0 0 0 0

Table 7.8 Compatibility D1 D2 D3 D4 D5 D6 L1 L2 L3 L4 L5 L6 L7 H1 H2 H3 H4 H5 H6 H7 H8 D1 D2 D3 D4 D5 D6

1 0 0 0 1 0 0 0

3 0 0 0 0 0 0 0

0 0 0 0 4 0 0 0

1 1 0 0 0 0

100 495 299 500 29 400

P1 P2 P3 P4 P5 P6 P7

5 6 7

1 1 1 0 1 0 0 1

1 1 2 1 1 1

7

Table 7.7 Compatibility

Criteria 1 2 3 4

Criteria 1 2 3 4 5 6

2 2 2 2 1 2 2

Table 7.6 Estimates of DAs

H1 H2 H3 H4 H5 H6 H7 H8

Table 7.5 Estimates of DAs

0 0 0 0 0 0 0 0

0 0 0 0 5 0 0 0

0 0 0 0 0 0 0 1

0 0 1 0 0 0 0 0 1 0 0 0 0 0

3 0 1 0 4 0 0 0 1 3 4 0 0 0

0 0 1 0 5 0 0 0 1 0 0 0 5 0

0 0 2 1 1 1 1 0 2 0 0 0 0 1

0 0 2 1 1 1 1 0 2 0 0 0 0 1

0 0 2 1 1 1 1 0 2 0 0 0 0 1

0 0 1 0 4 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

101

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Composite Systems Decisions

Table 7.9 DAs of subsystems DAs

Criteria 1

A1 A2 A3 A4 A5 A6 B1 B2 B3 B4

= M3 P 1 = M4 P 1 = M5 P 3 = M3 P 4 = M1 P 4 = M6 P 4 = D1 H1 L2 = D2 H1 L2 = D5 H5 L3 = D3 H5 L2

N

23456789

992 743 940 963 959 928 3450 3845 3229 3999

2 2 2 1 1 2 2 2 1 1

2 2 2 1 1 1 1 1 1 1

3 3 1 1 1 1 2 2 2 1

1 0 0 1 1 0 1 1 0 1

1 1 2 1 1 1

4 2 3 4 4 1

3 3 3 3 2 3

2 2 3 2 3 0

2; 2, 0, 0, 0 3; 1, 1, 0, 0 4; 0, 2, 0, 0 3; 1, 1, 0, 0 3; 1, 1, 0, 0 5; 0, 1, 1, 0 1; 3, 0, 0, 0 3; 2, 1, 0, 0 5; 0, 2, 0, 1 4; 1, 2, 0, 0

7.5.6 Redundancy of Alternatives Usually, redundancy of system components is examined for increasing the system reliability (e.g. [80, 818]). In our case (software), a system with redundancy may actually provide an improvement with respect to of usability because it implies the availability of alternative software packages. Let us examine a numerical example for subsystem B with the use of the following alternative (two-element redundancy) L7 = L2 &L3 . We consider the aggregative estimates with respect to the (1) sum, (2) maximum, and (3) minimum (Table 7.1) of element estimates. The compatibility estimate of L7 equals the minimum of corresponding estimates of the involved DAs (Table 7.8). The priority of L7 will be equal to 1. Finally, we get the composite decision as follows: D1 H5 L7 with N = (1; 1, 2, 0, 0). This decision is not an element of the Pareto-eﬀective set, but it can be examined as a point for the improvement (Table 7.12). Figure 7.4 depicts our composite decision with redundancy. H7 H6 H5 H4 H3 H2 H1

5 1 D6 D5 D4 D3 D2 D1 5

5 3 L1 L2 L3 L4 L5 L6

1

Figure 7.2 Concentric presentation of composite DAs

7 Synthesis of Composite Packaged Software

103

Table 7.10 Compatibility A1 A2 A3 A4 A5 A6 B1 B2 B3 B4

2 1 0 0

1 2 0 0

0 0 0 0

0 3 4 0

1 0 0 5

0 0 0 0

Table 7.11 DAs of system Composite DAs S1 S2 S3 S4 S5

= A5 B4 = A4 B3 = A1 B1 = A4 B2 = A2 B2

N

= (M1 P4 ) (D3 H5 L2 ) = (M3 P4 ) (D5 H5 L3 ) = (M3 P1 ) (D1 H1 L2 ) = (M3 P4 ) (D2 H1 L2 ) = (M4 P1 ) (D2 H1 L2 ) Ideal point S

N (S3 ), S N (S5 ) S S S S S w=2

S

S

S

S N (S4 )S S w=3

S

S

S

S

S

5; 0, 0, 2, 0 4; 0, 2, 0, 0 2; 2, 0, 0, 0 3; 1, 1, 0, 0 2; 2, 0, 0, 0

S N (S2 )S S w=4

S

S S N (S1 ) w=5

Figure 7.3 Space of system quality and Paretoeﬀective points

D1

H5 @ @

L L L7 3 2

Figure 7.4 Composite decision with redundancy

7.6 Example of Multistage Design Several versions of a multistage modular design on the basis of HMMD are described in [497, 504]. Note this approach diﬀers from traditional software

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evolution processes in (e.g. [146, 480]). Combinatorial evolution of composite systems on the basis of combinatorial system changes and HMMD is proposed in [505]. In this section, a three-stage modular design for subsystem B is examined. It is assumed that the compatibility estimates between DAs are improved (step-by-step) at each stage. The following two methods are applied: 1. Aggregation Method: An aggregation of the compatibility estimates and searching for a composite decision on the basis of the aggregated (average) estimates. 2. Trajectory Method: Two-level hierarchical solving process consisting of two phases as follows: 2.1 Solving the design problem (synthesis of composite subsystem B) at each stage. 2.2 Composing the composite decisions of the previous phase (for each stage) into a series composite decision (trajectory). We consider the following improvement of compatibility: (H1 , D1 ): 2 (stage 2), the aggregated compatibility estimate equals 2; (H1 , D2 ): 4 (stage 2), 5 (stage 3), the aggregated compatibility estimate equals 2; (H2 , D1 ): 3 (stage 2), 5 (stage 3), the aggregated compatibility estimate equals 3; (H5 , D3 ): 5 (stage 2), the aggregated compatibility estimate equals 5; (H5 , D5 ): 5 (stage 2), the aggregated compatibility estimate equals 5; (H1 , L2 ): 4 (stage 2), 5 (stage 3), the aggregated compatibility estimate equals 4; (H2 , L2 ): 2 (stage 2), the aggregated compatibility estimate equals 2; (H5 , L2 ): 5 (stage 2), the aggregated compatibility estimate equals 5; (D1 , L2 ): 2 (stage 2), 3 (stage 3), the aggregated compatibility estimate equals 2; (D2 , L2 ): 4 (stage 2), 5 (stage 3) the aggregated compatibility estimate equals 4; (D2 , L3 ): 3 (stage 2), 4 (stage 3), the aggregated compatibility estimate equals 3; (D3 , L2 ): 5 (stage 2), the aggregated compatibility estimate equals 5; and (D5 , L3 ): 5 (stage 2), the aggregated compatibility estimate equals 5; 7.6.1 Aggregation Method Here we solve the composition problem for the aggregated compatibility estimates. The resultant composite DAs are the following: (a) B1a = D3 H5 L2 , N (B1a ) = (5; 1, 2, 0, 0); (b) B2a = D1 H1 L2 , N (B2a ) = (2; 3, 0, 0, 0); and (c) B3a = D1 H2 L2 , N (B3a ) = (2; 3, 0, 0, 0). Thus the improvement with respect to interconnection leads to a new Pareto-eﬀective composite decision B3a .

7 Synthesis of Composite Packaged Software

105

Table 7.12 Bottlenecks and improvement actions Composite DAs

Bottlenecks DAs

A1 = M3 P1 A2 = M4 P1 A2 = M4 P1 A3 = M 5 P 3 A3 = M 5 P 3 A3 = M 5 P 3 A4 = M3 P4 A4 = M 3 P 4 A5 = M 1 P 4 A5 = M 1 P 4 A6 = M6 P4 A6 = M6 P4 B2 = D2 H1 L1 B3 = D5 H5 L3 B3 = D5 H5 L3 B4 = D3 H5 L2 B4 = D3 H5 L2 S1 = A5 B4 S1 = A5 B4 S2 = A4 B3 S2 = A4 B3 S2 = A4 B3 S3 = A1 B1 S4 = A4 B2 S4 = A4 B2 S5 = A2 B2 D1 H5 L7

M4

P3 P4 P4 P4 M6 D2 H5 L3 D3 H5 A5 B4 A4 B3 A4 H5

IC (M3 , P1 ) (M4 , P1 ) (M3 , P4 ) M5 (M3 , P4 ) (M1 , P4 )

(A4 , B1 ) (A1 , B1 ) (A4 , B2 ) (A4 , B2 )

Actions w/r 2⇒3 2⇒1 3⇒4 2⇒3 2⇒1 2⇒1 2⇒1 3⇒4 2⇒1 3⇒4 2⇒1 3⇒2 2⇒1 2⇒1 2⇒1 2⇒1 2⇒1 3⇒2 3⇒3 2⇒1 2⇒1 4⇒5 2⇒3 2⇒1 3⇒4 2⇒3 2⇒1

7.6.2 Trajectory Method Our numerical example for the trajectory method is the following. For the ﬁrst stage we can use Pareto-eﬀective composite DAs for subsystem B from Table 7.9 as follows: B11 = D1 H1 L2 , N (B11 ) = (1; 3, 0, 0, 0); B21 = D2 H1 L2 , N (B21 ) = (3; 2, 1, 0, 0); B31 = D5 H5 L3 , N (B31 ) = (5; 0, 2, 0, 1); and B41 = D3 H5 L2 , N (B41 ) = (4; 1, 2, 0, 0). The composite DAs for stage 2 are the following: (a) Pareto-eﬀective decisions: B12 = D1 H1 L2 , N (B12 ) = (2; 3, 0, 0, 0); B22 = D2 H1 L2 , N (B22 ) = (4; 2, 1, 0, 0); and B32 = D3 H5 L2 , N (B32 ) = (5; 1, 2, 0, 0);

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(b) near Pareto-eﬀective decisions (they are dominated by the abovementioned Pareto-eﬀective DAs): B42 = D5 H5 L3 , N (B22 ) = (5; 0, 2, 0, 1). The composite DAs for stage 3 are the following: (a) Pareto-eﬀective decisions: B13 = D1 H1 L2 , N (B13 ) = (2; 3, 0, 0, 0); B23 = D2 H1 L2 , N (B23 ) = (5; 2, 1, 0, 0); and B33 = D1 H2 L2 , N (B33 ) = (2; 3, 0, 0, 0); (b) near Pareto-eﬀective decisions (they are dominated by the abovementioned Pareto-eﬀective DAs): B43 = D3 H5 L2 , N (B43 ) = (5; 1, 2, 0, 0); and B52 = D5 H5 L3 , N (B22 ) = (5; 0, 2, 0, 1). Note near optimal composite DAs may be useful from the following viewpoint. A change of components into a trajectory can require some eﬀorts, and it necessary to solve an additional top-level composition problem as follows: to combine a trajectory while taking into account quality of composite DAs at each stage and a cost of the component changes (e.g., retraining of users, change of ﬁle formats). Here we obtain the following basic trajectories (without the changes): α1 =< B11 , B12 , B13 >, α2 =< B21 , B22 , B23 > . The example of the trajectory with the component change is the following: α =< B11 , B12 , B33 > with the change H1 → H2 . Another strategy can be based on an improvement of a component. For example, the improvement of H5 at stage 3 will lead to the following trajectory: α =< B31 , B32 , B43 >. Figure 7.5 illustrates the trajectory method. 1 - B3 - B2 1 1 α1 : B1 1 - B3 - B2 2 B 2 2 α : 2 - B2 1 B33 3 α : B3 - B3 B2 B1

B

Stage 1

Stage 2

Stage 3

4

4

4 3 5

T -

Figure 7.5 Illustration for trajectory method

7.7 Summary In the chapter, three system design problems for the modular system synthesis are described: (a) integration of the system, (b) improvement of obtained design decisions, and (c) multistage design. An extended version of HMMD (selection/composition of system components and improvement of system elements) was used. A next step can be targeted to an examination of an extended composite computer system which includes software, algorithms, databases, etc.

8 Improvement of Buildings

8.1 Evaluation and Redesign of Buildings The main general principles to system diagnosis/evaluation have been described in [680] and the diagnosis process for composite tree-structure systems is described in [802]. The chapter addresses a framework of the system analysis, evaluation/diagnosis, and improvement (redesign) on the basis of a hierarchical decision-making framework for a certain applied domain [516]: buildings from the viewpoint of earthquake engineering (Table 8.1) [20, 158, 221, 249, 332, 386, 411, 432, 452, 469, 482, 520, 547, 598, 641, 653, 681, 725, 735, 866, 884]. The material of the chapter does not address risk management (e.g. [375]), post-earthquake restoration and reconstruction (e.g. [451, 621]), damage diagnosis of concrete structures using artiﬁcial intelligence techniques (e.g., neural networks) (e.g. [145, 828, 829]), optimal and multiple criteria land use analysis and planning (e.g. [260, 896]), probabilistic approaches to seismic risk analysis (e.g. [117, 531]), simulation techniques (e.g. [262, 382, 769]), stochastic approaches to preventive maintenance (e.g. [298, 299, 847]), and economical issues of seismic design (e.g. [872]). We consider a building as a composite (decomposable, modular) system. Some methodological issues for the design and redesign of buildings (mainly on the basis of special languages) have been described in (e.g. [47, 48, 57, 376]). Note some evaluation models for new products are considered in (e.g. [271, 626, 770]), special signal ﬂow graphs are used for evaluation of design process alternatives in [393], fuzzy sets approach is applied for evaluation of design alternatives in [441]. Four basic redesign problems for buildings can be formulated on the basis of the following two dimensions: (1) architectural requirements or requirements of earthquake engineering and (2) redesign of a building project or redesign of an existing building.

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Table 8.1 Some bibliography sources in earthquake engineering and building design Topics

Sources

1. Design management and design framework 2. Earthquake engineering and seismic design (general) 3. Description of earthquakes and regions 4. Modeling of earthquake situations 5. Economical issues of seismic design 6. Evaluation and assessment of buildings and damage

[47, 48, 57, 516]

7. Strengthening and improvement of buildings 8. Description of requirements to seismic design 9. Seismic stability of auxiliary elements 10. Conﬁguration of buildings

[39, 123, 221, 233, 386, 432, 530, 535], [598, 641, 705, 725, 866, 884] [38, 221, 266, 452, 535, 905] [266] [872] [20, 117, 123, 145, 248, 249, 332, 421], [482, 516, 531, 547, 587, 601, 653, 681], [725, 735, 770, 828, 829] [82, 123, 158, 197, 248, 249, 516, 547], [735, 835] [123, 221, 386, 432, 530, 535, 547, 705], [725, 866, 884] [469, 520] [39, 51, 635, 756]

In addition, it is reasonable to point out the basic kinds of the improvement (redesign) problem ([497]): Problem 1. Find the best improvement plan to reach a required level for the resultant system while taking into account the following two parts: (i) results (a quality level for the resultant system) and (ii) required resources (a set of admissible improvement actions). Problem 2. Find the best level for the resultant system(s) while taking into account the following: (i) admissible limited resources (a set of admissible improvement actions) and (ii) some constraints for the improvement plan. Evaluation problems can be considered as follows: (1) evaluation of a building or a project; (2) evaluation of a real building after a earthquake. In this chapter, the following parts of the redesign scheme are proposed: (a) schemes for evaluation of buildings/projects; (b) a basic set of redesign/improvement actions (operations); (c) basic requirements for buildings; and (d) multicriteria description and binary relations (equivalence, complementarity, and precedence) for improvement actions; and (e) combinatorial problem formulations and solving schemes for the evaluation and redesign processes.

8 Improvement of Buildings

109

Note our material leads to a hybrid approach that integrates decision making techniques and ordinal expert judgment as a special knowledge base. Some approaches to earthquake engineering on the basis of traditional artiﬁcial intelligence methods are described in (e.g. [332, 587]). A numerical illustrative example illustrates the redesign framework for a building project.

8.2 Scheme for Improvement/Redesign Our framework for a system (building) (on the basis of HMMD from [497]) consists of the following: I. Design of hierarchical model and description for a system. 1.1. Design of hierarchical model for a system. 1.2. Design of multicriteria (multifactor) hierarchical description of the model nodes (building parts, components) including ordinal scales for each criterion. II. Evaluation. 2.1. Assessment of the system parts/components upon criteria. 2.2. Step-by-step aggregation of information to get a multicriteria estimate for a higher level of the model hierarchy (on the basis of multicriteria decision making techniques from [305] and [497]). III. Analysis of the building and revelation of bottlenecks [497]. 3.1. Analysis of the resultant integrated estimate for the system, analysis of system parts/components and their interconnection. 3.2. Revelation of the bottlenecks as some weak building parts/components or their interconnection (if this is necessary). IV. Design of improvement actions for the system [497]. 4.1. Generation/selection of a set of some possible improvement actions. 4.2. Selection/composition of the best subset of the improvement actions while taking into account certain design and technological requirements (situations). 4.3. Scheduling of the improvement actions above. The list of basic procedures supporting our framework involves the following: 1. Selection of items (e.g., design/redesign alternative operations). 2. Selection of items while taking into account some resource constraints. 3. Deﬁnition of parameter values for items. 4. Integration/synthesis of items into a composite system (subsystem). 5. Ranking of items while taking into account their attributes. 6. Ordering/scheduling the items. The list of some basic support models for the above-mentioned procedures is as follows: 1. Knapsack problem for selection of improvement actions while taking into account their utility and some resource constraints (e.g. [281, 428, 551]).

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Composite Systems Decisions

2. Multiple-choice problem for selection of improvement actions while taking into account their utility and some resource constraints. In this case, the actions are divided into groups and we select actions from each group [428, 551]. 3. Multiple criteria ranking for ordering the actions while taking into account their estimates upon criteria. 4. The morphological clique problem or combinatorial synthesis [497]. 5. Scheduling the redesign actions can be based on well-known scheduling problems. Formulations of scheduling problems are described in (e.g. [90]). 6. For some complicated situations, it may be reasonable to examine nonlinear mixed integer programming models (e.g. [267, 326]). Here our eﬀorts are oriented not only to select the best operations while taking into account their utilities and resource constraints but to deﬁne some continuous parameter values for the operations.

8.3 Structure of Building, Criteria, and Scales Here, the following is examined: (i) tree-like model for a building; (ii) criteria for the improvement/redesign of building; and (iii) weights and scales for the criteria. Note a weight system for the criteria is oriented to a certain redesign problem. Here, the problem of project redesigning from the viewpoint of earthquake engineering is considered. In the example, it is assumed a certain earthquake situation (8-mark estimate, scale of seismic intensivity MSK-64). Other redesign problems can be studied on the basis of other improvement (redesign) actions and a weight system for the criteria. Note classiﬁcation of building types and main classes of structural failures and damages are considered in [421]. Here the following basic hierarchical structure of a building is examined: 1. Building S. 1.1. Foundation A. 1.2. Basic structure B. 1.2.1 Bearing structures D. 1.2.1.1. Frame E. 1.2.1.2. Rigidity core G. 1.2.1.3. Staircase H. 1.2.2 Nonbearing structures F . 1.2.2.1. Filler walls I. 1.1.2.2. Partitioning walls J. 1.3. Floors C. Note that conﬁguration of buildings (e.g., symmetry) plays a crucial role (e.g. [39, 51, 635, 756]). The following scale can be used for conﬁguration: 1 corresponds to bad, 2 corresponds to good, 3 corresponds to excellent (symmetrical, etc.). In our opinion, the good conﬁguration deals to decreasing of building damage (i.e., decreasing an damage estimate by one level). Our hierarchical criteria set is based on the following two parts:

8 Improvement of Buildings

111

1. Characteristics of the building including the following main parameters: (a) volume-plan design decisions (regularity of a building system, symmetry, location of rigidity building mass or mass of rigidity core for building, dimensions); (b) engineering-geological situation, etc. 2. A hierarchical criteria set for the evaluation of a certain building at a certain situation (on the basis of extremal inﬂuence): (a) volume; (b) type (vertical, horizontal); (c) correspondence between direction of inﬂuence and plan of building; and (d) dynamical character of oscillations. The following basic coordinated ordinal scales for the building parts/ components are proposed: 1. global destruction; 2. local destruction; 3. chinks; 4. small chinks (hair-like); and 5. without damage. For each building part/components we use a special ordinal scale that is a part of the scale above (Table 8.2). Table 8.2 Ordinal scale for evaluation of building components Parts Scales of building Destruction Destruction Chinks Small (global) (local) chinks 1 1.1 1.2 1.2.1 1.2.1.1 1.2.1.2 1.2.1.3 1.2.2 1.2.2.1 1.2.2.2 1.3

* *

* * * *

* * * * * * * * * *

* * * * * * * * * * *

Without damage * * * * * * * * * * *

Note ordinal multi-level/state classiﬁcation decisions are used in many engineering domains (a small survey is contained in [497]). An example of the ordinal four-state classiﬁcation to classify ﬁrms is the following: healthy, divided reduction, debt default, and bankrupt [11].

8.4 Basic Set of Improvement Actions Upgrading issues for structures/buildings including strengthening of an existing building have been considered by many authors [82, 158, 197, 248, 530, 547, 835, 884]. Here the following basic set of improvement actions (redesign operations) for buildings from the viewpoint of earthquake engineering is considered:

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Composite Systems Decisions

A. Internal actions. 1. Decreasing the weight: 1.1. insulating materials (e.g., thermal, acoustic); 1.2. bearing walls (a frame); 1.3. non-bearing walls; and 1.4. ﬂoors. 2. Modiﬁcation of static scheme: 2.1. design of rigidity core and 2.2. increasing a static indetermination of structure (2.2.1 redesign of hinge joints into rigid ones; 2.2.2. design of additional supporters; 2.2.3. design of additional joints; and 2.2.4. design of additional connectors). 3. Strengthening some structural elements and connectors (design of additional elements): 3.1. beams; 3.2. columns; 3.3. walls; 3.4. ﬂoor slabs; 3.5. partition walls; 3.6. connectors; 3.7. ﬂoors (dome, vanet, etc.); and 3.8. foundation. 4. Additional structural systems and elements: 4.1. ﬂexible antiseismic girt; 4.2. rigid antiseismic girt (metal, concrete); 4.3. metal rigidity frame; 4.4. concrete rigidity frame; and 4.5. shear wall. B. External decisions. In addition, it is reasonable to deﬁne the following three kinds of binary relations on the improvement actions set: (1) equivalence of actions Re ; (2) complementarity Rc ; and (3) precedence Rp . @ @

@ @

Parapet wall

O8

@

@ @

@

@ @

O7

Cantilever balcony O10 O6

O11

O9

Figure 8.1 Draft of a building example and redesign operations

8 Improvement of Buildings

113

8.5 Numerical Examples Here an illustrative example for the improvement (redesign) of a project from the viewpoint of earthquake engineering is described. The example can be used as the basic one for many other practical cases. We examine a simple two-ﬂoor building (Figure 8.1) that is widely used in Greece, Cyprus, Turkey, and Israel. Note the earthquake situation in this region is described in (e.g. [38, 535]). Thus we consider two evaluation problems: (i) generation of a compressed list of improvement actions and (ii) composition of a redesign schedule. Note we do not consider criteria of aesthetic evaluation (e.g. [286]). 8.5.1 Evaluation Example: Integration Tables Here an evaluation example for a building after earthquake is examined. Integration tables are presented in Figures 8.2, 8.3, and 8.4 (’−’ corresponds to impossible situations). Nonbearing structure 1.2.2 [2, ..., 5]

Basic structure 1.2 [2, ..., 5]

2

2

− −

3

3

− − 3

2

3

3

3

4

3

4

− 4

4

Filler − 4 walls 1.2.2.1 5 5

2 3 4 5 Partitioning walls 1.2.2.2

− 4

− − 3 Bearing 4 − 4 structures 1.2.1 5 5 5

2 3 4 5 Nonbearing structures 1.2.2

Figure 8.2 Integration for system and parts 1.2 and 1.2.2 As a result, it is now possible to evaluate a building after earthquake: Example 1. Local expert evaluation of a building: 1.1: 4, 1.2.1.1: 3, 1.2.1.2: 4, 1.2.1.3: 3, 1.2.2.1: 2, 1.2.2.2: 2, and 1.3: 2; resultant estimate for building 1 equals 2. Example 2. Local expert evaluation of a building: 1.1: 5, 1.2.1.1: 4, 1.2.1.2: 5, 1.2.1.3: 4, 1.2.2.1: 4, 1.2.2.2: 3, and 1.3: 4; resultant estimate for building 1 equals 4. Example 3. Local expert evaluation of a building: 1.1: 5, 1.2.1.1: 3, 1.2.1.2: 5, 1.2.1.3: 4, 1.2.2.1: 3, 1.2.2.2: 3, and 1.3: 4; resultant estimate for building 1 equals 3. Example 4. Local expert evaluation of a building: 1.1: 5, 1.2.1.1: 5, 1.2.1.2: 5, 1.2.1.3: 5,

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1.2.2.1: 4, 1.2.2.2: 4, and 1.3: 5; resultant estimate for building 1 equals 5. 1.1 1.2 1.3 [3...5] [4...5] [3...5] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5

2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5

1 2 − − − 2 3 3 − − − − − − − − − 2 − − − − − 3 3 − − 4 4 − − − 5

1.1 1.2 1.3 [3...5] [4...5] [3...5] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5

2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5

1 2 − − − − 3 3 − − − 4 4 − − − −

Figure 8.3 Integration for building 1 ([2, ..., 5])

8.5.2 Evaluation Example: Morphological Design In this section, an evaluation example for a building project is described. First, let us generate DAs for building components as follows (priorities from the viewpoint of earthquake engineering are shown in parentheses): Foundation: A1 , strip foundation (2), A2 , bedplate foundation (1), A3 , foundation consisting of isolated parts (2).

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Frame: E1 , monolith frame (1), E2 , precast frame (2). Rigidity core: G1 , monolith rigid core (1), G2 , precast rigid core (2). Staircase: H1 , monolith staircase (1), H2 , precast staircase (2), H3 , composite staircase consisting of precast and monolith elements (3). Filler walls: I1 , small elements (2), I2 , curtain panel walls (2), I3 , precast enclosure panel walls (1), I4 , frame walls (1). Partitioning walls: J1 , precast panel walls (1), J2 , small elements (3), J3 , frame walls (2). Floors: C1 , monolith slabs (1), C2 , composite slabs (3), C3 , precast slabs (3). 1.2.1.1 1.2.1.2 1.2.1.3 1.2.1 [3...5] [4...5] [3...5] 3 3 3 3 3 3 5 5 5 5 5 5

4 4 4 5 5 5 4 4 4 5 5 5

3 4 5 3 4 5 3 4 5 3 4 5

3 3 − 3 3 − 3 4 4 4 4 5

1.2.1.1 1.2.1.2 1.2.1.3 1.2.1 [3...5] [4...5] [3...5] 4 4 4 4 4 4

4 4 4 5 5 5

3 4 5 3 4 5

3 4 − 3 4 4

Figure 8.4 Integration for bearing structures 1.2.1 ([3, ..., 5]) Note the example is a compressed one. It is reasonable to use many criteria to evaluate the above-mentioned DAs. Here, the following composite DAs are considered: D1 = E1 G1 H1 , N (D1 ) = (3; 3, 0, 0), D2 = E1 G1 H2 , N (D2 ) = (1; 2, 1, 0), D3 = E1 G1 H3 , N (D3 ) = (1; 2, 0, 1), D4 = E1 G2 H1 , N (D4 ) = (2; 2, 1, 0), D5 = E1 G2 H2 , N (D5 ) = (1; 1, 2, 0), D6 = E1 G2 H3 , N (D6 ) = (1; 1, 1, 1), D7 = E2 G1 H1 , N (D7 ) = (2; 2, 1, 0), D8 = E2 G1 H2 , N (D8 ) = (1; 1, 2, 0), D9 = E2 G1 H3 , N (D9 ) = (1; 1, 1, 1), D10 = E2 G2 H1 , N (D10 ) = (1; 1, 2, 0), D11 = E2 G2 H2 , N (D11 ) = (1; 3, 0, 0), D12 = E2 G2 H3 , N (D12 ) = (1; 2, 0, 1); F1 = I1 J1 , N (F1 ) = (1; 1, 1, 0), F2 = I1 J2 , N (F2 ) = (1; 0, 1, 1), F3 = I1 J3 , N (F3 ) = (1; 0, 2, 0),

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F4 = I2 J1 , N (F4 ) = (2; 1, 1, 0), F5 = I2 J2 , N (F5 ) = (1; 0, 1, 1), F6 = I2 J3 , N (F6 ) = (2; 0, 2, 1), F7 = I3 J1 , N (F7 ) = (3; 2, 0, 0), F8 = I3 J2 , N (F8 ) = (1; 1, 0, 1), F9 = I3 J3 , N (F9 ) = (3; 1, 1, 0), F10 = I4 J1 , N (F10 ) = (3; 2, 0, 0), F11 = I4 J2 , N (F11 ) = (1; 1, 0, 1), F12 = I4 J3 , N (F12 ) = (3; 1, 1, 0). Compatibility of DAs is shown in Tables 8.3, 8.4, 8.5, and 8.6. Thus, we can select for our next examination the following four best and good DAs for D (Figure 8.5): (a) D1 (ideal solutions, priority equals 1); (b) D4 , D7 , and D11 (some Pareto-eﬀective solutions without taking into account D1 , priority equals 2). Analogous, we can select for our next examination the following four best and good DAs for F (Figure 8.6): (a) F7 , F10 (ideal solutions, priority equals 1); (b) F9 , F12 (good solutions, priority equals 2). Generally, we can assume that the priority of other DAs for D and F will equal 3. Now let us consider 12 composite DAs for B on the basis of the abovementioned selected four DAs for D and for F (accordingly): B1 = D1 F7 , N (B1 ) = (2; 2, 0, 0), B2 = D1 F9 , N (B2 ) = (2; 1, 1, 0), B3 = D1 F10 , N (B3 ) = (2; 2, 0, 0), B4 = D1 F12 , N (B4 ) = (3; 1, 1, 0), B5 = D4 F7 , N (B5 ) = (2; 0, 1, 1), B6 = D4 F9 , N (B6 ) = (2; 0, 2, 0), B7 = D4 F10 , N (B7 ) = (2; 1, 1, 0), B8 = D4 F12 , N (B8 ) = (2; 0, 2, 0), B9 = D7 F7 , N (B9 ) = (2; 0, 1, 1), B10 = D7 F9 , N (B10 ) = (2; 0, 2, 0), B11 = D7 F10 , N (B11 ) = (2; 1, 1, 0), B12 = D7 F12 , N (B12 ) = (2; 0, 2, 0), B13 = D11 F7 , N (B13 ) = (3; 1, 1, 0), B14 = D11 F9 , N (B14 ) = (2; 0, 2, 0), B15 = D11 F10 , N (B15 ) = (2; 1, 1, 0), B16 = D11 F12 , N (B16 ) = (2; 0, 2, 0). As a result, we have to select the following DAs for B (Figure 8.7): (a) N = (3; 1, 1, 0): B4 = D1 F12 , B13 = D11 F7 ; (b) N = (2; 2, 1, 0): B1 = D1 F7 , B3 = D1 F10 . Evidently, these DAs have a priority that equals 2 (priority for all others equals 3). Finally, we get the following composite DAs for our system (building, Figure 8.8): (a) N = (3; 2, 1, 0): S1 = A2 B1 C1 , S2 = A2 B3 C1 , S3 = A2 B4 C1 (resultant quality level equals 2); (b) N = (2; 2, 1, 0): S4 = A2 B13 C1 (resultant quality level equals 3).

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117

For other combinations of DAs for considered here A, B and C priority will equal 4 and for all others resultant quality level will equal 5. Here resultant quality level 1 is impossible, e.g., the ideal decision from the viewpoint of earthquake engineering is absent. A reason of this situation consists in the following: ﬁller walls and partitioning walls are not ideal ones. We can obtain an ideal decision if the above-mentioned walls will be designed as monolith concrete. But in this case, we will get another kind of building structure: building with monolith concrete walls which are strengthening by frames. Note the obtained building will have an increased weight and a decreased level of thermotechnic and acoustic properties. A way to an ideal decision is based on the usage of monolith light concrete or light composite non-structural elements. Table 8.3 Compatibility for D Table 8.4 Compatibility for F G1 G2 H1 H2 H3 E1 E2 G1 G2

3 2

2 1

3 2 3 2

1 1 2 1

I1 I2 I3 I4

2 2 1 1

J1 J2 J3

1 1 1

2 1 2

3 1 3

3 1 3

Table 8.5 Compatibility for B F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12

3 2 2 2 2 2 2 2 2 2 1 2

3 2 2 2 2 2 2 2 2 2 1 2

3 2 2 2 2 2 2 2 2 2 1 2

2 2 2 2 2 2 2 2 2 2 3 2

2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 3 2

2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2

3 2 2 2 2 2 2 2 2 2 2 2

Thus we get an ordinal scale for composite DAs [1, ..., 5] (1 corresponds to the best level). Let us consider the following examples: (i) S i = A2 (E1 G1 H1 ) (I3 J1 ) C1 , resultant quality level equals 2. (ii) S ii = A2 (E2 G2 H2 ) (I3 J1 ) C1 , resultant quality level equals 2. (iii) S iii = A1 (E2 G2 H2 ) (I3 J1 ) C3 , resultant quality level equals 3. (iv) S iv = A2 (E2 G2 H2 ) (I3 J1 ) C3 , resultant quality level equals 3. (v) S v = A1 (E2 G1 H1 ) (I3 J3 ) C3 , resultant quality level equals 4.

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Table 8.6 Compatibility for S C1 C2 C3 B1 B3 B4 B13 A1 A2 A3 C1 C2 C3

2 3 2

2 2 2

2 2 2

2 3 2 3 3 2

2 3 2 3 3 2

2 3 2 3 3 2

Ideal points: N (F7 ), N (F10 )

Ideal point N (D1 )

A

A

Good point S S N (D11 ) S K S GoodSpoints: S S S N (D4 ), N (D7 ) S S K S S S S S S S S w=3 w=2 w=1 Figure 8.5 System excellence (D)

1 2 1 2 2 3

S S S

S

S

S

S S

w=1

S

KS S Good points: S S N (F ), N (F 9 12 ) S S S S w=3 w=2 S

Figure 8.6 System excellence (F )

8.5.3 Improvement Actions and Criteria Our list of the basic improvement actions (operations) for the example is the following: Operation group I (frames): 1. Increasing a geometrical dimension and active reinforcement O1 . 2. Increasing of active reinforcement O2 . Operation group II (joints): 3. Increasing a level for ﬁxing a longitudinal active reinforcement in zone of joints O3 . 4. Decreasing the step of reinforced cross rods in zone of joint O4 . Operation group III (cantilever and cantilever balcony): 5. Decreasing the projection cantilever O5 . 6. Supplementary supporting the cantilever O6 . Operation group IV (fronton and parapet wall): 7. Fixing a bottom part O7 . 8. Designing a 3D structure (special) O8 .

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119

Operation group V (connection between frame and ﬁller walls): 9. Design of shear keys O9 . 10. Design of mesh reinforcement O10 . 11. Partition of ﬁller walls by auxiliary frame O11 . Ideal point Good points: IdealApoint A N (S4 ) N (B1 ), N (B3 ) S S K S S @ S S KS K S @ S @ S S S S Good points: K S N (S1 ), N S (S2 ), S S S S N (B ), N (B ) 4 13 S S )SS N (S 3 S S S S S S S S S S S S S w=3 w=3 w=2 w=2 w=1 w=1 Figure 8.7 System excellence (B)

Figure 8.8 System excellence (S)

Application of several redesign operations is depicted in Figure 9. Binary relations on the above-mentioned operations are the following: (1) equivalence Re = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (5, 6), (7, 8), (9, 10), e = {(3, 4)}; (9, 11), (10, 11)}, nonequivalence R (2) complementarity Rc = {(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (2, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (3, 10), (3, 11), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (4, 10), (4, 11), (5, 7), (5, 8), (5, 9), (5, 10), (5, 11), (6, 7), (6, 8), (6, 9), (6, 10), (6, 11), (7, 9), (7, 10), (7, 11), (8, 9), (8, 10), (8, 11)}, c = {(5, 6), (7, 8), (9, 10), (9, 11), (10, 11)}; and noncomplementarity R p (3) precedence R = {(1, 2)(1, 3)(1, 4)(1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (2, 3)(2, 4)(2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (2, 10), (2, 11), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (3, 10), (3, 11), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (4, 10), (4, 11), (5, 9), (5, 10), (5, 11), (6, 9), (6, 10), (6, 11), (7, 9), (7, 10), (7, 11), (8, 9), (8, 10), (8, 11)}. The following criteria are considered (corresponding ordinal scales and criterion weights are pointed out in parentheses): Improvement of earthquake resistance: 1. Decreasing a dead weight (or loading) ([−2, ..., 2], 3): K1 . 2. Increasing a load capacity ([1, ..., 5], 5): K2 .

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3. Increasing a reliability ([1, ..., 5], 5): K3 . Quality of architecture and plan decisions: 4. Facade ([0, ..5, ], −3): K4 . 5. Plan ([0, ..., 4], −3): K5 . 6. Free space ([0, .., 2], −3): K6 . Utilization properties: 7. Thermotechnics ([0, .., 2], −1): K7 . 8. Acoustics ([0, 1], −1): K8 . 9. Fire-risk ([0, 1, 2], −4): K9 . Expenditure: 10. Materials ([0, .., 10], −3): K10 . 11. Cost ([0, ..., 10], −4): K11 . 12. Time expenditure ([0, ..., 10], −3): K12 . Table 8.7 contains expert estimates for the above-mentioned building improvement actions upon criteria and a resultant priority (rank). 8.5.4 Improvement Process The structure (model) of the process is based on binary relation Rc as follows: (a) operations for frame (e.g., O1 , O2 ); (b) operations for joints (e.g., O3 , O4 ); (c) operations for parapet wall (e.g., O5 , O6 ); (d) operations for cantilever balcony (e.g., O7 , O8 ); and (e) operations for connection between frame and ﬁller wall (e.g., O9 , O10 , O11 ). Note precedence of the above-mentioned operation groups is the following: (a); (b); (c) and (d) concurrently; (e). Binary relation Rc is a basis to generate the following aggregated operations: O1 &O2 and O3 &O4 . Binary c is a reason to delete the following aggregated operations O5 &O6 , relation R O7 &O8 , O9 &O10 , O9 &O11 , O10 &O11 , and O9 &O10 &O11 . The structure of the multi-stage improvement/redesign process and generated operations are shown in Figure 8.9. All operations pointed out are compatible (by relation Rc ). Now let us consider some models the improvement strategy: Knapsack problem: The use of knapsack problem is based on independence of the items/ operations ({O1 , ..., O11 }), the only one objective function (mainly), and quantitative nature of the required resources. In our case, we can examine the following problem formulation: (i) objective function: improvement of earthquake resistance, i.e., criterion K1 or K2 or K3 ; (ii) restrictions for resources: (a) quality of architecture and plan decisions: K4 , K5 , and K6 ; (b) utilization properties: K7 , (K8 ), and K9 ; and (c) expenditure: materials (K10 ), cost (K11 ), time (K12 ). Unfortunately, our redesign operations are interconnected (i.e., binary relations of equivalence, complementarity, and precedence) and it is reasonable to use more a complicated model.

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Table 8.7 Estimates of improvement actions Improvement actions

K1 K2 K3 K4 K5 K6 K7 K8 K9 K10 K11 K12

O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 O11 O1 &O2 O3 &O4

−2 0 0 0 2 −1 2 1 0 0 0 −2 0

Criteria

5 4 2 3 2 3 3 4 2 3 2 5 3

5 4

1 0 30 0 3 5 0 2 0 0 0 1 0

4 4 5 4 5 3 4 4 5 4

3 0 0 0 4 1 0 1 0 0 0 3 0

P = A B (C D) E

2 0 0 0 1 1 0 1 0 0 0 2 0

Rank

0 0 0 0 1 0 0 0 0 0 2 0 0

1

3

5

2

4

6

2

3

4

0 0 0 0 1 2 1 1 1 1 0 0 0

5 3 1 2 0 5 1 2 1 4 5 8 3

5 3 1 3 0 4 2 3 1 3 5 8 4

5 3 1 3 0 5 2 4 1 4 5 8 4

3 1 2 1 3 4 1 2 3 2 3 4 2

z

x C xA xB x u OO (3) u OO (3) u OO (2) (1) (1) u O &O (4) u O &O (2) u (4) u None u u u None None 1

0 0 0 0 1 0 0 0 0 0 1 0 0

xD u OO (1) u (2) u None 7 8

xE u OO (3)(2) u O (3) u u None 9

10 11

Figure 8.9 Structure of redesign process (priorities are shown in parentheses) Multiple-choice problem: In this case, we can consider the approach to problem formulation from the previous section while taking into account operation grouping (Figure 8.9), i.e., the structure of the redesign process. In addition, it is necessary here to deﬁne resource restrictions for each operation group. Note, quantitative scales are basic ones for this model. Multiple criteria ranking: Table 8.7 contains the results of multicriteria selection (ranks of operations). This model is the basic one in multicriteria decision making and can be recommended as a signiﬁcant part of more general solving schemes. Morphological clique problem: This approach is based on multicriteria ranking and taking into account operation dependence or the structure of the redesign process (Figure 8.9). Evidently, the best redesign strategy here is as follows: O2 ⇒ O4 ⇒ O5 &O7 ⇒ O10

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8.6 Summary In this chapter the decision making framework for hierarchical analysis, evaluation and redesign/improvement of a composite system with the example for buildings has been described. Clearly, it is reasonable to consider the following two basic future research directions: 1. Usage of the described framework for other kinds of complex composite systems. 2. Extension of the set of real world applications in the ﬁeld of civil engineering, e.g., multiple criteria analysis of land use and post-earthquake reconstruction [260, 451, 621]. On the other hand, other approaches can be used for the system evaluation and improvement processes, including techniques of artiﬁcial intelligence (e.g., linguistic geometry [797] for system improvement planning).

9 Planning in Concrete Macrotechnology

9.1 Preliminaries In this chapter, the following typical compressed structure of product life cycle is examined: combinatorial design (synthesis) of materials and manufacturing process. In addition, the following problems are studied: system reﬁnement, series–parallel production process, and multistage design (design of product trajectories). Note many researches are based only on selection of materials and/or technology (e.g. [180, 300, 359, 460]). Here, the technological strategy is represented as a composite hierarchical system. The problem is [497]: Describe the composite system (i.e., technological trajectory) as a treelike structure with design alternatives (DAs) and combine a resultant strategy while taking into account ordinal estimates of DAs and their interconnection (compatibility) IC. In our case, a realistic numerical example for concrete macrotechnology (composing of concrete from constituents, and selection of manufacturing alternatives) illustrates the approach [514].

9.2 Concrete Macrotechnology Here, a hierarchical combinatorial framework for concrete macrotechnology is examined, including the following three problems: (a) combinatorial description and analysis of the concrete macrotechnology, including two basic parts: (i) concrete (alternative components and their compatibility) and (ii) technology for its manufacturing (alternatives); and (b) adaptation of the macrotechnology for certain applied situations on the basis of hierarchical combinatorial design [497].

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These framework and techniques cover are the material and manufacturing process selection in [300]. A multicriteria description (manufacturing, economics, and ecology) of components and composite decisions is applied. Essentially, attention is oriented to the use of substitutes (furnace bottom ash, crushed stone, etc.) [46, 115, 613, 845]. The hierarchical combinatorial synthesis is based on a design morphology which corresponds to an initial hierarchical knowledge structure (design alternatives, their interconnection, etc.). The approach consists of the following two main phases: 1. Design of the basic design morphology, including assessment of its design alternatives and their interconnection. 2. Bottom-up multicriteria selection and synthesis of design alternatives to get resultant technological strategies. In many practical situations there exists a need to plan concrete manufacturing on the basis of one of target concrete classes while taking into account general requirements (objectives, restrictions). Thus our management problem, oriented to a certain applied situation, is: Find the best combination of concrete aggregates and manufacturing technology while taking into account a target class of concrete and the requirements. Here, the following hierarchical structure of concrete-macrotechnology is examined (DAs are pointed out in parentheses): 0. Concrete macrotechnology S = D X U Z 1. Aggregates D = A B 1.1 Coarse aggregates A (A0 , A1 , A2 , A3 , A4 , A5 ). 1.2 Fine aggregates B (B0 , B1 , B2 , B3 , B4 , B5 ). 2. Cement X (X1 , X2 , X3 , X4 , X5 ). 3. Manufacturing U (U1 , U2 , U3 , U4 ). 4. Classes of concrete (branch of goal) Z (Z1 , Z2 , Z3 , Z4 , Z5 ). In fact, this structure contains R & D stage (D, X, etc.). We take into account the requirements above on the basis of a multicriteria description of design alternatives for the above-mentioned parts of the concrete macrotechnology. 9.2.1 Basic Initial Information In this section, basic initial information is described: the morphological scheme of concrete macrotechnology, requirements (criteria), and DAs for components (technological parts, constituents). In our example, the following DAs are examined [45, 46, 115, 611–613]: A0 (none), A1 (crushed stone), A2 (gravel), A3 (crushed gravel), A4 (blast-furnace slag), A5 (bottom ash of thermal power station), etc.; B1 (sand), B2 (crushed sand), B3 (screenings of crushing), B4 (analogue of A4 ), B5 (analogue of A5 ), etc.; X1 (cement 300), X2 (cement

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125

400), X3 (cement 500), X4 (cement 600), X5 (cement 700); U1 (plant making), U2 (making at building site, usage of available mix of aggregates), U3 (making at building site, a mix of aggregates), U4 (making in concrete delivery truck); Z1 (concrete 200 or B15), Z2 (concrete 300 or B22.5), Z3 (concrete 400 or B30), Z4 (concrete 500 or B40), and Z5 (concrete 600 or B45). For U1 , making of concrete and articles is executed at a plant. The criteria are shown in Table 9.1 (weights of criteria correspond to target concrete Z2 ). Table 9.1 Criteria (weights for concrete 300) Components

Criteria C1 C2 C3 C4 C5 C6

Cost Positive inﬂuence to ecology Transportation expenditure Quality Time of making of concrete Time of making of articles

A

B

X

U

−1 2 −1 3

−1 2 −1 2

−2

−3

3 2 2

9.2.2 Example for Normal Weight Concrete 300 Here, we consider composing a management strategy to get concrete 300 (Z2 ). Note, composition of A5 and B5 is oriented to lightweight concrete. Estimates of DAs and resultant priorities are presented in Tables 9.2, 9.3, 9.4, and 9.5. Computation of priorities is based on DSS COMBI PC [492, 497], but it is possible to use simple techniques, e.g., additive utility function: v(αi ) =

n

βj bj (αi )

j=1

where i is the number of alternatives α, j is the number of criteria, βj is the weight (importance) of criterion j, bj (αi ) is the estimate of alternative αi upon criterion j, and v(αi ) is rating of alternative αi . Thus, we compute ratings (v) for DAs (for A) as follows: v(A0 ) = (−1)0 + (2)0 + (−1)0 + (3)0 = 0, v(A1 ) = (−1)6 + (2)0 + (−1)1 + (3)5 = 8, v(A2 ) = (−1)4 + (2)1 + (−1)1 + (3)4 = 9, v(A3 ) = (−1)5 + (2)1 + (−1)1 + (3)5 = 11, v(A4 ) = (−1)3 + (2)3 + (−1)1 + (3)3 = 11, and v(A5 ) = (−1)1 + (2)3 + (−1)2 + (3)4 = 15. The ratings of DAs can be transformed into priorities. The compatibility is presented in Tables 9.6, 9.7, 9.8, and 9.9. The resultant composite decisions for D = A B are as follows: D1 = A5 B5 , D2 = A1 B1 , D3 = A1 B2 , D4 = A1 B3 , D5 = A2 B1 , D6 = A2 B2 , D7 = A2 B3 , D8 = A3 B1 , D9 = A3 B2 , D10 = A3 B3 , and D11 = A4 B4 .

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Quality vectors for the decisions are as follows: N (D1 ) = (5; 1, 1, 0, 0), N (D2 ) = (5; 0, 1, 1, 0), N (D3 ) = (5; 0, 1, 0, 1), N (D4 ) = (5; 0, 1, 0, 1), N (D5 ) = (5; 0, 1, 1, 0), N (D6 ) = (5; 0, 1, 0, 1), N (D7 ) = (5; 0, 1, 0, 1), N (D8 ) = (5; 0, 1, 1, 0), N (D9 ) = (5; 0, 0, 1, 1), N (D10 ) = (5; 0, 1, 0, 1), and N (D11 ) = (5; 1, 1, 0, 0). Table 9.3 Estimates for B

Table 9.2 Estimates for A DAs

Criteria DAs

C1 C2 C3 C4 Priority A0 A1 A2 A3 A4 A5

0 6 4 5 3 1

0 0 1 1 3 3

0 1 1 1 1 2

0 5 4 5 3 4

DAs

C1 C2 C3 C4 Priority

3 2 2 2 2 1

Table 9.4 Estimates for X

B1 B2 B3 B4 B5

4 6 3 2 2

0 0 1 1 1

1 2 2 1 2

4 5 3 3 4

3 4 4 1 2

Table 9.5 Estimates for U

Criteria C1

X1 X2 X3 X4 X5

1 2 3 4 5

Priority

C2 1 2 3 4 5

2 1 1 2 2

Table 9.6 Compatibility (A, B)

DAs U1 U2 U3 U4

0 5 5 5 3 0

0 5 5 5 3 0

0 5 5 5 3 0

0 3 3 3 5 0

0 0 0 0 0 5

Criteria C1

C2

C3

6 3 4 5

3 2 1 1

0 3 3 3

Priority 2 1 3 2

Table 9.7 Compatibility (X, Z)

B1 B2 B3 B4 B5 A0 A1 A2 A3 A4 A5

Criteria

X1 X2 X3 X4 X5 Z1 Z2 Z3 Z4 Z5

5 4 2 0 0

4 5 4 2 0

3 4 5 4 2

2 3 4 5 4

1 2 3 4 5

9 Planning in Concrete Macrotechnology

Table 9.8 Compatibility (X, U )

Table 9.9 Compatibility (U, Z)

U1 U2 U3 U4 X1 X2 X3 X4 X5

4 4 5 5 5

5 5 4 4 4

5 5 4 4 4

127

U1 U2 U3 U4 Z1 Z2 Z3 Z4 Z5

5 5 4 4 4

5 5 5 4 3

4 4 4 4 4

5 5 5 5 5

5 5 5 5 5

Clearly, DAs D1 and D11 are Pareto-eﬀective points. We consider other composite DAs for the next stage too (expert judgment). It is assumed that priorities of the decisions equal 1. The compatibility of DAs for composite concrete D and DAs for other parts of macrotechnology are presented in Table 9.10, 9.11, and 9.12. Table 9.10 Compatibility (D, X)

Table 9.11 Compatibility (D, Z)

X1 X 2 X3 X4 X5 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11

5 5 5 5 5 5 5 5 5 5 5

0 5 5 5 5 5 4 5 5 4 5

0 5 5 4 5 5 3 5 5 3 0

0 5 5 0 0 0 0 5 5 0 0

Z1 Z2 Z3 Z4 Z5 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11

0 5 5 0 0 0 0 5 5 0 0

5 5 5 5 5 5 5 5 5 5 5

4 5 5 5 5 5 5 5 5 4 5

0 5 5 4 4 4 4 4 4 3 3

Table 9.12 Compatibility (D, U ) U1 U2 U3 U4 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11

5 5 5 4 5 5 4 4 5 4 3

5 5 5 5 5 5 3 5 5 3 3

5 5 5 3 5 5 3 5 5 3 3

3 5 5 2 5 5 2 5 5 2 3

0 5 5 3 0 0 3 0 0 2 0

0 5 5 0 0 0 0 0 0 0 0

128

Composite Systems Decisions

The resultant composite DAs for Z2 are as follows (Pareto-eﬀective points): S1 = Z2 X2 U2 D2 ; S2 = Z2 X2 U2 D3 ; S3 = Z2 X2 U2 D4 ; S4 = Z2 X2 U2 D5 ; and S5 = Z2 X2 U2 D9 . Quality vector for the decisions is the following: N = (4; 3, 0, 0).

9.2.3 Example for System Improvement First, let us examine improvement actions for the Pareto-eﬀective composite decisions above (S1 , ..., S5 ): 1. Reﬁnement of priorities for existing DAs: A1 , 2 ⇒ 1; A2 , 2 ⇒ 1; A3 , 2 ⇒ 1; B1 , 3 ⇒ 1; B2 , 4 ⇒ 1; and B3 , 3 ⇒ 1. 2. Usage of new DAs, e.g., combined ones: A6 = A1 &A5 , B6 = B1 &B3 , and U5 = U2 &U4 . 3. Reﬁnement of compatibility for some pairs: (U2 , Z2 ), 4 ⇒ 5. These improvement actions can be based on some special technological eﬀorts. At the next stage, it is possible to consider the following two problems: (i) selection of improvement actions (while taking into account required resources and eﬀectiveness), and (ii) scheduling of selected improvement actions. These problems can be solved on the basis of HMMD too [497]. 9.2.4 Example for Series–Parallel Production Process Here, we add the above-mentioned combined DAs to the basic design morphology. The estimates of the combined DAs (including corresponding compatibility) equal to the best estimates for their elements: A6 = A1 &A5 , priority equals 1; B6 = B1 &B3 , priority equals 1; and U5 = U2 &U4 , priority equals 2. We will consider the following combined DAs for D: D12 = A6 &B6 ; D13 = A6 &B3 ; and D14 = A1 &B6 . As a result, we can get the following composite parallel–series decisions (for the Pareto-eﬀective layer): S6 = Z2 X2 U5 D12 ; S7 = Z2 X2 U5 D13 ; and S8 = Z2 X2 U5 D14 . Figure 9.1 depicts the parallel-series decisions. 9.2.5 Example for Multistage Design Now we can consider a multistage situation. For each stage, it is reasonable to solve a corresponding design problem while taking into account special requirements (criteria, etc.). Here, it is assumed that the basic set of composite decisions is Y = {S1 , ..., S8 }, and we get the following decision sets for the stages: Stage 1: Y 1 = {S1 , S5 , S6 }. Stage 2: Y 2 = {S1 , S3 , S4 , S6 , S7 }. Stage 3: Y 3 = {S2 , S3 , S4 , S7 , S8 }.

9 Planning in Concrete Macrotechnology

129

At the additional level of system hierarchy, we have to examine coordination of decisions of neighbor stages. It is reasonable to deﬁne proximity of decisions (a cost of decision change) as a number of diﬀerent changed elements (Tables 9.13 and 9.14). The following system trajectories can be considered as good ones: < S6 → S3 → S3 >, < S6 → S6 → S3 >, < S6 → S6 → S7 >, < S6 → S6 → S8 >, < S6 → S7 → S7 >, and < S6 → S7 → S8 >. Figure 9.2 illustrates our situation for the system trajectories.

9.3 Summary The material of this chapter can be applied in the integrated product and process design environments (e.g. [300, 423]). Other prospective applications may be targeted to complex (e.g., virtual) enterprises (e.g. [128, 301]).

S6 :

U2

A1

B1

U4

A9

B3

U2

A1

X2

S7 :

X2

B3 U4

A9

U2 S8 :

X2

B1 A1

U4

B3

Figure 9.1 Illustration for parallel–series DAs Table 9.13 Dissimilarity Y1 →Y2

Table 9.14 Dissimilarity Y2 →Y3 S2 S3 S4 S7 S8

S1 S3 S4 S6 S7

S1 1

1

1

2

2

S3 1

0

2

2

2

S1 0

1

1

3

2

S4 2

1

0

4

3

S5 2

2

2

4

3

S6 2

0

1

0

0

S6 0

0

1

0

0

S7 2

2

1

0

0

130

Composite Systems Decisions

S1 S3 S4 S1 S6 S5 S7 S6

S2 S3 S4 S7 S8

0 t2 t1 Figure 9.2 Illustration for system trajectories

t3

T -

10 Transformation of a Specialist’s Proﬁle

10.1 Preliminaries In this chapter, an initial specialist’s proﬁle has to be transformed into a new important kind. For example, technologists/researchers can be transformed into managers/leaders in high-tech technologies (e.g. [161]). Evidently, this process requires the following: (a) analysis of the initial specialists and design of their proﬁle; (b) deﬁnition of the resultant professional proﬁle; (c) selection of admissible transformation (educational, etc.) operations and their evaluation; and (d) planning the transformation process while taking into account required resources. We consider a realistic educational example for the ﬁelds of information technology and software engineering for retraining a specialist. Basic information on the topic is contained in [273, 486], for example. Note, the similar problems of human resource management have been studied in [303].

10.2 Example of Retraining Our educational example has the following structure: 0. Proﬁle 1. Mathematics 1.1 Discrete mathematics and mathematical logic 1.2 Probability theory and statistics 1.3 Algorithms 1.4 Optimization and multicriteria analysis 2. Basic software engineering 2.1 Basic programming 2.1.1 Basic languages 2.1.1.1 C 2.1.1.2 JAVA 2.1.1.3 Pascal 2.1.1.4 Assembler

132

Composite Systems Decisions

2.1.2 Special issues 2.1.2.1 Operating systems 2.1.2.2 Object-oriented programming and design 2.1.2.3 Computer security 2.1.2.4 Graphics and visualization 2.2 Data structures and information systems 2.2.1 Data structures 2.2.2 File systems and database management systems (DBMSs) 2.2.3 Knowledge based systems 2.3 Special software issues 2.3.1 Telecommunication systems and networking 2.3.2 Real-time systems 2.3.3 Human–computer interface (HCI) and human factors 3. Engineering 3.1 Quality management 3.2 Systems engineering 3.3 Distributed systems 4. Complementary studies 4.1 Business management and enterpreneurship 4.2 Technology in society 4.3 Project management Here, we will use poset-like scale case 2 for each leaf node of the structure above (expert judgment): 1 corresponds to expert, 2 corresponds to experience, 2 corresponds to educational background, 3 corresponds to novice. On the other hand, multicriteria assessment for each DA can be applied with corresponding mapping of estimates obtained into a resultant element of the poset-like scale. Thus we can consider the following problems: (i) to compare specialists (specialist’s proﬁles); (ii) evaluation of a specialist (i.e., to generate a point in a quality space and/or to compare proximity to a target point); and (iii) composition of an education curriculum for a specialist (student, student group). In the last case, the following set of DAs for each leaf node can be used: X1 (none, resultant level corresponds to 3); X2 (a small introduction course and a project, resultant level corresponds to 2’); X3 (complete course, resultant level corresponds to 2”); X4 (complete course and project, resultant level corresponds to 1). Clearly, the following criteria for DAs may be applied here: (i) cost; (ii) required time; (iii) future need/signiﬁcance. The following target types of specialist in software engineering are often considered: 1. analyst, 2. designer, 3. programmer, 4. database specialist, 5. user interface specialist, and 6. project manager. Table 10.1 contains examples of target proﬁles and an individual proﬁle.

10 Transformation of a Specialist’s Proﬁle

133

Table 10.1 Illustration for proﬁles Leaf node of proﬁle 1.1 1.2 1.3 1.4 2.1.1.1 2.1.1.2 2.1.1.3 2.1.1.4 2.1.2.1 2.1.2.2 2.1.2.3 2.1.2.4 2.2.1 2.2.2 2.2.3 2.3.1 2.3.2 2.3.3 3.1 3.2 3.3 4.1 4.2 4.3

Proﬁle of programmer 2 2 2 2 1 1 1 1 2 1 2 2 2 2 2 2 2 2 2 2 2 -

Proﬁle of project manager 2 2 2 2 2 2 1 2 2 2 2 2 1

Example of an individual proﬁle 2 2 1 1 2 2 2 2 2 3 3 3 3 2 3 2 2 1 1 1 2 2 2 1

Now let us consider an example to design a composite course. A generalized solution scheme may consist of: Stage 1. Description of an initial individual proﬁle. Stage 2. Selection or construction of a target proﬁle. Stage 3. Analysis of a diﬀerence between the proﬁles. Generation of structure and candidate elements (DAs) for a target composite educational plan. Stage 4. Evaluation of the elements (DAs) and their compatibility. Stage 5. Design of the composite educational plan. Now let us consider a small example on the basis of a part of the proﬁle: A (2.1.2.1 Operating systems) with corresponding DAs: A1 (1), A2 (2); B (2.1.2.2 OO Programming and design) with DAs: B3 (2), B4 (1); C (2.1.2.3 Computer security) with DAs: C3 (2), C4 (1); D (2.1.2.4 Graphics and visualization) with DAs: D1 (2), D2 (1); E (2.2.1 Data structures) with DAs: E3 (2), E4 (1); F (2.2.2 File systems and DBMSs) with DAs: F2 (1), F3 (1), F4 (2); H (2.2.3 Knowledge based systems) with DAs: H3 (1), H4 (2).

134

Composite Systems Decisions

We point out ordinal estimates for each DA in parentheses while taking into account the initial proﬁle and a target proﬁle for programmer (Table 10.1). Table 10.2 contains an example of compatibility with the ordinal scale [0, 1, 2, 3, 4]. Here symbol * corresponds to independence, i.e., in this case, we will use for computation the maximum value. Resultant composite DAs are the following: S1 = A1 B4 C4 D2 E4 F2 H3 , N (S1 ) = (2; 7, 0, 0); S2 = A1 B4 C4 D2 E4 F3 H3 , N (S1 ) = (2; 7, 0, 0); S3 = A2 B4 C4 D2 E4 F2 H3 , N (S1 ) = (3; 6, 1, 0); S4 = A1 B4 C4 D2 E4 F3 H3 , N (S1 ) = (3; 6, 1, 0). Table 10.2 Compatibility of DAs B3 B4 C3 C4 D1 D2 E3 E4 F2 F3 F4 H3 H4 A1 A2 B3 B4 C3 C4 D1 D2 E3 E4 F1 F2 F3

* *

* *

2 4 2 3

2 4 3 3

* * 1 3 1 1

* * 3 3 3 3

2 4 3 3 4 4 1 3

2 4 3 4 4 4 1 3

3 3 3 3 4 4 1 4 4 4

3 4 4 4 4 4 1 4 4 4

3 4 4 4 1 1 1 4 4 4

* * 3 3 3 3 3 3 4 4 4 4 4

* * 3 4 3 3 3 4 4 4 4 4 4

10.3 Summary An understandable numerical example has been examined for a ﬁeld of engineering/computer science/information technology. Similar problems can be considered for many other domains. Thus, our material can be used, for example, for the following: (i) curriculum design, (ii) management of personnel, (iii) career planning, and (iv) planning in private life.

11 Planning of Medical Treatment

11.1 Preliminaries This chapter 1 addresses composing a medical treatment plan. Computeraided systems in medicine are widely used [3, 5, 68, 72, 73, 81, 134, 163, 166, 184, 220, 276, 314, 364, 365, 431, 474, 483, 575, 644, 661, 662, 728, 753, 776, 790, 820]. In the main, three kinds of problems have been studied: (a) medical diagnosis including image processing; (b) information/decision support in health care administrations (e.g., design and maintenance of various databases, planning); and (c) design and redesign of large distributed healthcare systems (networks, environments, services). A list of some new topics involves usage of discrete mathematics and optimization [217]. At the same time, the signiﬁcance of medical treatment planning is increasing (e.g. [204, 335, 347, 627, 743, 821, 891]). In the chapter, an applied example for medical treatment is described [515]. Initially, a one-stage composite decision is examined. We examine children’s asthma and composing medical and organizational actions into a global composite medical plan. The problem is signiﬁcant for many countries (e.g., USA, Europe, Japan, New Zealand) [185, 548, 743]. Our numerical example is only an illustrative one. The hierarchical model of the medical treatment, DAs and criteria correspond to a realistic situation, but our numbers (estimates, criteria weights, etc.) are only illustrative. At the same time, the example describes all parts and stages of a real solving process and can be used as a basic one in many real situations.

11.2 Medical Treatment 11.2.1 Structure of Medical Plan and Alternatives The structure of the composite medical plan examined is as follows: 1

Reprinted from M.Sh. Levin, L.V. Sokolova, Hierarchical Combinatorial Planning of Medical Treatment, Computer Methods and Programs in Biomedicine, 73(1), 3-11, 2004 (with minor amendments); with permission from Elsevier.

136

Composite Systems Decisions

0. Medical plan S = X Y Z. 1. Basic treatment X = J M . 1.1. Physical therapy J. 1.2. Drug treatment M . 2. Psychological and ecological environment Y = P H G. 2.1. Psychological climate P . 2.2. Home ecological environment H. 2.2. General ecological environment G. 3. Mode, rest and relaxation Z = O K. 3.1. Mode O. 3.2. Relaxation/rest K. The alternatives are as follows: J: none J0 , massage J1 , inhalation J2 , sauna J3 , reﬂexological therapy J4 , laser-therapy J5 , massage for special centers/points J6 , reﬂexological therapy for special centers J7 , halo-cameras or salt mines J8 , J9 = J1 &J2 , and J10 = J4 &J5 . M : none M0 , vitamins M1 , sodium chromoglycate (1 month and two times in a year) M2 , sodium chromoglycate (2 months) M3 , and sodium chromoglycate (3 months) M4 . P : none P0 and consulting of a psychologist P1 . H: none H0 , water cleaning H1 , to clean book dust H2 , to take away cotton wool things (blanket, pillow, mattress) H3 , to take away carpets H4 , to exclude contact with home animals H5 , to destroy cockroach environment H6 , and to take away ﬂowers H7 . G: none G0 and improving the area of the residence G1 . O: none O0 , relaxation at noon O1 , special physical actions (drainage, expectoration) O2 , sport (running, skiing, swimming) O3 , comfort showerbath O4 , cold shower-bath O5 , exclude electronic games O6 , O7 = O2 &O4 , and O8 = O3 &O5 . K: none K0 , a rest at forest-like environment K1 , a rest near the sea K2 , a rest in the mountains K3 , special camps K4 , and treatment in salt mines K5 . 11.2.2 Criteria and Estimates In medical treatment planning, criteria are based on long-term goals and shortterm objectives (e.g. [204]). The design of the criteria set is a special crucial problem. Here, let us consider criteria for the alternatives as follows (the criterion weight importance is shown in parentheses): Criteria for J: eﬀectiveness Cj1 (+5); cost Cj2 (−4); time period of treatment course Cj3 (−3); necessity to repeat the medical course Cj4 (−3); accessibility Cj5 (+5); and secondary eﬀects (complication) Cj6 (−5). Criteria for M : eﬀectiveness Cm1 (+5); cost Cm2 (−4); time period of treatment course Cm3 (−3); necessity to repeat the medical course Cm4 (−3); accessibility Cm5 (+5); and secondary eﬀects (complication) Cm6 (−5).

11 Planning of Medical Treatment

137

Criteria for P : eﬀectiveness Cp1 (+5); cost Cp2 (−6); and accessibility Cp3 (+5). Criteria for H: eﬀectiveness Ch1 (+5); cost Ch2 (−6); and accessibility Ch3 (+5). Criteria for G: eﬀectiveness Cg1 (+5); cost Cg2 (−6); and accessibility Cg3 (+5). Criteria for O: eﬀectiveness Co1 (+5); accessibility Co2 (+5); and secondary eﬀects (complication) Co3 (−3). Criteria for K: eﬀectiveness Ck1 (+5); cost Ck2 (−5); and time period of treatment course Ck3 (−5); necessity to repeat the medical course Ck4 (−3); accessibility Ck5 (+5); and secondary eﬀects (complication) Ck6 (−3). Tables 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, and 11.7 contain estimates of alternatives (DAs) and resultant priorities. Table 11.1 DAs and estimates (J) DAs

C1

C2

C3

C4

C5

C6

Priority

J0 J1 J2 J3 J4 J5 J6 J7 J8 J9 J10

0 2 1 2 3 3 4 4 4 3 4

0 4 1 3 4 4 5 5 3 4 5

0 1 1 1 1 1 3 3 1 1 1

0 1 1 1 1 1 1 1 1 1 1

0 4 5 1 3 2 1 1 2 2 2

0 1 2 3 4 3 1 3 3 3 4

2 2 2 3 3 3 3 4 2 2 3

Table 11.2 DAs and estimates (M ) DAs

C1

C2

C3

C4

C5

C6

Priority

M0 M1 M2 M3 M4

0 4 3 4 5

0 5 3 4 5

0 4 3 4 5

0 3 3 3 3

0 5 4 4 4

0 4 3 3 3

2 3 2 3 4

11.2.3 Compatibility of Local Decisions Compatibility estimates for local DAs are presented in Tables 11.8, 11.9, 11.10, and 11.11.

138

Composite Systems Decisions

Table 11.3 DAs and estimates (P ) DAs P0 P1

C1

C2

C3

Priority

0 4

0 5

0 2

3 2

Table 11.4 DAs and estimates (G) DAs G0 G1

C1

C2

C3

Priority

0 5

0 0

0 1

4 1

Table 11.5 DAs and estimates (H)

Table 11.6 DAs and estimates (O) DAs

DAs H0 H1 H2 H3 H4 H5 H6 H7

C1

C2

C3

Priority

0 3 3 4 3 5 4 4

0 1 3 2 2 4 3 2

0 5 4 4 5 3 3 4

3 1 2 1 1 2 2 1

O0 O1 O2 O3 O4 O5 O6 O7 O8

C1

C2

C3

Priority

0 2 3 5 4 5 3 4 5

0 5 4 3 3 3 3 3 3

0 0 0 3 1 4 2 1 4

3 1 1 1 1 2 2 1 2

Table 11.7 DAs and estimates (K) DAs K0 K1 K2 K3 K4 K5

C1

C2

C3

C4

C5

C6

Priority

0 4 4 4 3 4

0 3 5 5 4 4

0 3 3 3 2 1

0 3 3 3 3 3

0 4 4 3 3 1

0 2 2 1 1 2

2 2 3 4 3 3

11.2.4 Composite Decisions On the basis of priorities and compatibility, we will compute the best intermediate composite decisions: 1. For X (N (X) = (5; 0, 2, 0, 0)): X1 = J0 M2 , X2 = J1 M0 , X3 = J1 M2 , X4 = J2 M0 , X5 = J2 M2 , X6 = J8 M0 , X7 = J9 M0 , X8 = J9 M2 . 2. For Y (N (Y ) = (5; 2, 1, 0, 0)): Y1 = P1 H1 G1 , Y2 = P1 H4 G1 , Y3 = P1 H7 G1 . 3. For Z (N (Z) = (5; 2, 0, 0, 0)): Z1 = O1 K0 , Z2 = O1 K1 , Z3 = O2 K0 , Z4 = O2 K1 , Z5 = O3 K0 , Z6 = O3 K1 , Z7 = O4 K0 , Z8 = O4 K1 , Z9 = O7 K0 .

11 Planning of Medical Treatment

139

On the basis of expert judgment, we select the following local composite DAs (priorities are shown in parentheses): X6 = J8 M0 (1), X8 = J9 M2 (2), Y1 = P1 H1 G1 (1), Y2 = P1 H4 G1 (1), Y3 = P1 H7 G1 (1), Z2 = O1 K1 (2), Z6 = O3 K1 (1), Z8 = O4 K1 (1), Z9 = O7 K0 (1). Table 11.9 Compatibility

Table 11.8 Compatibility M0 M1 M2 M3 M4 J0 J1 J2 J3 J4 J5 J6 J7 J8 J9 J10

0 5 5 5 5 5 5 5 5 5 5

5 5 5 5 5 5 5 5 4 5 5

5 5 5 5 5 5 5 5 4 5 3

5 5 5 4 4 4 5 5 4 5 3

5 5 5 4 4 4 5 5 4 5 3

K0 K1 K2 K3 K4 K5 O0 O1 O2 O3 O4 O5 O6 O7 O8

0 5 5 5 5 5 5 5 5

5 5 5 5 4 5 5 4 3

5 5 5 5 4 5 5 4 5

5 5 5 5 4 5 5 4 3

5 5 4 5 4 5 5 4 5

5 5 5 5 4 5 5 4 4

Table 11.10 Compatibility G0 G1 H0 H1 H2 H3 H4 H5 H6 H7 P0 P1 G0 G1

0 5

5 5

0 4 0 4

5 5 5 5

5 5 5 5

4 4 4 4

5 5 5 5

4 4 4 4

5 5 5 5

5 5 5 5

Table 11.11 Compatibility Y1 Y2 Y3 Z2 Z6 Z8 Z9 X6 X8 Y1 Y2 Y3

5 5

4 4

5 4

5 5 5 4 5

3 5 5 4 5

1 5 5 4 5

2 5 5 4 5

Compatibility estimates of the selected DAs are presented in Table 11.11. As a result, we get the following two groups of composite decisions (Paretoeﬀective points): 1. N (S) = (5; 2, 1, 0, 0): S1 = X8 Y1 Z6 , S2 = X8 Y1 Z8 , and S3 = X8 Y1 Z9 . 2. N (S) = (3; 3, 0, 0, 0): S4 = X6 Y1 Z6 and S5 = X6 Y3 Z8 . Figure 11.1 contains the hierarchical model of the medical treatment plan, including DAs, composite DAs and priorities (in parentheses). Figure 11.2 depicts the discrete space of system excellence, the ideal point, and the abovementioned composite DAs (Pareto-eﬀective points) for the medical plan.

140

Composite Systems Decisions

NS = X Y Z S1 S2 S3 S4 S5

KX = J M X1 X2 X3 X4 X5 X6 X7 X8

H

= J0 M 2 = J1 M 0 = J1 M 2 = J2 M 0 = J2 M 2 = J8 M0 (1) = J9 M 0 = J9 M2 (2)

H

M J M0 (2) J0 (2) M1 (3) J1 (2) M2 (2) J2 (2) M3 (3) J3 (3) M4 (3) J4 (3) J5 (3) J6 (3) J7 (4) J8 (2) J9 = J1 &J2 (2) J10 = J4 &J5 (3)

H

P P0 (3) P1 (2)

= X 8 Y1 Z 6 = X 8 Y1 Z 8 = X 8 Y1 Z 9 = X 6 Y1 Z 6 = X 6 Y3 Z 8

K

KY = P H G

Z =OK Y1 = P0 H2 G1 (1) Z1 = O1 K0 Y2 = P0 H5 G1 (1) Z2 = O1 K1 (2) Y3 = P1 H0 G1 (1) Z3 = O2 K0 Z4 = O2 K1 Z5 = O3 K0 Z6 = O3 K1 (1) Z7 = O 4 K 0 Z8 = O4 K1 (1) Z9 = O7 K0 (1)

H

H H0 (3) H1 (1) H2 (2) H3 (1) H4 (1) H5 (2) H6 (2) H7 (1)

H

G G0 (4) G1 (1)

H

H

K O K0 (2) O0 (3) K1 (2) O1 (1) K2 (3) O2 (1) K3 (4) O3 (1) K4 (3) O4 (1) K5 (3) O5 (2) O6 (2) O7 = O2 &O4 (1) O8 = O3 &O5 (2)

Figure 11.1 Hierarchical model of medical treatment plan

11.3 Adaptation, Improvement, and Multistage Planning 11.3.1 Adaptation In previous sections, a hierarchical model of medical treatment is described, that includes a tree-like model, DAs, criteria, DA estimates, and compatibility estimates. Evidently, in each particular medical situation it is necessary to build a unique hierarchical model for the medical treatment plan while taking into account many facts (e.g., the patient kind, their family situation, the area of the patient residence). The proposed treatment model is a basic one. In each particular case it is reasonable to change the following: (a) the criteria set (to compress or to extend); (b) the weights of the criteria; (c) the sets of DAs for each leaf node of the model; (d) the estimates of the DAs; and (e) the compatibility estimates. The adaptation process is described in [497, 504].

11 Planning of Medical Treatment

141

Ideal point

D H S

N (S4 ), N (S5 )

S

S

K

K NS(S1 ), N (S2 )

S

S

S

S

S

S

S S

S

...

w=3

S S

N (S S3 ) S S

w=5

w=4

Figure 11.2 Space of system excellence and Pareto-eﬀective points 11.3.2 Improvement of Decisions The improvement process is based on the following: 1. Selection of composite decisions (some basic treatment plans) for the improvement. 2. Improvement of local DAs. 3. Improvement of compatibility between local DAs. Table 11.12 illustrates the improvement process. Note, real situations of improvements are based on special kinds of actions, e.g., additional ﬁnancial support will lead to increasing a quality of some DAs. Table 11.12 Bottlenecks and improvement actions Composite DAs Bottlenecks Actions w/r DAs IC S2 S2 S3 S4 S5

= X 8 Y1 Z 6 = X 8 Y1 Z 8 = X 8 Y1 Z 9 = X 6 Y1 Z 6 = X 6 Y3 Z 6

X8 X8 X8

(X6 , Z6 ) (X6 , Z6

2⇒1 2⇒1 2⇒1 3⇒5 3⇒5

11.3.3 Multistage Planning Several versions of the multistage design/planning are described in [497, 504]. The trajectory method is based on the examination of several series stages (preliminary stage, next stage, etc.). The method is a two-level hierarchical solving process consisting of two phases as follows: 1. Solving the problem (to design the treatment plan) at each stage.

142

Composite Systems Decisions

2. Composing the decisions for each stage into a series composite decision (trajectory). For example, the resultant trajectories can be as follows (Figure 11.3): β1 =< S11 , S42 , S33 >, β2 =< S31 , S22 , S53 >, where Sji is a composite DA, i corresponds to the stage number and j corresponds to the number of DAs at stage i.

S

β1 : S11 HH H H S21 HH 1 HH β2 : S3 0

1 4 S51

S13 S12 S23 S22 HH H 2 H S33 S3 HH 2 HH HH S43 S4 H 2 H S53 S5

-T

Stage 1 Stage 2 Stage 3 Figure 11.3 Illustration for multistage planning

11.4 Discussion 11.4.1 Towards Medical Decision Support Systems Medical diagnosis DSSs have been analyzed in [575]. The following approaches are the basic ones: 1. various expert and knowledge-based systems (e.g. [166, 276, 314, 410, 474, 728, 815, 848, 893]); 2. machine learning (e.g. [448]); 3. operational research techniques (e.g. [68]); and 4. multicriteria decision making (e.g. [72, 73, 220]). In recent years, computational intelligence techniques (i.e., contemporary artiﬁcial intelligence methods) have been used in medical diagnosis, including knowledge bases, expert systems, neural networks, neuro-fuzzy systems, evolvable systems (e.g. [728]). Uncertainty is a crucial part of medical diagnosis processes. As a result, contemporary approaches for modeling uncertain information (e.g., fuzzy sets or soft computing, Demster– Shafer theory, rough sets) are widely used in many medical DSSs (e.g. [893]). Our approach is oriented to a special complicated medical problem: one stage or multistage planning of medical treatment (i.e., decision synthesis). This problem corresponds to design of composite systems and is often based on the following engineering methods: (a) formal design methods; (b) expert systems; (c) operations research techniques (or the use of optimization models); (d) organizational procedures on the basis of expert judgment [119, 464, 497, 504]. In our opinion, this planning problem and patient monitoring problem will be more and more important in the near future. 11.4.2 Issues of Knowledge Acquisition In knowledge-based health-care organizations, there are the following three strategic information and knowledge processes (a knowing cycle): sense making, knowledge creation, and decision making [165]. On the other hand, the

11 Planning of Medical Treatment

143

following three domains are the basic ones in health systems [790]: (i) medical, (ii) organizational, and (iii) technological. Models for representing experience in computers are examined in [447]. Contemporary issues in automatic medical knowledge acquisition are described in [166]. Note, the following basic approaches for knowledge organization in medical systems are well known: (i) KADS methodology for the design of knowledge–based systems in hospital management [590]; (ii) medical knowledge: the PROforma approach [276]; and (iii) full and contradiction-free knowledge bases for medical diagnosis [278, 474, 776]. A key issue is the design of a task structure [143]. In our HMMD, we use a special kind of tree-like structure (And–Or tree with morphology of alternatives) that was suggested in [494, 497]. In our case, the knowledge acquisition procedure is based on the following principles: 1. Special tree-like structure (or knowledge hierarchy) of the problem (the task space) as partitioning the problem into simple subproblems. This is very useful for the domain expert (or several diﬀerent domain experts). 2. Usage of ordinal scales (useful for experts). 3. Possibility to check the problem formulation and local decisions for each subtask and each stage of the solving process. This check process can be based on a context analysis of all local decisions and it is a very good basis for feedback to redesigning the subproblems: (a) other estimates of DAs and IC; (b) other criteria sets; (c) other criteria weights; and (d) other problem structures (i.e., another tree-like model). Finally, the design issues of DSSs which are oriented to top-level specialists are signiﬁcant and require special approaches [105]. Medical DSSs for diagnosis and medical treatment can be considered as DSSs of the above-mentioned kind. Our hierarchical combinatorial approach is one of the eﬀorts in this new direction above.

11.5 Summary In this chapter, an application of our hierarchical combinatorial approach for planning of medical treatment has been described. Our example is mainly an illustrative one. This material can be used as a basic example for similar combinatorial eﬀorts in medicine.

12 Design of Immunoassay Technology

12.1 Preliminaries This chapter 1 addresses composing a immunoassay technology. The material focuses on the following [517]: (a) hierarchical morphological modeling of a composite biological technology and generation of the design alternatives for each stage of a ﬁve-stage system; and (b) design (composition or synthesis) of the optimal conditions for this multistage technology. The investigation is based on multicriteria decision making and combinatorial morphological models [49, 494, 497, 914] (i.e., HMMD) using modular design (e.g. [387, 464, 494, 497, 504, 576]). Note, combinatorial modeling has been applied to a number of ﬁelds [687].

12.2 Immunoassay Immunoassay technology remains one of the most widely applied analytical tools in immunology, biochemistry, and medicine [9, 139, 456, 462, 629, 640, 741, 881]. Many authors have studied the design of immunoassay technology [75, 124, 139, 256, 258, 259, 324, 456, 640, 665, 741, 791, 881]. The immunoassay is an analytical bioassay based on the use of antibodies for the immunological detection and measurement of analytes. The molecular selectivity of antibodies for their targets confers on the assay high speciﬁcity. Immunoassays have been used for over 40 years in a variety of formats [135]. The format studied in this section is the sandwich immunoassay, which consists of a number of steps schematically illustrated in Figure 12.1. The assay is based on the availability of several types of antibody. While immunoassay is today widely applied throughout biochemistry, biology, medical diagnostics and drug discovery, many of the parameters are often not optimized. 1

Reprinted from M.Sh. Levin, M.A. Firer, Hierarchical Morphological Design of Immunoassay Technology, Computers in Biology and Medicine, 35(3), 229-245, 2005 (with minor amendments); with permission from Elsevier.

146

Composite Systems Decisions

Wash ⇒

(a) Coating of plastic support (b) Only bound antibody with capture antibody retained Stage 1.

D K

KD

D K

Wash D K KD KD ⇒ (a) Blocking uncoated sites on (b) Plastic support coated plastic with irrelevant protein Stage 2.

KD

KD

♦

KD

⊕

Wash ⇒ ♦ ♦ ♦ D♦ K KD ♦ KD ♦ KD KD KD (a) Add target analyte mixture (b) Target is captured by antibody Stage 3. ⊗ ⊗ Wash ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⇒ ♦ ♦ ♦ ♦ ♦ KD♦ K D K D KD KD KD (a) Add signal-labeled 2nd (b) Only target-bound 2nd antibody antibody retained Stage 4. ♣

KD♦

♣

KD ♦

♣

KD ♦

Stage 5. Signal activation and detection Figure 12.1 Scheme of the sandwich type of immunoassay

12.3 Structure of Immunoassay System The following hierarchical structure of our immunoassay system is examined: 0. System: S = H B I D M . 1. Stage 1: H = P Q. 1.1. Phase coating: P . 1.2. Wash: Q. 2. Stage 2 (blocking): B.

12 Design of Immunoassay Technology

147

3. Stage 3: I = O T . 3.1. Sample incubation: O. 3.2. Wash: T . 4. Stage 4: D = J E. 4.1. Detection of sample: J. 4.2. Wash: E. 5. Stage 5 (measurement): M .

12.4 Numerical Example 12.4.1 Alternative Local Decisions Now we consider stage 1. The morphological table that generates DAs for component coating P is presented in Table 12.1. As a result, ﬁve DAs were selected P1 , P2 , P3 , P4 , and P5 . The priorities of these DAs based on expert judgment are presented in Section 12.6. Table 12.2 presents three DAs for Q: Q1 , Q2 , and Q3 . The priorities of these DAs are based on expert judgment. The following abbreviations, used in Tables 12.2, 12.3, 12.5, and 12.6, have the meanings as follows: phosphate-buﬀered saline (PBS), bovine serum albumin (BSA), tween (Tw). The information for stage 2 is as follows. Table 12.3 presents four DAs for B (blocking): B1 , B2 , B3 , and B4 . The following two criteria to evaluate the DAs are used: (1) K1 time (minimal value is the best one; hour), the assessment scale is the following: 0.5, 1.0, 2.0; (2) K2 low background or quality (minimal value is the best one; %), the assessment scale is the following: 1%, 5%, 10%; Estimates and resultant priorities (on the basis of multicriteria computing) are presented in Table 12.4. Our examination for stage is as follows. Table 12.5 presents ﬁve DAs for O (sample incubation): O1 , O2 , O3 , O4 , and O5 . Priorities of these DAs are based on expert judgment. For stage 4 we get the following. Table 12.6 presents ﬁve DAs for J (sample incubation): J1 , J2 , J3 , and J4 . Priorities of these DAs based on expert judgment. Finally, stage 5 is examined. Table 12.7 presents four DAs for M (measurement): M1 , M2 , M3 , and M4 . The following two criteria to evaluate the DAs are used: (1) K1 cost (ordinal scale: high, medium, low; weight equals 3); (2) K2 time (hours, minimal value corresponds to the best one; hour; weight equals 5); and (3) K3 easy to perform (ordinal scale: diﬃcult, moderate, easy; weight equals 5). The estimates and resultant priorities (on the basis of multicriteria computing) are presented in Table 12.8.

148

Composite Systems Decisions

Table 12.1 Morphological generation of DAs for P Property 1. Biological: (a) Protein (b) Lipid (c) Nucleic acid 2. Biochemical (I): (a) Small (b) Large 3. Biochemical (II): (a) Hydrophobic (b) Hydrophilic 4. Concentration (µg/ml): (a) 0.5 (b) 1 (c) 2 (d) 4 (e) 8 (f) 16 5. Kind of plastic: (a) PVP (b) PS 6. UV pretreatment of plastic: (a) None (b) Low (c) High 7. Solvent: (a) Solire (b) Water (c) Phosphate (d) Carbonate (e) Methanol 8. Type of bonding to solid phase: (a) Covalent (b) Non-covalent 9. Time of incubation (h): (a) 0.5 (b) 2 (c) 8 (d) 16 10. Temperature of incubation ( o C): (a) 4 (b) Ambient (c) 37 11. Special mixing process: (a) None (b) Rotation (c) Shaking

P1

P2

*

P3

P4

*

*

P5

* *

*

*

*

*

*

*

*

*

*

*

* * * *

*

*

*

*

*

*

*

*

*

*

*

*

*

* *

* *

*

*

*

*

*

*

*

*

* *

*

*

*

*

*

*

*

*

*

12 Design of Immunoassay Technology

Table 12.2 Morphological generation of DAs for Q (analogous for T /E) Property

Q1 Q2 Q3

1. Type of solution: (a) Water (b) PBS/detergent * (c) PBS 2. Number of cycles: (a) 1 (b) 2 (c) 3 * (d) 4 3. Time of each cycle: (min): (a) 0.5 (b) 1 (c) 3 * (d) 5

* *

* *

*

*

Table 12.3 Morphological generation of DAs for B Property 1. Solution: (a) PBS/glycine (b) PBS/detergent (c) PBS – 1% BSA 2. Time of incubation (hour): (a) 0.5 (b) 1 (c) 2 3. Temperature of incubation ( o C): (a) 4 (b) Ambient (c) 37

B1 B2 B3 B4 * * *

*

*

* *

*

* *

*

*

149

150

Composite Systems Decisions

Table 12.4 Estimates and priorities for B DAs K1 K2 Priority B1 B2 B3 B4

1 0.5 1 2

10 1 10 10

2 1 2 3

Table 12.5 Morphological generation of DAs for O Property 1. Volume of sample: (a) 50 (b) 100 (c) 200 2. Incubation time and temperature: (a) 4 (b) Ambient (c) 37 3. Lower limit of (concentration µg/ml): (a) 0.01 (b) 1 (c) 10 4. Higher limit of (concentration µg/ml): (a) 10 (b) 100 (c) 1000 5. Characteristics of the solution used (proportion): (a) Pure (b) Simple mixture (c) Complex mixture 6. Type of sample: (a) Serum (b) Culture ﬂuid (c) PBS or similar 7. Characteristic of sample: (a) PBS (b) PBS/BSA/Tw (c) PBS/animal serum/Tw

O1 O2 O3 O4 O5 *

* *

* *

*

*

*

*

*

*

*

*

*

*

*

*

* *

*

*

* *

* *

*

* *

*

* *

*

*

*

*

12 Design of Immunoassay Technology

Table 12.6 Morphological generation of DAs for J Property 1. Type of physical signal (attached to detection): (a) Radio (b) Fluorescent (c) Biological 2. Incubation time (hour): (a) 0.5 (b) 1 (c) 2 (d) 6 3. Incubation temperature ( o C): (a) 4 (b) Ambient (c) 37 4. Characteristic of solution (proportion): (a) PBS (b) PBS/BSA/Tw (c) PBS/animal serum/Tw

J1 J2 J3 J4

* * *

*

* * * *

* *

*

* *

*

*

*

Table 12.7 Morphological generation of DAs for M Property

M1 M2 M3 M4

1. Type of signal generated: (a) Radiation * (b) Flourescent (c) Chemical illuminescence (d) Colorometric 2. Type of detection apparatus: (a) Scintillator counter * (b) Flourometer (c) Light emission (d) Spectrometer 3. Time of measurement (hour): (a) 0.1 (b) 0.15 (c) 0.5 (d) 1.0 *

* * *

* * * *

* *

151

152

Composite Systems Decisions

Table 12.8 Estimates, priorities for M DAs

K1

K2

M1 M2 M3 M4

High Mod Mod Low

1.0 0.1 0.1 0.15

K2

Priority

2 3 2 3

3 1 2 1

12.4.2 Compatibility of Local Decisions Compatibility estimates for local DAs are presented in Tables 12.9, 12.10, and 12.11. Table 12.9 Compatibility P1 P2 P3 P4 P5 Q1 Q2 Q3

3 3 1

Table 12.10 Compatibility

2 1 1

2 2 1

2 2 2

2 2 2

2 1 1

2 2 2

2 1 1

1 3 0

Table 12.11 Compatibility J1 J2 J3 J4

O1 O2 O3 O4 O5 T1 T2 T3

2 1 1

E1 E1 E3

2 2 2

2 2 2

2 2 2

2 2 2

12.4.3 Design of Composite Decisions for Stages Let us now consider composite DAs for stage 1 H, stage 3 I, and stage 4 D. The composite DAs for H are as follows: H1 = P1 Q1 , N (H1 ) = (3; 2, 0, 0), H2 = P1 Q2 , N (H2 ) = (3; 1, 1, 0), H3 = P1 Q3 , N (H3 ) = (1; 1, 0, 1), H4 = P2 Q1 , N (H4 ) = (2; 1, 1, 0), H5 = P2 Q2 , N (H5 ) = (1; 0, 2, 0), H6 = P2 Q3 , N (H6 ) = (1; 0, 1, 1), H7 = P3 Q1 , N (H7 ) = (2; 1, 1, 0), H8 = P3 Q2 , N (H8 ) = (2; 0, 2, 0), H9 = P3 Q3 , N (H9 ) = (1; 0, 2, 0), H10 = P4 Q1 , N (H10 ) = (2; 1, 0, 1), H11 = P4 Q2 , N (H11 ) = (1; 0, 1, 1), H12 = P4 Q3 , N (H12 ) = (1; 0, 0, 2), H13 = P5 Q1 , N (H13 ) = (1; 1, 0, 1), H14 = P5 Q2 , N (H14 ) = (3; 0, 1, 1), and H15 = P5 Q3 , N (H15 ) = (0; 0, 0, 2). First, we delete H15 as the impossible decision. Second, we select the following best decisions: (a) ideal decision H1 , priority equals 1; (b) H4 and H7 , priority equals 2; (c) H2 , H10 , H11 , and H13 , priority equals 3. The composite DAs for I are as follows: I1 = O1 T1 , N (I1 ) = (2; 2, 0, 0), I2 = O1 T2 , N (I2 ) = (2; 1, 1, 0), I3 = O1 T3 , N (I3 ) = (2; 1, 0, 1), I4 = O2 T1 , N (I4 ) = (2; 2, 0, 0), I5 = O2 T2 , N (I5 ) = (2; 1, 1, 0), I6 = O2 T3 , N (I6 ) = (2; 1, 1, 0), I7 = O3 T1 , N (I7 ) = (2; 2, 0, 0), I8 = O3 T2 , N (I8 ) = (1; 1, 1, 0),

12 Design of Immunoassay Technology

153

I9 = O3 T3 , N (I9 ) = (1; 1, 0, 1), I10 = O4 T1 , N (I10 ) = (2; 2, 0, 0), I11 = O4 T2 , N (I11 ) = (2; 1, 1, 0), I12 = O4 T3 , N (I12 ) = (2; 1, 0, 1), I13 = O5 T1 , N (I13 ) = (2; 2, 0, 0), I14 = O5 T2 , N (I14 ) = (1; 1, 1, 0), and I15 = O5 T3 , N (I15 ) = (1; 1, 0, 1). It is reasonable to select the following best decisions (priorities equal 1): I1 , I4 , I7 , I10 , and I13 . The composite DAs for D are as follows: D1 = J1 E1 , N (D1 ) = (2; 2, 0, 0), D2 = J1 E2 , N (D2 ) = (2; 1, 1, 0), D3 = J1 E3 , N (D3 ) = (2; 1, 0, 1), D4 = J2 E1 , N (D4 ) = (2; 2, 0, 0), D5 = J2 E2 , N (D5 ) = (2; 1, 1, 0), D6 = J2 E3 , N (D6 ) = (2; 1, 0, 1), D7 = J3 E1 , N (D7 ) = (2; 2, 0, 0), D8 = J3 E2 , N (D8 ) = (2; 1, 1, 0), D9 = J3 E3 , N (D9 ) = (2; 1, 0, 1), D10 = J4 E1 , N (D10 ) = (2; 2, 0, 0), D11 = J4 E2 , N (D11 ) = (2; 1, 1, 0), and D12 = J4 E3 , N (D12 ) = (2; 1, 0, 1). It is reasonable to select the following best decisions (priorities equal 1): D1 , D4 , D7 , and D10 . 12.4.4 System Structure with Design Alternatives Thus, the hierarchical structure of immunoassay technology (consisting of ﬁve series stages, priorities of DAs are shown in parentheses, components Q, T , and E are equivalent ones) is as follows: 0. System: S = H B I D M . 1. Stage 1: H = P Q. Composite DAs: H1 = P1 Q1 (1), H4 = P2 Q1 (2), H7 = P3 Q1 (2), H2 = P1 Q2 (3), H10 = P4 Q1 (3), and H13 = P5 Q2 (3). 1.1. Phase coating: P . DAs: P1 (1), P2 (2), P3 (2), P4 (3), and P5 (3). 1.2. Wash: Q. DAs: Q1 (1), Q2 (2), and Q3 (3). 2. Stage 2 (blocking): B. DAs: B1 (2), B2 (1), B3 (2), and B4 (3). 3. Stage 3: I = O T . Composite DAs: I1 = O1 T1 (1), I4 = O2 T1 (1), I7 = O3 T1 (1), I10 = O4 T1 (1), and I13 = O5 T1 (1). 3.1. Sample incubation: O. DAs: O1 (1), O2 (1), O3 (1), O4 (1), and O5 (1). 3.2. Wash: T . DAs: T1 (1), T2 (2), and T3 (3). 4. Stage 4: D = J E. Composite DAs: D1 = J1 E1 (1), D4 = J2 E1 (1), D7 = J3 E1 (1), and D10 = J4 E1 (1). 4.1. Detection of Sample: J. DAs: J1 (1), J2 (1), J3 (1), and J4 (1). 4.2. Wash: E. DAs: E1 (1), E2 (2), and E3 (3). 5. Stage 5 (measurement): M . DAs: M1 (3), M2 (1), M3 (2), and M4 (1).

154

Composite Systems Decisions

12.4.5 Compatibility for Stages Compatibility estimates for H and B, I, D, and M are presented in Table 12.12. Compatibility equals 3 for other pairs: (1) B and I, D, M ; (2) I and D, M ; and (3) D and M . Table 12.12 Compatibility B1 B2 B3 B4 I1 I4 I7 I10 I13 D1 D4 D7 D10 M1 M2 M3 M4 H1 H4 H7 H2 H10 H12

1 1 1 1 1 0

3 0 3 3 3 0

1 0 1 1 1 0

2 0 2 2 2 0

3 2 3 3 3 2

3 2 3 3 3 2

3 3 3 3 3 3

3 3 3 3 3 3

3 3 3 3 3 3

3 2 3 3 3 2

3 2 3 3 3 2

3 3 3 3 3 3

3 3 3 3 3 3

3 2 3 3 3 2

3 2 3 3 3 2

3 3 3 3 3 3

3 3 3 3 3 3

12.4.6 Resultant Composite Decisions Now we can obtain the following 40 composite DAs for immunoassay technology (N = (3; 5, 0, 0)): S1 = H1 B2 I1 D1 M2 , S2 = H1 B2 I1 D4 M2 , S3 = H1 B2 I1 D7 M2 , S4 = H1 B2 I1 D10 M2 , S5 = H1 B2 I4 D1 M2 , S6 = H1 B2 I4 D4 M2 , S7 = H1 B2 I4 D7 M2 , S8 = H1 B2 I4 D10 M2 , S9 = H1 B2 I7 D1 M2 , S10 = H1 B2 I7 D4 M2 , S11 = H1 B2 I7 D7 M2 , S12 = H1 B2 I7 D10 M2 , S13 = H1 B2 I10 D1 M2 , S14 = H1 B2 I10 D4 M2 , S15 = H1 B2 I10 D7 M2 , S16 = H1 B2 I10 D10 M2 , S17 = H1 B2 I13 D1 M2 , S18 = H1 B2 I13 D4 M2 , S19 = H1 B2 I13 D7 M2 , S20 = H1 B2 I13 D10 M2 , S21 = H1 B2 I1 D1 M4 , S22 = H1 B2 I1 D4 M4 , S23 = H1 B2 I1 D7 M4 , S24 = H1 B2 I1 D10 M4 , S25 = H1 B2 I4 D1 M4 , S26 = H1 B2 I4 D4 M4 , S27 = H1 B2 I4 D7 M4 , S28 = H1 B2 I4 D10 M4 , S29 = H1 B2 I7 D1 M4 , S30 = H1 B2 I7 D4 M4 , S31 = H1 B2 I7 D7 M4 , S32 = H1 B2 I7 D10 M4 , S33 = H1 B2 I10 D1 M4 , S34 = H1 B2 I10 D4 M4 , S35 = H1 B2 I10 D7 M4 , S36 = H1 B2 I10 D10 M4 , S37 = H1 B2 I13 D1 M4 , S38 = H1 B2 I13 D4 M4 , S39 = H1 B2 I13 D7 M4 , and S40 = H1 B2 I13 D10 M4 .

12.5 Summary The material of the chapter addresses optimal design of the immunoassay technology on the basis of HMMD. Evidently, this applied example can be used to examine similar composition problems in combinatorial chemistry.

13 Common Part of Digraphs

13.1 Preliminaries In this chapter, we examine the largest common part of digraphs [506]. Digraphs (preference relations, posets, scales) are deﬁned over the same set of vertices (e.g., alternatives). The nature of arcs can be of various kinds in diﬀerent digraphs. In the general case, the problem considered is NP-hard [281]. Note, similar problems are very important for the deﬁnition of similarity/dissimilarity of structures in many domains: (a) mathematical psychology and social sciences (e.g. [94, 320, 429, 589, 838]); (b) decision making and expert judgment (e.g. [179, 374, 497, 670]); (c) chemistry and biology (e.g. [25, 160, 201, 241, 351, 466, 585, 586, 655, 672, 692, 767, 812, 883]); (d) information processing and retrieval (e.g. [99, 230–232, 330, 392, 407, 459, 518, 570, 855, 874]); and (e) artiﬁcial intelligence, e.g. knowledge structures [522, 596, 657, 871]. Closely related problems have been studied for preference relations and posets in [687] and for various kinds of hierarchies (trees, etc.) in [25, 99, 241, 318, 546, 586, 692, 871]. The problem of integration/aggregation for preference relations is similar to building a consensus [62, 160, 179, 318, 374, 403, 418, 429, 497, 585, 687]. In the main, the following three basic approaches for graphs (structures) are investigated and used: (i) some traditional metrics/distances [65, 94, 99, 231, 319, 320, 392, 497, 570, 582, 584, 670, 687, 838, 871, 874]; (ii) minimum cost transformation of a structure into another one (or graph edit distance) [60, 125, 351, 655, 745, 811, 908], for example, rotation distance for binary trees [167, 190, 542, 630]; and (iii) maximum common substructure/maximum agreement substructure [19, 25, 54, 125, 126, 253, 383, 466, 518, 559, 596, 645, 655, 672, 673, 747, 767, 789, 812, 819, 868, 883]. At the same time, our problem has to be examined as an approximation of a hypergraph by an ordinary digraph (e.g. [79, 154]). This case is faced

156

Composite Systems Decisions

when n digraphs are considered, because at the ﬁrst stage the initial digraphs can be transformed into a hypergraph. In the book, a new special condition for graph elements of common parts is proposed. Our solving process consists of several stages. The selection of arcs and vertices for the common part, while taking into account the condition above, is reduced to a morphological clique problem, i.e., a hierarchical morphological approach [494, 497]. The material describes the problem for two digraphs [511] and its extension for an n-digraph problem [506]. Concurrently, we consider ordinal weights for comparison of diﬀerent digraph arcs. Our numerical examples demonstrate the problems and solving processes.

13.2 Common Part of Two Digraphs 13.2.1 Problem Formulation This section is an extension of the problem for two digraphs which was described in [511]. Let H1 = (U, V1 ) and H2 = (U, V2 ) be two digraphs (posets) with the same set of vertices U and diﬀerent sets of arcs V1 and V2 . Let H0 = (U0 , V0 ) (U0 ⊆ U , V0 ⊆ V1 , V0 ⊆ V2 ) be a resultant digraph. The problem is (Figure 13.1):

' ' &&

$ $ %%

Find the largest common subgraph or the best approximation of it.

H1

H0

H2

Figure 13.1 Illustration for coordination of two digraphs Let us consider the following two stages:

Phase 1. Analysis of H1 , H2 and their dissimilarity. In this case, when the dissimilarity is big we get the claim that the result is negative. Phase 2. Building the common subgraph. Figure 13.2 depicts two linear ordered digraphs with the maximum dissimilarity. In the general case, maximum dissimilarity corresponds to the following situation: (i) elements of V1 and V2 connect the same vertices; (ii) the orientations of arcs in V1 and in V2 are inverse. An example of structures with maximum dissimilarity is the following: in-tree and out-tree (i.e., two trees are deﬁned on the same set of vertices while there is inverse orientation of arcs).

13 Common Part of Digraphs

H2

H

H

H

H

H

H

1

2 -H

3 -H

4 -H

5 -H

6 -H

H

157

H1 Figure 13.2 Illustration for maximum dissimilarity Here we consider the second phase above with the following two objective functions: max |U0 | and max |V0 |. It is reasonable to examine a situation when H0 does not lead to some contradiction. This requirement is used as a constraint in the optimization problem. Figure 13.3 depicts the following contradiction: arcs (2, 1) and (4, 3) are the same in graphs H1 and H2 , but arc (1, 3) in H1 and arc (3, 1) in H2 have diﬀerent orientations. Figure 13.3c demonstrates all possible edges with the possible contradiction for the arcs (2, 1) and (4, 3). Thus, our vector-like objective function for the resultant digraph H0 = (U0 , V0 ) is (|U0 |, |V0 |). Let us consider the numerical example above (Figure 13.3) from the viewpoint of preference relations (i.e., for a decision-making situation): digraph H1 corresponds to expert 1, digraph H2 corresponds to expert 2; a traditional common part of these digraphs consists of two common arcs (2, 1) and (4, 3), i.e., H1 &H2 = ({1, 2, 3, 4}, {(2, 1), (4, 3)}). At the same time, this digraph contains a possible contradiction over the vertices 1 and 3. On the other hand, digraphs H0 = ({1, 2, 4}, {(2, 1)}) and H0 = ({2, 3, 4}, {(4, 3)}) do not contain a possible contradiction over the above-mentioned vertices. 1

H1 -H 3 6 6

2

H

H

(a)

H

4

1 H 6

H2

1

H

2 H 4 (b) Figure 13.3 Source of contradictions

H

2

H

3 6

H

6 @ @

3 6

H

@H 4 (c)

Figure 13.4 illustrates this case for two digraphs. Point a corresponds to the problem above. Here, we assume a part of arc set (V1 &V2 ) cannot be taken into account. So, the problem is to deﬁne these arcs. Interestingly, we get an auxiliary knapsack-like problem on a subset of arcs which leads to the above-mentioned contradiction. In the case of n digraphs, the corresponding levels for axis V0 are the following: (i) |&m l=1 Vl | and (ii) max1≤l≤m {Vl }. Here, the following approach is used (basic heuristic solving scheme): Stage 1. Analysis of digraphs and their dissimilarity. A big dissimilarity leads to the claim of a negative result, and STOP. Stage 2. Building a common digraph with a maximum number of arcs (or weighted arcs, etc.) while taking into account the contradictions above. Stage 3. Enlargement of the resultant common digraph by maximum additional admissible vertices (or weighted vertices) while taking into account the contradictions above.

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|U0 |

6

H

|U |

Pareto-eﬀective points

K

K

H H AH a

|V0 | |V1 &V2 | max(|V1 |, |V2 |) Figure 13.4 Vector-like objective for coordination of two digraphs The basic problem examined can be generalized in the following way: 1. increasing the number of vertices (5, ..., k); 2. usage of special binary relations on vertices and for comparison of arcs in diﬀerent digraphs; and 3. increasing the number of digraphs. 13.2.2 Basic Relations Let us consider simple cases for three and four vertices. For the case of three vertices {1, 2, 3} (two corresponding digraphs H1 , H2 ) we consider two basic vertex pairs: (i) 1 and 2 and (ii) 1 and 3. The basic condition is that arcs for basic vertex pairs are the same in both digraphs (H1 and H2 ). Situation with contradiction: for the vertex pair (2, 3) there exists arc e that has a diﬀerent direction in H1 and H2 . Situation without contradiction: for the vertex pair (2, 3), arc e has the same direction for both digraphs or is absent (in one digraph and both digraphs). For the case of four vertices {1, 2, 3, 4} and digraphs H1 and H2 , we examine two basic vertex pairs as follows: (a) 1 and 2 and (b) 3 and 4 (Figure 13.3). The basic condition is that arcs for basic vertex pairs are the same in both digraphs (H1 and H2 ). Situation with contradiction: there exists a vertex pair in {(1, 3), (1, 4), (2, 3), (2, 4)} where corresponding arcs in H1 and H2 have diﬀerent directions. Situation without contradiction: in the set of vertex pairs {(1, 3), (1, 4), (2, 3), (2, 4)}, each arc has the same direction in both digraphs or is absent (in one digraph and both digraphs). Now we consider case the for k vertices. The set of vertices is: U = {1, ..., k}. The set of all vertex pairs is: B = B ∪ B ∗ , (| B&B ∗ |= 0), where B is a basic set of vertex pairs (with the same orientation for both digraphs) and B ∗ is an additional set of vertex pairs. Note, our two digraphs are: H1 = (U, V1 ), H2 = (U, V2 ), V1 = V2 and V1 ∈ B, V2 ∈ B, B ∈ V1 , B ∈ V2 . Here, the basic condition is (u1 , u2 ∈ U ): ∀(u1 , u2 ) ∈ B the corresponding arc e is the same in H1 and H2 .

13 Common Part of Digraphs

159

Situation with contradiction: there exists a vertex pair (u1 , u2 ) ∈ B ∗ that corresponding arcs v1 ∈ V1 and v2 ∈ V2 are diﬀerent (i.e., have diﬀerent directions). Situation without contradiction: ∀(u1 , u2 ) ∈ B ∗ the following holds for the corresponding arcs: (i) the same arc: v ∈ V1 and v ∈ V2 ; (ii) v ∈ V1 and the corresponding arc in V2 is absent; (iii) v ∈ V2 and the corresponding arc in V1 is absent; (iv) corresponding arcs are absent.

H * 2 B H 1 HH jH 3 H

H 2 * H1 H 1 HH jH?3 H

2 *H6 H2 H 1 HH jH 3 H (a)

1 B

6 @ I @H5 H? 2 3 H -H 4 H

H

1 H H 6 *@ H1 I @H5 ? H 2 3 H -H 4 1 6 H *H H2 I @H5 @ H? 2 3 H -H 4 (b) Figure 13.5 Digraph examples

B

H 5 I @ @H 4 1H 6 2 H? H 3

H 5 H1 @ I @H 4 1 HH@ @ H 2? jH63 H H

H2 1 2

H 5 @ I @H 4 Y@ H @ H 6 H? HH 3 (c) H

Now we can consider examples: Example 1 (Figure 13.5a): U = {1, 2, 3}, B = {(1, 2), (1, 3)}, B ∗ = {(2, 3)}. Example 2 (Figure 13.3): U = {1, 2, 3, 4}, B = {(1, 2), (3, 4)}, B ∗ = {(1, 3), (1, 4), (2, 3), (2, 4)}. Example 3 (Figure 13.3): U = {1, 2, 3, 4}, B = {(1, 2), (1, 4), (3, 4)}, B ∗ = {(1, 3)(2, 3), (2, 4)}. Example 4 (Figure 13.5b): U = {1, 2, 3, 4, 5, 6}, B = {(1, 2), (3, 4), (5, 6)}, B ∗ = {(1, 5), (1, 6), (2, 5), (2, 6), (1, 3), (1, 4), (2, 3), (2, 4), (3, 5), (3, 6), ((4, 5), (4, 6)}. Example 5 (Figure 13.5c): U = {1, 2, 3, 4, 5}, B = {(1, 2), (3, 4), (1, 5), (4, 5)}, B ∗ = {(2, 3), (1, 3), (1, 4), (2, 4), (2, 5), (3, 5)}. As a result, it is possible to formulate our problem as follows. Let U0 ⊆ U and a common part H0 = (U0 , V0 ), V0 ⊆ V1 and V0 ⊆ V2 . The problem is: Find H0 such that: (1) H0 is the largest by two criteria (i.e., H0 corresponds to the Paretoeﬀective decision(s)): (i) | U0 |→ max and (ii) | V0 |→ max. (2) The basic set of vertex pairs V0 corresponds to situation without contradiction.

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Thus, we search for the required common part of digraphs as a solution of a two-criteria optimization problem and this solution corresponds to a set of Pareto-eﬀective decisions (one or more). Figure 13.6 depicts common parts for the examples (Examples 1, 4, and 5) from Figure 13.5. The solutions are: Example 1 (Figure 13.6a): H0 and H0 . Example 4 (Figure 13.6b): H0 . Example 5 (Figure 13.6c): H0 . H0 H 1 HH jH 3 H * H0 H 1 (a)

H

H0

6 @ I @H5 3 H -H 4

H

1

H

H0 2

H

H 5 @ I @H 4 6 H 3

1 H 5 6 H *H H0 H0 H H? 1 2 2 H? 3 H -H 4 (c) (b) Figure 13.6 Examples of common parts

2

Thus, we consider the following algorithm: Step 1. Selection of arcs with the same orientation: V = V1 &V2 (note: V = B). Step 2. Building (on the basis of V ) a preliminary common digraph without the contradictions above. Step 3. Analyzing the set of vertices which are not connected with vertices corresponding to V . Selection of vertices without contradiction. The addition of the set to the result of Step 2.

Note, Step 2 can be realized on the basis of the morphological clique problem because we can deﬁne for each pair from V the possible contradiction (incompatibility); we formulate the morphological clique problem as follows: 1. Each element of V is considered as a subsystem. 2. For each element of V we deﬁne two DAs: (i) inclusion into the resultant graph (priority equals 1, index 2 for DA) and (ii) rejection (priority equals 2, index 1 for DA). 3. For each pair of elements of V the compatibility is deﬁned as follows: 0 corresponds to the contradiction, 1 corresponds to an admissible case. A numerical example now follows. Figure 13.7 depicts two digraphs. Contradictions for vertices 2 and 3, 3 and 4, 5 and 6 are shown for graph H1 . Further, we study a system consisting of the following seven components: A, DAs: A1 , A2 ; B, DAs: B1 , B2 ; C, DAs: C1 , C2 ; D, DAs: D1 , D2 ; E, DAs: E1 , E2 ; F, DAs: F1 , F2 ; and G, DAs: G1 , G2 . Compatibility estimates are presented in Table 13.1. Now we get the following composite DAs: S1 = A2 B1 C1 D2 E2 F2 G1 , N (S1 ) = (1; 4, 3); S2 = A2 B1 C1 D2 E2 F1 G2 , N (S2 ) = (1; 4, 3).

13 Common Part of Digraphs

161

H2 AH 1 a b @ d 2 3A@ 4 ? RH H H A @ P PP c A @ e PP PP A @ PP AUH q @ RH H 5@ 6 7 g f@ H @ R H H 8 9 10

H1 H 1 a b @ d 2 3@ 4 @ RH -? H H @ @ e @ c @ @ @ @ R? @ RH @ RH H 5@ 6 7 g f@ -H @ RH H9 8 10

Figure 13.7 Two digraphs Table 13.1 Compatibility of DAs B1 B2 C1 C2 D1 D2 E1 E2 F1 F2 G1 G2 A1 A2 B1 B2 C1 C2 D1 D2 E1 E2 F1 F2

1 1

1 0

1 1 1 1

1 0 1 1

1 1 0 1 1 1

1 1 1 1 1 0

1 1 1 1 1 1 1 1

1 1 1 1 1 0 1 1

1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 0

Thus, resultant versions of preliminary common digraph H0 are the following: H0 = ({1, 2, 4, 7, 5, 8}, {a, d, e, f }) and H0 = ({1, 2, 4, 7, 6, 8}, {a, d, e, g}). Analogically we can realize step 3 of the algorithm: to consider vertices as subsystems, and to select a subset without contradictions. For our example, we have to add vertices 9 and 10. Resultant common digraphs are the following (Figure 13.8): H0 = ({1, 2, 4, 7, 5, 8, 9, 10}, {a, d, e, f }) and H0 = ({1, 2, 4, 7, 6, 8, 9, 10}, {a, d, e, g}). Let us consider complexity (by operations) of the algorithm. Complexity of step 1 equals O(m2 ). Complexity of step 2 (step 3) corresponds to complexity of dynamic programming approach for knapsack problem (O(2m ), m is the number of vertices).

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1 H H a @ d @ 4 2 @ RH H @ e @ @ RH H 5@ 7 f@ @ RH H9 H 8 10

1 H H a @ d @ 4 2 H @ RH @ e @ H @ RH 6 7 g 8

H

H

9

H

10

Figure 13.8 Resultant digraphs

13.2.3 Ordinal Weights of Arcs and Comparison Binary Relation Now let us examine relations on vertices. The basic case was used in the previous section as follows (u1 , u2 ∈ U ): (i) u1 → u2 (→); (ii) u1 ← u2 (←); and (iii) the arc is absent (−). We denote this case X 0 . Figure 13.9a depicts this case, where c corresponds to contradiction and corresponds to a concordance of two arcs in H1 and H2 . Here, a description of an arc on the same two vertices in H1 and H2 is very simple: (a) contradiction and (b) concordance. We will denote this binary relation (comparison relation) as Y 0 . Figure 13.9b depicts another case where c corresponds to contradiction, corresponds to a concordance of two arcs in H1 and H2 , and wd corresponds to weak diﬀerence (or weak contradiction). Thus, the following ordinal scale is used: big diﬀerence or contradiction, weak diﬀerence, concordance or equivalence. We will denote the comparison relation in this case as Y 1 ({c, wd, }). On the other hand, it is reasonable to consider a case when an arc (u1 , u2 ∈ U ) has weights with the following scale: (i) u1 ⇒ u2 (strong preference) (⇒); (ii) u1 → u2 (preference) (→); (iii) u1 ← u2 (←); and (preference with the inverse direction) (iv) u1 ⇐ u2 (⇐); and (strong preference with the inverse direction) (v) the arc is absent (−). We denote this case X 1 . As a result, we get the case < X 1 , Y 1 > (Figure 13.9c) and an extended comparison relation with strong contradiction (cc): case Y 2 (Figure 13.9d), < X 1 , Y 2 >. Thus, we present the following four cases (Figure 13.9): (a) < X 0 , Y 0 >, (b) < X 0 , Y 1 >, (c) < X 1 , Y 1 >, and (d) < X 1 , Y 2 >. As a result, it is possible now to use a generalized description of our problem as follows: <m|X|Y > where m corresponds to the number of initial digraphs, X denotes the binary relation over vertices of the digraphs, and Y denotes the comparison relation. Clearly, the ﬁve examples in Section 13.2.2 correspond to the basic case < 2 | X 0 | Y 0 >.

13 Common Part of Digraphs

< X 0, Y 1 > H1 H2

< X 0, Y 0 > H1 H2

→ − ←

→ − ← →

c

→

wd c

−

−

wd wd

←

c

←

c wd (b)

(a)

H1

163

< X 1, Y 1 > H2

H1

< X 1, Y 2 > H2 ⇒ → − ← ⇐

⇒ → − ← ⇐ ⇒

c

c

⇒

→

wd c

c

→

wd c

−

c wd wd c

−

c wd wd c

←

c

c wd

←

cc c wd

⇐

c

c

⇐

cc

c

c

(c)

c

cc cc

cc c

cc

(d)

Figure 13.9 Examples for ordinal weights The algorithm is as follows. Figure 13.10 illustrate two kinds of the possible relation comparison: (a) an ordinal scale and (b) a poset. In both cases it is reasonable to consider a boundary between admissible (without contradiction) and inadmissible (with contradiction) parts.

D Part of contradiction

D Part of contradiction D

? ? ... @ @@ @@ @@ @@ @@ @@ @ ...

K Equivalence ?

D

@ @ R ?@

D

D

? ? ... Z Z Z Z Z Z @ @@ @@ @@ @@ @ ... ?

K

K

@ R? @ Equivalence

K

(b) (a) Figure 13.10 Illustration for comparison relation

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Composite Systems Decisions

As a result, we get a situation which was examined for the basic case < 2 | X 0 | Y 0 > in Section 13.2.2 and can use the same algorithm. Note, in these cases, which are more complex than X 1 , it is necessary to change the deﬁnition for the basic set of vertex pair B (see case examined for k vertices). Some examples for complex cases now follow. An example for < 2 | X 0 | 1 Y > (on the basis of previous example 5) is depicted in Figure 13.11.

B

H 5 H0 @ I @H 4 1H 2 H?

H 5 I @ @H 4 1H 6 H 3 2 H?

Common part for only c 5 H1 @ I @H 4 1 HH@ @ HH 2? jH63 H H

H 5 H2 @ I H H 1H YH@64 2 H? HH 3

H

H0 1H 2? H

5

Common part for c & wd

Figure 13.11 Example for case < X 0 , Y 1 > The next example for < 2 | X 1 | Y 1 > is shown in Figure 13.12 (arc with strong preference is depicted by an additional circle). Here, c corresponds to vertex pairs (1, 3), (2, 3); wd corresponds to vertex pairs (3, 4), (4, 6).

B

1 2

H1 1 2

H2 1 2

H 6 5 H @ I @H 4 H H? H 6 6 5H @ I H @H 4 H I H H -H 3 j ? IH H6 5H @ I @H 4 H YHI 6 H H? HH 3

H 6 5 H H0 @ I @H 4 1H 2 H?

Common part for only c H

H 5 H

H0

1 2 H?

6 H0 H

H 5 @ I @H 4

1 2 H?

Common part for c & wd

Figure 13.12 Example for case < X 1 , Y 1 > For the case < 2 | X 1 | Y 2 >, the example is presented in Figure 13.13 (an arc with strong preference is depicted by an additional circle). Here, cc corresponds to the vertex pair (1, 3); c corresponds to vertex pairs (2, 3),

13 Common Part of Digraphs

165

(6, 7); wd corresponds to vertex pairs (3, 4), (4, 6). Let H0 (cc) be a common part for only cc, let H0 (cc & c) be a common part for cc & c, and let H0 (cc & c & wd) be a common part for cc & c & wd. Evidently, generally we get the following: ∀ H0 (cc & c &wd) ∃ H0 (cc & c) such that H0 (cc & c &wd) ⊆ H0 (cc & c) ∀ H0 (cc & c) ∃ H0 (cc) such that H0 (cc & c) ⊆ H0 (cc) 7 7 B

H 6 @ I @ H 5 @ I @H 4 H H

1 2 H?

H I -H 6 @ I @ H 6 H1 5@ I @H 4 H 1 IH H -H 3 j IH H 2?

7

7H H6 I @ @H H2 5@ I @ 4 H 1Y HHI H6 2 H? HH 3

H0

H 6 @ I 5@H @ I @H 4 H H

1 2 H?

Common part for only cc 7H H 6 @ I H H0 5 H 5@H 0 I @ I @H 4 @H 4 1 H @ 1H 2 H? 2 H? Common part for cc & c 7H @ I H0 @H 5 @ I @H 4 1H 2 H? Common part for cc & c & wd

Figure 13.13 Example for case < X 1 , Y 2 >

13.3 Common Part of Several Digraphs In this section, the problem for n initial digraphs {Hi } = {H1 = (U, V1 ), H2 = (U, V2 ), ..., Hn = (U, Vn )} is examined. 13.3.1 Description of Arcs and Compatibility Now we will examine a fuzzy (vector-like) description and corresponding ordinal value for arcs. Let us consider any vertices a, b ∈ U . So, let k+ (a, b) be equal to the number of cases when a → b, k − (a, b) equals a number of cases when a ← b, and k 0 (a, b) equals a number of cases when vertices a and b are disconnected. Clearly, k + (a, b) + k − (a, b) + k 0 (a, b) = n. Thus, a quantitative estimate of compatibility for vertices a and b is deﬁned by the vector K(a, b) = (k + (a, b), k− (a, b), k0 (a, b))

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Now we can construct an ordinal compatibility. There are the following basic points: K + = (n, 0, 0); K − = (0, n, 0); K 0 = (0, 0, n). Thus, the following deﬁnition of ordinal compatibility can be applied (ρ is the distance for threedimensional space): c(a, b) = p if ρ(K + , K(a, b)) ≤ n/2p or ρ(K − , K(a, b)) ≤ n/2p or ρ(K 0 , K(a, b)) ≤ n/2p c(a, b) = (p − 1) if n/2p < ρ(K + , K(a, b)) ≤ 2n/2p or n/2p < ρ(K − , K(a, b)) ≤ 2n/2p or n/2p < ρ(K 0 , K(a, b)) ≤ 2n/2p c(a, b) = (p − 2) if 2n/2p < ρ(K + , K(a, b)) ≤ 3n/2p or 2n/2p < ρ(K − , K(a, b)) ≤ 3n/2p or 2n/2p < ρ(K 0 , K(a, b)) ≤ 3n/2p . . . c(a, b) = 1 if (p − 1)n/2p < ρ(K + , K(a, b)) ≤ n/2 or (p − 1)n/2p < ρ(K − , K(a, b)) ≤ n/2 or (p − 1)n/2p < ρ(K 0 , K(a, b)) ≤ n/2; c(a, b) = 0 otherwise Figure 13.14 depicts an example of a deﬁnition for ordinal compatibility.

k− n

6

K

@

@ 2 @ @ 1

@ @

@ @ @

n/2 I @ @ @ @ @ 0 @ @ @ @ @ @ @ @ @ 1 @ @ 1 @ @ @ @ @ 2 2@ @ K @K @ @I (0, 0) n/2 n k+ Figure 13.14 Illustration for deﬁnition of ordinal compatibility

13 Common Part of Digraphs

167

13.3.2 Solving Scheme and Algorithm Here, the problem and solving scheme are similar to the problem and solving scheme in the previous section (case for k vertices) while taking into account a fuzzy description of arcs which is transformed into ordinal estimates (for arcs and for compatibility). First, we have to consider a preliminary stage to get the ordinal estimates (for arcs and for compatibility). The other part of the solving scheme is the same. But we get a more general case of the morphological clique problem (basic version, with compatibility estimates as 0, 1, 2, etc.) [497]. It is necessary to use other descriptions for similarity/dissimilarity and a negative result (i.e., when digraphs are not coordinated). In fact, we examine the hypergraph and fuzzy description of arcs (e.g. [79]). Note here that similarity/dissimilarity has a more complicated character because the initial set of digraphs can have high dissimilarity but some subsets of the digraph set above are coordinated. Thus, we can describe a generalized dissimilarity (chaos) as a high dissimilarity for each subset of the initial digraph set. Evidently, aggregation rules are based on the use of the thresholds. Let us consider the following rule to select a common arc set: aggregated value is more than 1. 13.3.3 Example In this section we examine a numerical example for the aggregation of four digraphs (six vertices). The following digraphs (on the same set of six vertices) are studied: (a) H1 and H2 (Figure 13.6, only vertices 1, 2, 3, 4, 5, and 6); (b) H3 and H4 (Figure 13.15). H3 H 1 a b @ d 2 3@ 4 @ RH H H -? j c

H

5

-? H 6

H4 H 1 @ d a b A 2 3A@ 4 ? RH H H A @ @ c @ A j @ @A AU? H @ RH @ R 5 6

Figure 13.15 Two additional digraphs We implement Step 1 of the algorithm and preliminary arc set V = {(1, 2), (1, 3), (1, 4), (3, 5), (4, 6)}. Thus, we study a system consisting of the following ﬁve components: A, DAs: A1 , A2 ; B, DAs: B1 , B2 ; C, DAs: C1 , C2 ; D, DAs: D1 , D2 ; J, DAs: J1 , J2 . Estimates for arcs (Table 13.2) and for compatibility of local decisions (Table 13.3) are based on Section 13.3.1 (including Figure 13.14). Table 13.2 contains vector-like descriptions of arcs and corresponding ordinal values (after the slash symbol).

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Table 13.2 Vector-like description of arcs 2 (4, 0, 0)/2

1 2 3 4 5

3 (4, 0, 0)/2 (2, 2, 0)/0

4 (4, 0, 0)/2 (0, 0, 4)/2 (2, 2, 0)/0

5 (0, 0, 4)/2 (2, 0, 2)/1 (3, 1, 0)/1 (0, 0, 4)/2

6 (2, 0, 2)/1 (1, 0, 3)/1 (2, 0, 2)/1 (3, 0, 1)/1 (2, 1, 1)/0

Table 13.3 Compatibility of DAs B1 B2 C1 C2 D1 D2 J1 J2 A1 A2 B1 B2 C1 C2 D1 D2

2 2

2 0

2 2 2 2

2 0 2 2

2 2 2 2 2(1) 2 2 2 2 2 0 2 2 2 2 2 0 2 2 2

2 1 2 1 2 0 2 1

As a result, we get the following composite DAs: S1 = A2 B1 C1 D2 J2 , N (S1 ) = (1; 3, 2) S2 = A2 B1 C1 D2 J1 , N (S2 ) = (2; 2, 3) S3 = A1 B2 C2 D1 J1 , N (S3 ) = (2; 2, 3) The resultant versions of the preliminary common digraph H0 are as follows: H0 = ({1, 3, 4, 6}, {b, d, j}); H0 = ({1, 2, 4}, {a, d}); and H0 = ({1, 3, 5}, {b, c}). Here, step 3 of the algorithm is not required. Finally, Figure 13.16 depicts three resultant digraphs. Clearly, only H0 is the solution. 1 H @ b d @ 4 RH H? 3 @ j H

H H 1 a @ d @ 4 2 RH @ H

? 6

H

H

1

b

3 ? c H

H

H

5 Figure 13.16 Resultant digraphs

13.3.4 Discussion Here, we faced a more complicated situation for the deﬁnition of our contradiction. In the example, arcs a and d have no contradiction on the basis of our deﬁnition. On the other hand, the four digraphs considered contain two inverse types of path between vertices 2 and 4: (i) (2, 3) and (3, 4), and (ii) (4, 3) and (3, 2). As a result, a weak contradiction (e.g., in Section 13.2.3)

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169

can be considered. This case is pointed out in Table 13.3 (new value is presented in parentheses). Thus, it is reasonable to select digraphs H and H . Note, the case of weighted arcs (vertices) is similar to the problem considered because then we can analyze an ordinal scale for arcs (vertices) quality, and application of the morphological clique problem is possible too.

13.4 Additional Issues It is reasonable to point out some prospective research issues and problems as follows: 1. Analysis of complexity for the problem considered and its special cases. 2. Building the common part for the simpliﬁed structures; for example: (a) chains, (b) trees, and (c) parallel–series graphs. 3. Approximation approaches to our problem (i.e., building a superstructure or a substructure), including the following: 3.1 approximation by arcs, 3.2 approximation by vertices, 3.3 approximation by a maximum it super common part that contains a limited number of errors (e.g., the resultant structure involves a limited number of contradictions of certain kinds or has a limited total weight of the contradictions), and 3.4 building an approximate common part of a certain structural kind (e.g., a tree-like common part). 4. Examination of fuzzy approaches for relations X and/or Y . 5. Design and analysis of composite solving strategies; for example: (i) searching for the common part for approximated initial digraphs, (ii) solving the problem for n digraphs as follows: (a) ﬁnding the common part for each digraph pair, (b) aggregation of the common parts into a resultant decision (e.g., with a limited number of errors). Let us consider some simple cases. We examine the case < X 0 , Y 0 > for two chains. Here, B is a set of subchains. The following lemma is evident: Lemma 1. Let H1 and H2 be two linear orderings (i.e., chains, without transitivity). Then H0 equals B. This lemma is also true in the case when H1 and H2 are chain sets. For the case of trees this result is not correct (Figure 13.17). Thus, we get the following (Figure 13.18): (1) series integration of subgraphs does not lead to contradiction; (2) parallel integration of subgraphs can lead to contradiction. In the case of approximation, we examine a structure that is between (by inclusion) B and H0 . Figure 13.19 illustrates two approximate common parts 0 (1) (with one contradiction) and H 0 (2) (with two (super substructures): H 0 (1) ⊂ H 0 (2) ⊆ B. Generally, contradictions, it equals B); and H0 ⊂ H the above-mentioned relation of inclusion corresponds to a hierarchy in which

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B is the only root and structures such as H0 are leaf nodes (Figure 13.20, without additional disconnected vertices). H1

1H 1 6 @ H 3 @ 2 @ I @ I @H7 4 H 5@H 6 H 6 8H H

B

H 1 H 2 6 @ I H H @ H 3 4 5 @ I 6 @H7 6H 8H

H2 2 i H P PP @ I PPH H 1 4 5@H 6 6 H H 3 8 @ I @H7 6H H0

H 2 I @ H 3 @H 5 4 @ I 6 @H7 6H 8H H

Figure 13.17 Example for trees Part B

Part A

Part B

6

Part A

6

Part A

Part B

(a) Initial subgraphs

(c) Series integration

Part A

3 Part A

Part B

Q kQ Part B Q

(c) Parallel integration Figure 13.18 Integration of subgraphs

13.5 Summary In this chapter, a new speciﬁc combinatorial problem has been described: to extract a common part for preference relations which are deﬁned over the same set of elements (e.g., alternatives) while taking into account a speciﬁc constraint. The above-mentioned problem is considered from the viewpoint of the design of a composite decision. On the other hand, it is possible to examine more general cases; for example: 1. weighted digraphs including

13 Common Part of Digraphs

171

weights for vertices, for arcs, and for vertices and arcs; 2. relations over the diﬀerent element sets. Also, a special study has to be oriented to some simple kinds of digraph structures, e.g., chains, trees, parallel–series digraphs. In addition, we have to point out a crucial problem of correspondence (e.g., equivalence) between graph edit distances and distances based on the maximum common subgraph [125, 864]. H1

3

4 5 1H H 6 @ H RH @ 2 * 6 6 H H 7 1 H H -H ? 10 9 8 H

3

B

4 -H

H

2H 6 1H

5 @ RH @

H 10

H

9

0 (1) H

9

H H

6 H 7

H

8 H

5 @ @ RH 6 H

10

8 H

5 @ RH @ H 10

4 -H -H5 ]J J BMB @ H @ RH 6 2 J B 6 6 H 1 J B H 7 I @ H JH BH @? 10 9 8 H

6 7

H

2H 6 1H

3

H0

H

H

H2

0 (2) H 3 H

H

9 4 -H

H

H

H

2H 6 1H

5 @ @ RH 6 H

10 H

9

7

8 H

7

8

Figure 13.19 Approximate common parts B = H1 &H2 K

@ @ R ...

k contradictions ...

... @ H RH @ 2 contradictions @ @ RH @ RHX H H? H @ 1 contradiction XX @ @ RH without contradiction @ @ RH @ @ RH XXX H z ... H0 H0 Figure 13.20 A hierarchy of common parts

14 The Last Mile Problem

14.1 Preliminaries Here, the last mile problem is considered (e.g. [199, 334, 666]). The problem consists of the design of the home delivery service for the customer (a communication operator). In this situation, it is necessary to combine requirements from the following two sides: (i) proﬁtability for the communication operator and (ii) high level of service for home users. In [334], this problem is formulated as a traditional multicriteria decision-making model: (a) generation of alternatives decisions, (b) design of criteria, (c) assessment of alternatives upon criteria, and (d) choice of the best alternative(s). In this chapter, the last mile problem is ﬁrst examined as a morphological hierarchical design on the basis of HMMD [509].

14.2 Description of the Problem Figure 14.1 illustrates the problem considered: (a) a communication operator and (b) users of a region. In our case, the following user groups can be examined: (i) group companies A = E F ; (ii) group educational institutes B = I J M ; (iii) group government organizations C = O P R; and (iv) group plants D = Y Z. Thus, a structure of the resultant composite decision is the following (Figure 14.2): S = A B C D. Further, for each user it is necessary to generate a set of possible alternatives (i.e., DAs) and to compute their priorities on the basis criteria and estimates upon the criteria.

14.3 Alternatives, Criteria, and Compatibility Here, the following set of basic DAs from [334] is examined (common basic set for all users): X1 (ADSL): telephone network, X2 (DACSIS): cable TV network,

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Composite Systems Decisions

X3 Ethernet, X4 (power line): power network, X5 (FTTH): optical cable, X6 (LMDS): wireless communication (2.5–2.7 GHz), X7 (4G): wireless communication (800–2000 MHz), and X8 (WMAN, WiMAX): wireless communication (2.4, 3.5, 5.8 GHz). In [334], a set of criteria is described for the assessment of DAs in the last mile problem as follows: volume of initial investment, cost of equipment, speed of information transmission, installation time for system, installation time for a user, cost of maintenance, reliability, mobility of service, connection with an existing communication environment, etc. Here, some resultant user decisions are examined for each user as a set of selected DAs and their ordinal priorities (expert judgment) (Figure 14.2). Tables 14.1, 14.2, 14.3, and 14.4 contain estimates of compatibility for DAs (expert judgment).

Government oﬃce O

Plant Z

Company E

College I

Communication operator

Plant Y

School J

Government oﬃce P Company F

Government oﬃce R

School K

Figure 14.1 Illustrative scheme

14.4 Composite Decisions The resultant composite decisions for the user groups are as follows: 1. A1 = E7 F7 , N (A1 ) = (3; 2, 0). 2. B1 = I8 J2 M1 , N (B1 ) = (1; 3, 0, 0); B2 = I8 J1 M1 , N (B2 ) = (1; 3, 0, 0); and B3 = I8 J8 M8 , N (B3 ) = (3; 1, 2, 0). 3. C1 = O8 P8 R8 , N (C1 ) = (3; 2, 1, 0); C2 = O7 P7 R7 , N (C2 ) = (3; 2, 1, 0); C3 = O7 P5 R7 , N (C3 ) = (2; 3, 0, 0); C4 = O8 P5 R7 , N (C4 ) = (2; 3, 0, 0); C5 = O7 P5 R8 , N (C5 ) = (2; 3, 0, 0); and C6 = O8 P5 R8 , N (C6 ) = (2; 3, 0, 0). 4. D1 = Y3 Z5 , N (D1 ) = (2; 2, 0); D2 = Y3 Z8 , N (D2 ) = (2; 2, 0); and D3 = Y4 Z4 , N (D3 ) = (3; 1, 1). Further, we can consider two ways as follows:

14 The Last Mile Problem

175

1. To examine 54 possible resultant composite decisions: S1 = A1 B1 C1 D1 , S2 = A1 B1 C2 D1 , etc. 2. To formulate and to solve an additional morphological clique problem at the higher level of our model for composition of components A, B, C, and D while taking into account corresponding priorities of DAs for A, B, C, and D, and their compatibility estimates.

OS = A B C D S1 = A1 B1 C1 D1 , etc.

NB = I J M B1 = I8 J2 M1 B2 = I8 J1 M1 B3 = I8 J8 M8

AI N A=EF A1 = E 7 F 7 AE

F2 (3) F3 (2) F5 (2) F6 (1) F7 (1) F8 (1)

M A M1 (1) M2 (2) M8 (2)

J1 (1) J2 (1) J8 ()

C =OP R C1 = O8 P8 R8 C2 = O7 P7 R7 C3 = O7 P5 R7 C4 = O8 P5 R7 C5 = O7 P5 R7 C6 = O8 P5 R8

A

F

E2 (3) E3 (2) E5 (2) E6 (2) E7 (1) E8 (1)

AJ

I1 (3) I2 (3) I6 (2) I7 (2) I8 (1)

AO

O5 (2) O6 (2) O7 (1) O8 (1) Figure 14.2 Structure

Table 14.1 Compatibility

AP

D =Y Z D1 = Y3 Z5 ND2 = Y3 Z8 D3 = Y4 Z4

N

AE

F

Y2 (2) Y3 (1) Y4 (1) Y5 (3) Y8 (3)

R A P5 (1) R5 (2) P6 (2) R6 (2) P7 (2) R7 (1) P8 (2) R8 (1) of composite decision

Table 14.2 Compatibility J1 J2 J8 M1 M2 M8

F2 F3 F5 F6 F7 F8 E2 E3 E5 E6 E7 E8

3 1 2 2 2 2

2 3 2 2 2 2

2 2 3 2 2 2

2 2 2 3 2 2

2 2 2 2 3 2

2 2 2 2 2 3

I1 I2 I6 I7 I8 J1 J2 J8

3 2 1 1 1

2 3 2 2 2

1 2 2 2 3

3 2 1 3 1 3 2 1

A

Z2 (3) Z3 (3) Z4 (2) Z5 (1) Z8 (1)

2 3 2 2 2 2 3 2

1 2 2 2 3 1 2 3

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Composite Systems Decisions

Table 14.4 Compatibility

Table 14.3 Compatibility P1 P2 P8 P1 R2 R8 R2 R8 O5 O6 O7 O8 P5 P6 P7 P8

3 2 2 2

2 3 2 2

2 2 3 2

2 2 2 3

3 2 2 2 3 2 3 2

2 3 2 2 2 3 2 2

2 2 3 2 2 2 3 2

2 2 2 3 2 2 2 3

Z2 Z3 Z4 Z5 Z8 Y2 Y3 Y4 Y5 Y8

3 2 1 2 2

2 3 1 2 2

1 1 3 1 1

2 2 1 3 2

2 2 1 3 3

14.5 Summary In this chapter a new hierarchical morphological approach is suggested for the last mile problem. Now it is possible to consider more realistic applied examples and to extend the problem formulation as follows: (i) multistage design, (ii) examination of several communication operators, and (iii) design under uncertainty.

15 Combinatorial Model of Political Administration

15.1 Preliminaries This chapter addresses a preliminary step to using our hierarchical morphological approach for modeling some components of a political administration (or a political situation) [458]. Organizational issues of political administration play a central role in many political and social domains (e.g. [544]). Evidently, the usage of structural modeling in political studies is signiﬁcant and prospective (e.g. [687]). Here, a structural description for components of a political administration is described as a simple general frame and a morphological hierarchy (tree-like And–Or structure) that corresponds to an organizational system of political administration in a community (i.e., system for preparation and making decisions). From the practical view-point, two hierarchical structures of political administration (as case studies) are brieﬂy described: (a) in Russia and (b) in the USA.

15.2 General Frame The following basic concepts are examined: 1. Kinds of authority (or political administration) as the basic authority and special types of political administration. 2. Assignment of authority (i.e., assignment of decision-making procedures): (i) by election, (ii) by succession, and (iii) external assignment (e.g., occupation administration, assignment of governor). 3. Hierarchical levels. Here, only two levels are examined: state (h) and region (r). 4. Functions (e.g., decision-making procedures). The following basic functions are under examination: 1. defense (A); 2. public order (B); 3. lows (C); 4. taxes (D); 5. ideology (E); 6. education and medicine (F); and 7. business (manufacturing, commerce, etc.) (G). The basic kinds of authority (political administration) are as follows: (1) state authority, (2) church, (3) political parties, (4) trades unions, (5) families and individuals, (6) professional groups and societies, (7) groups

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Composite Systems Decisions

and societies by interests, (8) sports societies, (9) social groups (e.g., clan, crime family), (10) oligarch groups, and (11) mass media. The general frame is depicted in Figure 15.1. Assignment of authority (political administration) (i.e., assignment of decision-making procedures): (i) by election,(ii) by succession, and (iii) external assignment (e.g., occupation administration, assignment of governor). Kinds of political administration (governmental, non-governmental) including special types of non-governmental kinds: (1) church, (2) political parties, (3) trades unions.

-

?

KE 6

Hierarchical levels: 1. country (h) 2. region (r)

Functions: 1. Defense (A) 2. Public order (B) 3. Lows (C) 4. Taxes (D) 5. Ideology (E) 6. Education and medicine (F ) 7. Business (manufacturing, commerce, etc.) (G) Figure 15.1 General frame

15.3 Schemes of Political Administration Figure 15.2 illustrates a morphological hierarchy (as a tree-like And – Or structure) that corresponds to an organizational system of a political administration in a community (i.e., a system for preparation and making decisions). It is assumed that assignment of authority is ﬁxed. Modeling a certain political situation at the level of state and region(s) is based on alternatives as follows: Xzy , where X corresponds to a certain type of function (A, B, C, D, E, F, G), index y corresponds to hierarchical level (symbol h corresponds to country and symbol r corresponds to region), and index z corresponds to a kind of authority (i.e., political administration) as the number (z ∈ {1, ..., 11}), as in the previous section).

15 Combinatorial Model of Political Administration

179

Let us consider the situation in Russia in the following model: h h h , C1h &C6h &C10 , D1h , E1h &E2h &E11 , F1h , Gh1 &Gh10 > and < Ah1 , B1h &B10 r r r , C1r , D1r , E1r &E2r &E11 , F1r &F5r &F10 , Gr1 &Gr10 >. < B1r &B10 For the situation in the USA, the model is as follows: h h h , C1h &C3h &C6h &C7h &C9h &C10 &C11 , D1h , < Ah1 , B1h &B2h &B5h &B10 h h h h h h h h h h h h h , E1 &E2 &E3 &E5 &E9 &E10 &E11 , F1 &F2 &F7 &F8 &F9 &F10 h h h h h G1 &G4 &G5 &G9 &G10 > and r r , C1r &C2r &C3r &C4r &C5r &C6r &C7r &C9r &C10 , < B1r &B5r &B7r &B9r &B10 r r r r r r r r r r r D1 , E1 &E2 &E3 &E5 &E6 &E7 &E8 &E9 &E10 &E11 , r , Gr1 &Gr2 &Gr4 &Gr5 &Gr9 &Gr10 >. F1r &F2r &F5r &F6r &F8r &F9r &F10

System

Ah B h C h Dh E h F h Gh

Q Q

Q

Q

B r C r D r E r F r Gr

Figure 15.2 Organizational system for community Comparison of the above-mentioned schemes for Russia and the USA explains the following: a function in the USA consists of many diﬀerent kinds of authority. In other words, a composite kind of authority is applied. As a result, the function above is realized as more reliable. At the same time, in Russia, a function involves only one kind or a couple of kinds of authorities (less reliable case). For example, function public order (B) at the level of region (r) is as follows: r (ﬁve components) and (i) for the USA: B1r &B5r &B7r &B9r &B10 r r (ii) for Russia: B1 &B10 (two components).

15.4 Summary Thus, our hierarchical morphological approach has been used here for structural modeling of a political administration (situation) in countries/regions. A list for future examination involves several advanced problems as follows: Problem 1. Modeling of multistage political situations. Problem 2. Comparison analysis of the political situations: 2.1. for two or more countries/regions, 2.2. for several time moments in the same country. Problem 3. Designing an improvement plan as a composition of the best interrelated improvement actions.

Part IV

Educational Issues

16 General Engineering

16.1 Preliminaries This chapter focuses on a composite multidisciplinary approach to system engineering education known as general engineering. Recently, many eﬀorts oriented to new approaches in engineering education; for example: (a) usage of new technological environments (e.g., computers, the Internet) [4, 842]; (b) integration of education and research [26, 130, 223–226, 362, 472]; (c) special multidisciplinary systems engineering education [26, 112, 208, 499, 710, 748]; (d) integration of mathematics, software engineering, and design [26, 33, 814]; and (e) organization of student team projects [26, 472]. For many years systems engineering researches (SERs; e.g., analysis, design and planning of large-scale systems) were oriented to special applications (airspace industry, etc.). Right now, there are needs to use SERs in many other domains. For example, we can point out the following: (a) complex products; (b) product life cycle (R & D, manufacturing, marketing, utilization, etc.); (c) human–computer systems, including special computer environments (e.g., CAD/CAM systems); (d) distributed information systems; and (e) enterprise modeling, etc. Thus, contemporary scientiﬁc research technologies (e.g., mechanical manufacturing, biotechnology) are very complicated, multidisciplinary and require systems approaches [748, 894]. Some studies of complex systems are often really domain-dependent only (e.g., design of engines, software development). This situation depends on the human factors because many excellent specialists in the design of complex systems have obtained their experience in a certain engineering domain (e.g., structural design, communication systems, computer architecture, chemical engineering, VLSI design). In addition, it is reasonable to take into account that design processes require several design roles (e.g., innovation, decision making, engineering analysis, management) [209, 497]. Now, complex systems are multidisciplinary, including subsystems of various kinds: user teams, software, hardware/electronics, mechanical subsystems, distributed information subsystems and special needs of search technology, communication networks, mathematical models and algorithms, economical issues (marketing, etc.), and educational components. A new basic

184

Composite Systems Decisions

two-dimensional typology of project management styles which is dependent on system scope (array, system, assembly, component) and technological uncertainty (low level, medium level, high level, and super high level) has been proposed and analyzed in [749]. Domain-independent modularity in the design of products and systems has been described in [56, 387, 497], for example. Further, human resource has to be considered as a key factor. There exist two possible ways: 1. Searching for and selection of persons who have an inclination to the complex multidisciplinary system thinking, analysis, design, etc. 2. Organization of a special educational direction in the ﬁeld of domainindependent SERs (undergraduate, graduate and post-graduate studies, continuous education). In this chapter, the following basic directions are considered: (a) basic systems engineering; (b) concurrent engineering; (c) hierarchical design of complex systems (including systems decomposition); (d) history of technical systems and their evolution; (e) quality analysis and management; (f) project management; and (g) discrete structures, algorithms, and optimization (including multi-criteria decision making). The material of the chapter is targeted to all stages of a decision cycle (i.e., applied systems, applied problem(s), mathematical model(s), algorithms and solving processes, decision(s)), including the crucial stage of problem formulation.

16.2 Generalized Overview 16.2.1 Trends in Engineering Let us ﬁrst consider some basic recent trends in engineering. Changes of engineering practice in all domains of engineering (civil engineering, electrical engineering, circuit design, VLSI design, software engineering, information engineering, etc.) consist in the following movement: FROM design of some basic elements TO selection and integration of system components into whole system. In other words, the system part of engineering activity is increasing. Figure 16.1 depicts a system hierarchy and requirements of diﬀerent kinds. For many years, majority of engineers were oriented to the design of system components. Recent trends have led to the following situation: (i) There are many design results accumulated for the design of system components, and these local design decisions are collected as databases, libraries, catalogs, repositories, for example: local design decisions for VLSI design, software libraries/repositories, catalogs of construction elements in civil engineering, catalogs of elements, design blocks, and local design decisions in mechanical engineering, libraries of information blocks in information engineering, and catalogs of design decisions in chemical engineering. (ii) Complexity of system/subsystem design is increasing for the following reasons: (a) complexity of systems multidisciplinarity; (b) time requirements for new system design (decreasing of product life cycle from 12 years to 0.5– 2 years, e.g., in car industry); (c) distributed engineering design processes

16 General Engineering

185

when design groups are located in diﬀerent places (diﬀerent countries, diﬀerent continents); (d) integration of design engineering issues and other problems for product life-cycle design and maintenance (i.e., design, manufacturing, marketing, utilization); and (e) distributed computer-aided support environments (groupware, etc.).

N

System

AI

Subsystems Components

A

A A

@

@ @ A A A

IA

⇐ ⇐ ⇐

Politics Ecology Strategic planning

⇐ ⇐ ⇐

Systems engineering/ management

⇐ ⇐

Basic engineering

Figure 16.1 Illustration for system levels Thus, let us point out the following: the need for several systems persons is changed to thousands of required system specialists who can integrate in many basic engineering domains and some other disciplines (e.g., computer science, mathematical modeling, management). 16.2.2 Basic Design Flow Let us consider the following basic stages of design activity [53, 119, 155, 208, 311, 327, 461, 464, 497, 658, 711, 721, 849]: Phase 1. Conceptual design of new systems and/or system architecture (i.e., system structure), design of system speciﬁcations, requirements engineering. Phase 2. Requirements to searching for local design decisions for system components. Phase 3. Selection of the best local design decisions. Phase 4. Integration of the local design decisions into global system decisions (composite systems, product life cycle). Note, a comparative analysis of the main approaches to the system design process is described in [53]. Generally, the basic operations of traditional logic include the following [875]: 1. Deﬁnition. 2. Comparison and discrimination. 3. Analysis. 4. Abstraction. 5. Generalization. 6. Forming close concepts. 7. Subsumption. 8. Forming proposition. 9. Forming inference. 10. Forming syllogisms. Here, we consider the following basic functional systems engineering operations [119, 208, 225, 226, 464, 497, 658, 849]: 1. description /presentation/ modeling of complex systems; 2. analysis and evaluation; 3. design/synthesis; 4. transformation (modiﬁcation, improvement, adaptation); and 5. analysis and planning of system life cycle (including issues of reengineering, reuse, redesign, etc.). Thus, it is reasonable to point out some fundamentals for domainindependent engineering:

186

Composite Systems Decisions

1. Knowledge (information)–based systems engineering concept spaces (new information ﬁeld for engineering): FROM professional handbooks TO multidisciplinary engineering spaces. 2. New information retrieval technology (associative thinking, multidisciplinary thinking, engineering concept spaces): FROM traditional domain-oriented engineering education and practice TO multidisciplinary associative thinking. 3. Multicriteria decision-making technology. 4. Combinatorial thinking for combinatorial design of new systems on the basis of the following: (a) models (graphs and orders) and (b) combinatorial problems (applied combinatorics, combinatorial optimization). 5. Systems integration/synthesis technology. 6. Systems dynamics. 7. System evolution (e.g., as in biology: morphological genesis) 8. Extended background in socio-economical issues (marketing, ecology, maintenance, human factors). 9. Special approaches to evaluate system performance/excellence. 10. Systems simulation. As a result, the engineering community has faced new requirements in the ﬁeld of human resources as follows: (a) searching for persons with an inclination to domain-independent (general) engineering; (b) selection of persons with multidisciplinary thinking; (c) special educational student courses; and (e) continuous education. 16.2.3 Educational Components Basic examples of some domain-independent directions that are oriented to SERs are the following: (i) systems engineering; (ii) large-scale systems; (iii) system analysis; (iv) multi- and inter-disciplinary studies; (v) integrated engineering; analysis and integration of large systems; (vi) concurrent engineering; and (vii) quality analysis and management. Trends to SERs exist in many university departments, e.g.: systems engineering, mechanical engineering, electrical engineering, communication engineering, computer engineering, software engineering, information systems engineering, and management. Basic research topics are the following: (1) system modeling; (2) systems decomposition; (3) hierarchical approaches (to design, to decision making); (4) control theory; (5) simulation; (6) dynamical systems; (7) computer-aided systems (e.g., CAD/CAM); (8) information and knowledge engineering (including IS, MIS, DBMS, DSS, and AI, software engineering); (9) engineering and technological management; (10) concurrent engineering; (11) design of large-scale distributed systems; (12) integrated system design; (13) modeling of system evolution/development; (14) methods for evaluation of systems; and (15) quality analysis and management. Generally, we intend to cover the decision cycle (Figure 16.2).

16 General Engineering

187

Applied problems

Applied environment /system

@

@ R @ Models

6 ? Decisions Algorithm(s) H YH H Solving process

Figure 16.2 Decision cycle In our opinion, the number of educational institutions that are oriented to SERs will increase in the coming years. Here, it is reasonable to point out some crucial person requirements which correspond to basic goals as educational components (Table 16.1). 16.2.4 Educational Program We consider the following basic preliminary background (one or several): 1. civil and/or environmental engineering; 2. mechanical engineering; 3. software engineering; 4. computer engineering; 5. communication engineering; 6. chemical engineering; 7. material engineering; 8. industrial engineering and management; and 9. computer science. Tables 16.2 and 16.3 contain basic educational directions (C corresponds to a big course, SC corresponds to a small course/introduction, IP corresponds to an individual project, and TP corresponds to a large team project).

16.3 Implementation 16.3.1 Implementation of Program It is reasonable to consider a multi-level educational process in the ﬁeld of domain-independent engineering (Table 16.4) [497]. Level 3 is very important for associative and multidisciplinary thinking and communication skills. Here, some unique advanced composite topics have to be examined, e.g., (i) civil engineering, chemical engineering, discrete structures, issues of reuse and redesign; (ii) biotechnology, information systems, concurrent scheduling; (iii) computer architecture, biotechnology, knowledgebased systems, enterprise modeling; (iv) taxonomy in structural engineering, material engineering, distributed information systems, quality management; (v) structural engineering, life-cycle management, reengineering, coordination; and (vi) communication systems, multicriteria decision making, multi-agent systems, cooperative work-groups.

188

Composite Systems Decisions

Generally, composite projects can be based on the selection and composition of the following: Part 1. Engineering (mechanical engineering, etc.). Part 2. Information technology (e.g., information systems and the Internet, software, expert systems). Part 3. Economical, sociological, and ecological issues (e.g., human factors and usability, marketing). Part 4. Mathematical fundamentals. Table 16.1 Basic educational goals Educational goals 1. System domain-independent thinking

References [53, 119, 209, 275, 327], [389, 398, 409, 457, 565], [597, 628, 658, 711, 800], [849] [497, 658, 762]

2. Associative multidisciplinary thinking (not only in engineering/science disciplines, but also including economical, social, and ecological issues) [49, 409, 497, 875] 3. Combinatorial thinking, synthesis [2, 24, 311, 409, 610], 4. Creativity, usage of AI techniques [779] 5. Dynamical thinking (e.g., by systems [275, 712] evolution/development) [49, 497, 800] 6. Experience in strategic systems design [108, 209, 389, 628, 800] 7. Applied experience in the systems analysis, design and planning [281, 687] 8. Background in discrete mathematics and algorithms [293, 572, 788, 793, 911] 9. Experience in application of operations research (including optimization, multicriteria decision making)

The proposed approach is mainly oriented to levels 2, 3, and 4. Note that the analysis, design, and planning of the individual educational program are fundamental for the educational process, including the following: Stage 1. Description and analysis of an initial individual professional proﬁle. Stage 2. Design of a target professional proﬁle. Stage 3. Design of structure for courses/projects and selection of educational elements. Stage 4. Design/planning of the resultant composite concurrent individual educational plan while taking into account the following: (a) properties of educational elements (correspondence to individual goals, complementarity of educational elements, etc.); (b) resource constraints (time, auditorium, other students, professors, etc.); and (c) educational plans of other students.

16 General Engineering

189

Note, stage 4 has to be considered as a concurrent engineering approach in education. Figure 16.3 depicts a framework of systems engineering (SysEng) education where o corresponds to an educational input, * corresponds to an educational output, Ci corresponds to course/studies in SysEng at educational level i, and Ci− corresponds to another course/study at educational level i. We have examined the following educational path: C1− → C2 → W2 . Evidently, other educational paths are very important too; for example: (a) C1 → C2 → C3 , (b) C1− → C2 → W2 → C3 , and (c) C1 → W1 → C2− → C3 . o Undergrad course on SysEng C1 o

*

? o Graduate course on SysEng C2 o

*

? o PhD studies in SysEng C3 o

*

... ? * @ R Practical work @ W1 o . .?. ? * @ R Practical work @ W2 o . .?. ? * @ Practical work R @ W3 o

-

-

? Studies in SysEng o for continuous o education C4

* ? Figure 16.3 Framework of systems engineering education 16.3.2 Towards Organizational Structure Let us consider a basic organizational structure of an educational process (Figure 16.4a): (a) one professor–one student. At the same time, there exist some evident modiﬁcations of structure (a) (Figure 16.4): (b) one professor– student group; (c) one professor–intermediate level educators (e.g., junior faculty, postdoc researcher)–student group. In the structures above, all participants have about the same professional proﬁle. From the multidisciplinary viewpoint it is reasonable to examine the following structures (Figure 16.4d): (d) professor group–intermediate level educators–student group(s).

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Composite Systems Decisions

Table 16.2 Systems and engineering parts Parts of program 1. Domainindependent system thinking

2. Associative thinking including engineering concept spaces 3. Combinatorial thinking

4. Systems design

5. Systems evolution (life cycle, system generations)

Components (a) systems engineering C; (b) systems architecture SC; (c) combinatorial engineering (course and project) SC, IP; (d) quality analysis and management SC; (e) innovations and reengineering SC; (f) concurrent engineering C; (g) team design SC; (h) history of art (painting, theater) SC; (i) multicriteria decision making SC; (j) enterprise modeling SC; and (k) preparation of business-plans/proposals IP. (a) knowledge engineering SC; (b) ﬁnancial engineering (money ﬂows) SC; (c) distributed information systems SC; (d) marketing SC; (e) usability Sc; (e) (f) 4b. (a) discrete structures and algorithms (graph, networks, orders) C; (b) synthesis, chemical engineering SC; (c) material engineering SC; (d) 1c; and (e) 6b. (a) creativity techniques SC; (b) design of home-page for composite topic (methodology, models, algorithms, applications, bibliography, centers, conferences, journals, connection with other domains) IP; (c) multidisciplinary composite projects (large team composite project, connection with previous background) TP; (d) design of applied systems TP and C; (e) project management C; (f) 1c; and (g) 3 (a, b, and c). (a) evolution in biology SC; (b) history of engineering systems C; and (c) project on system evolution IP.

16 General Engineering

191

Table 16.3 Model and algorithm part Parts of program

Components

(a) systems dynamics SC; (b) applied combinatorics SC; (c) automata theory SC; (d) Petri-nets SC; (e) dynamics, chaos, self-organization SC. (a) simulation schemes, software, 2. Simulation sensitivity analysis SC; (b) simulation of applied system TP. (a) constraint approach, 3. Search (b) gradient-like approaches, strategies (c) branch-and-bound, (d) dynamic programming, (e) approximation of space, (f) evolutionary strategy, (g) partitioning/synthesis strategy SC. (a) complexity issues SC; 4. Algorithms and complexity (b) algorithms (exact, approximate) SC; (c) heuristics SC; (d) composite application TP. (a) main optimization model SC 5. Optimization, decision making, (b) multicriteria methods SC (c) fuzzy approach SC; fuzzy sets (d) composite application IP. (a) main models (knapsack, TSP, 6. Combinatorial optimization scheduling, assignment, etc. SC (b) application IP. (a) genetic algorithms SC 7. Evolutionary (b) multiobjective optimization SC computing (c) application IP. 1. Models

In this case, professors can have various professional proﬁles and this is a basis for multidisciplinary education and research processes. Note that students (student groups) can correspond to diﬀerent applied domains (e.g., engineering, computer science, management, psychology) and can be distributed in the world.

16.4 Summary The chapter contains some issues of general engineering education. Evidently, this educational direction is very prospective and it is reasonable to conduct new research eﬀorts, e.g.: new kinds of multidisciplinary courses.

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Table 16.4 Levels of educational process Examples

Level 1. Basic professional engineering domain (courses, project)

2. Analysis, design, planning of individual educational system/ program (IP) 3. Project for a composite engineering domain (IP or TP)

4. Multidisciplinary project (including engineering, economical, social issues) (IP or TP)

(a) design of an information system; (b) design of user interface; (c) design of hypertext; (d) design of team; and (e) design of packaged software. (a) planning of student career; (b) design of educational courses; (c) analysis of an initial professional individual proﬁle and planning an educational process. (a) information project on a system evolution as a home-page for Internet (a domain, information engineering, software engineering, system architecture); (b) designing/planning a composite engineering systems, e.g., mechatronic system (vibration conveyor [497]). (a) interdisciplinary project works e.g., at De Monfort University [397]; (b) design of a business plan; (c) planning of product life cycle.

Professor

Student (a) Professor

BB

B

Professor

B ... B Students (b)

... @ Professors @...@ @ Junior faculties @...@ Students

A A ... A Junior faculties @ @ ...@ Students (d) (c) Figure 16.4 Organizational education structures

17 Design of Systems (Structural Approach)

17.1 Preliminaries Educational eﬀorts in the ﬁeld of system design consist of several contemporary trends as follows: (1) systems engineering including life-cycle engineering [112, 208, 322, 499, 514, 710]; (2) multidisciplinary issues [112, 208, 225, 226, 499, 710, 748]; (3) modularity [56, 387, 464, 497, 628]; (4) concurrent engineering (e.g. [658]); (5) integration of various kinds of education (e.g., mathematical, computer science and engineering education) [33, 397, 748, 894]; (6) integration of education and research [131, 223–226, 362, 499]; (7) experiments in the design of new educational programs [112, 225, 226, 273, 362, 486, 499, 894]; (8) combinatorial modeling [477, 493, 496, 687]; (9) usage of new computer and network environments [4, 842]; (10) system design as a direction that leads to a design of some goal systems [119, 224, 362, 497, 597, 787, 843]; (11) system architecture and conceptual design [119, 322, 486, 497]; (12) decision making and problem solving [2, 24, 302, 497, 610, 762, 779, 787]; and (13) application of evolutionary optimization in engineering (e.g. [911]). This chapter describes the author’s experience in the preparation and implementation of a new undergraduate course Design of Systems: Structural Approach (for students in the ﬁeld of electrical, communication, computer engineering, and computer science). Two professional styles have been integrated: (1) scientiﬁc style (orientation to study and modeling of some applied problems / situations); (2) engineering style (orientation to design a goal equipment/system) [188]. The course consists of the following main parts [507]: (i) systems engineering/ life-cycle engineering; (ii) products/systems (including products families); (iii) basic technological problems (system modeling, design, evaluation/comparison, revelation of bottlenecks improvement/upgrade, multistage

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Composite Systems Decisions

design, modeling of system evolution and forecasting); (iv) basic structural system models (structures, graphs, etc.); (v) solving schemes (decision-making procedures, optimization, methods of artiﬁcial intelligence, and design frameworks); (vi) life-cycle engineering problems (e.g., maintenance, requirements, testing); (vii) realistic applied examples as case studies; and (viii) real-world applications. Product family

Goal systems:

Product

Disciplines:

System design

Technological problems:

Mode- Design ling

Structural models: Solving methods:

Upgrade

Product platform

Life-cycle engineering

Bottle- Evalu- Generaation tions necks

Graphs, networks, etc.

Decision making

Optimization

AI techniques

Design schemes

Case studies and real-world applications

Figure 17.1 Illustration for structure of course

17.2 Fundamentals In the course, our morphological multicriteria design approach HMMD is used as a basic approach to modular design [497, 504]. At the same time, the following prospective design methods are described: 1. several morphological design approaches (morphological analysis, etc.) [49, 408, 497, 914]; 2. hierarchical decision-making approaches to system design [453, 461, 497]; 3. design approach on the basis of global optimization and non-linear mixed integer programming [267, 268, 326]; and 4. PSI [768, 787]. Particular attention is oriented to the construction and analysis of applied engineering design spaces and corresponding search spaces (e.g. [155, 497, 816]). This direction is a crucial one and can help at the stages of problem formulation and solving. Here, structural (combinatorial) models (including hierarchical models) of applied domains, situations, and systems are very important [497, 687, 867]. Additional educational eﬀorts consist of the analysis of system changes (evolution, development). In this case, structural hierarchical models of system generations are examined and system change opera-

17 Design of Systems (Structural Approach)

195

tions (from one system generation to the next system generation) are revealed [497, 504, 912]. As a result, the system change operations can be considered as basic modules to design the next step in the system development process on the basis of combinatorial optimization problems (e.g., multicriteria selection, knapsack problem). The generalized structure of the course is illustrated in Figure 17.1. The lecturer and students are communicating during lectures, laboratory work, and via the Internet (Internet site of the course, email service).

17.3 Lectures The lecture plan contains four parts as follows: Part A. INTRODUCTION: 1. System issues (structure, life cycle, modularity, system decomposition/partitioning, concurrent engineering). 2. Structural models (graphs, networks, binary relations). 3. information technology including its components. 4. Design schemes. 5. Examples. Part B. SYSTEM ANALYSIS, OPTIMIZATION, DECISION MAKING: 1. System analysis (decision-making paradigm, basic decision making problems, kinds of scales, Pareto-eﬀective decisions, requirements/criteria, roles in decision-making process). 2. Methods of multicriteria decision making (utility function, pairwise comparison, outranking techniques, AHP, integration/aggregation of results). 3. Optimization models. 4. Basic models of combinatorial optimization (knapsack problem, multiplechoice problem, packing problems, traveling salesman problem, spanning tree problem, minimal Steiner tree problem, scheduling, covering problems, assignment/allocation problems, clique problem, graph coloring, alignment problem, maximal substructure and minimal superstructure). 5. Types of solution (exact solutions, approximate solutions) and types of algorithm (polynomial algorithms, enumerative algorithms, etc.). 6. Some basic design optimization schemes (e.g., PSI, multidisciplinary optimization, ellipsoid method, non-linear mixed integer programming). Part C. COMBINATORIAL MORPHOLOGICAL APPROACH: 1. Design morphological methods and HMMD. 2. System technological problems (design, multistage design, revelation of bottlenecks, improvement/redesign/uprgade, evaluation/diagnosis, modeling of system evaluation/development). 3. Examples (e.g., design and improvement of team, modeling and upgrade of computer, evaluation of building, design of multi-product systems with common modules). Part D. ADDITIONAL SYSTEM ISSUES: 1. Requirements engineering.

196

Composite Systems Decisions

2. System maintenance. 3. System testing.

17.4 Laboratory Work Generally, laboratory work involves three parts: (a) models and methods/ algorithms (multicriteria ranking, knapsack problem, evaluation and diagnosis, clustering); (b) system applied examples (e.g., analysis and evaluation, design). Thus, the following levels are considered: Level 1. Learning of some models and algorithms (e.g., decision making, combinatorial optimization, system analysis and diagnosis) and corresponding algorithms and solving schemes. This level involves realization of the abovementioned algorithms and solving schemes as programs in the MatLab environment. Level 2. Analysis of applications for the above-mentioned models and testing the designed programs on the basis of numerical examples, including realworld application examples. Level 3. Combination of the above-mentioned models into composite solving schemes for realistic system problems. In a recent version of the course, the basic laboratory work is as follows: 1. Multicriteria ranking (methods of utility functions, revelation of Paretoeﬀective points, outranking method ELECTRE). 2. Knapsack-like problems, including multiple criteria cases (basic knapsack problem, multicriteria knapsack problem, multiple-choice problem). 3. Evaluation of multicriteria alternatives on the basis of of proximity to the ideal point. 4. Clustering (agglomerative algorithm, clustering with intersection of clusters obtained). 5. Simple diagnosis (ordinal scales) for a composite system on the basis of integration tables. A basic composite system problem is examined as a special laboratory study (Figure 17.2) as follows: (i) design of an individual student’s plan (a tree-like hierarchy) and alternatives for each leaf node of the tree-like plan structure, generation of criteria for evaluation of the alternatives above; (ii) multicriteria ranking of the alternatives; (iii) morphological synthesis of composite decisions on the basis of HMMD (i.e., design of a composite plan). Note, the basic applied example of the student plan is contained in [497].

17 Design of Systems (Structural Approach)

Student’s

Educational courses Basic courses

Other courses

plan

197

Free time Temporary work

Sport

Art

Figure 17.2 Structure of student’s plan Some students examine special system problems as a hierarchical design of an applied system of the student’s interests (e.g., software, plans for software development, sports events, ﬁrm’s plans, communication protocols).

17.5 Textbooks In the main, the course is based on electronic materials: http://www.iitp.ru/mslevin/SYSD.HTM. On the other hand, additional bibliography involves traditional references for all course parts: (i) system issues and systems engineering [119, 464, 565, 710, 849]; (ii) system analysis and decision making [700, 706, 793]; (iii) optimization and combinatorial optimization [267, 268, 281, 551, 687, 793, 911]; (iv) design frameworks [209, 408, 628, 768, 787]; (v) morphological design approach [49, 408, 497, 914]; and (vi) additional issues of system life cycle (requirements engineering, maintenance, system testing) [413, 422, 519, 632, 689, 898].

17.6 Summary The chapter integrates three directions: (a) HMMD as a realization of partitioning/synthesis solving strategy; (b) a set of system technological problems which are targeted to system life cycle and system engineering issues; and (c) educational approach in the ﬁeld of system design. Generally, the material of the course provides a basis for the design of contemporary multidisciplinary high-tech applied systems while taking into account issues of life-cycle engineering.

18 Applied Combinatorial Optimization

18.1 Preliminaries Our community needs well-educated specialists who can formulate and solve multidisciplinary applied problems on the basis of contemporary methodologies of information technology. This chapter addresses a prospective course which is targeted to combinatorial modeling, including an ability in problem formulation. Note, the traditional teaching style in computer science and information technology often has a scientiﬁc orientation (scientiﬁc style) [188, 343]. At the same time, a successful problem solving process has another basis: (1) analysis and structuring of applied situations and problems; (2) analysis, selection or modiﬁcation of well-known mathematical models and/or algorithms, design of new mathematical models and/or algorithms (if this is required); and (3) building a solving framework of the models and algorithms. Thus, applied specialists are in need of special skills: usage of problem formulations, models and algorithms. As a result, we have to consider some special new kinds of educational courses the mathematical modeling which are based on engineering style [188, 226], such as analysis of an applied system and selection/design of models for the system modeling and design. Discrete, combinatorial models play a special central role. C.J. Colbourn has pointed out understanding a problem involves extracting the combinatorics at the heart of the problem [171]. Thus, teaching some basic combinatorial models and objects is a very prospective direction. In some books for applied specialists, basic sets of signiﬁcant applied problem groups and corresponding discrete (combinatorial) models/algorithms are described; for example: (1) application of graph theory (structural balance, transport ﬂows, graph coloring, stability and structures), Markov processes, game theory, group decision making, etc. [687]; (2) optimization problems on networks and graphs (spanning trees, routing, ﬂows problems, bipartite matching and covering, travelling salesman problem (TSP), allocation, critical path problems) [579].

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Composite Systems Decisions

The above-mentioned books are oriented to a certain group of applied specialists (e.g., social science [687]) or to a certain group of combinatorial problems (e.g., optimization on networks and graphs [579]). The basic professional description (a professional encyclopedia) of this domain was published many years ago [281]. This chapter describes an application-oriented educational approach: (i) applied problem, (ii) problem formulation/model, (iii) algorithm/solving scheme, (iv) implementation. Our attempt consists of the generalized description of combinatorial optimization for a wide range of applied specialists on the basis of the main combinatorial problem families. The material focuses on the usage of combinatorial optimization problems on the decision cycle basis (Figure 16.2): 1. analysis of applied problems, including multidisciplinary applications; 2. problem formulation (formulation/selection of mathematical models and/or a framework of mathematical models, search/selection of corresponding specialists in mathematical modeling); 3. design/selection of problem solving strategy (a framework of algorithms and man-machine procedures); 4. implementation of the designed problem solving strategy; and 5. analysis of results. A similar structural approach was used in [489]. The educational approach considered involves soft description of the following parts: (a) preliminaries of complexity theory, (b) main algorithm ideas, algorithm schemes (solving strategies) and their evaluation, (c) basic combinatorial optimization problems (each problem is examined as a family of problems, a family of corresponding algorithms, main applications). The material will lead to the specialist’s skill in supporting each stage of the above-mentioned decision cycle, including generalized analysis and design of the cycle.

18.2 Goals and Structure The course is based on the following fundamentals: (1) systems for searching for the best decisions (search strategies, architecture of optimization systems, DSSs, knowledge-based systems); (2) complexity issues for combinatorial optimization problems and algorithms; (3) kinds of algorithms and algorithm systems (exact algorithms, approximate algorithm schemes, heuristics, metaheuristics); (4) basic groups of combinatorial optimization problems and their applications in engineering, computer science, management, social sciences; and (5) real-world applications and corresponding composite combinatorial optimization problems. Students will develop skills in the analysis and modeling of complex applied problems, formulation of combinatorial optimization problems for various applications, and selection/design of corresponding algorithm frameworks. The course is oriented to applied specialists as engineers, computer scientists, managers, and social engineers. The target educational cycle contains the following steps:

18 Applied Combinatorial Optimization

201

Step 1. Analysis of literature and Internet sources. Step 2. Analysis of applied problems and formulation of combinatorial models. Step 3. Selection/design of solving strategies (search strategies, algorithms, algorithm frameworks). Step 4. Problem solving. Step 5. Analysis of results. Step 6. Preparation of reports. Step 7. Presentation of results at seminar/conference. Figure 18.1 depicts three interconnected domains (special kinds of repositories) which are the basis of the applied course considered. The following basic trend exists in applied domains: From product to product family or product platform. In the domain of models, the corresponding trend is as follows: From model to family of models or space of models. In the algorithmic domain, we get: From algorithm to algorithm family or algorithm scheme/system. A family of assignment-like problems is illustrated in Figure 18.2. A special multidimensional table (axes: number of processors, linear ordered set of objective functions, linear ordered set of precedence constraints) for a class of deterministic scheduling problems was suggested in [488]. Applied problems

HH HH H

Algorithms (solving schemes)

H Families of combinatorial problems (repositories)

Figure. 18.1 Interconnected domains

18.3 Multi-layer Teaching We consider the following structure of the course: (a) lectures, (b) homework (assignments, small projects), (c) test work, (d) team projects, and (e) exam. Four-layer educational framework involves the following (Table 18.1): 1. General system outline: decision cycle, some basic combinatorial optimization problems (knapsack problem, scheduling, packing problems, routing

202

Composite Systems Decisions

problems, etc.), basic search strategies, complexity issues, main algorithmic methods (branch-and-bound method, dynamic programming, local optimization, etc.). System architecture. 2. Basic families of combinatorial optimization problems, algorithmic approaches, real-world applications. This layer involves simple assignments and projects. 3. Composite problems. Intersection of diﬀerent problems. Composite algorithm systems. Real-world applications. This layer involves group student projects. 4. Preparation of reports and articles. Presentation at seminars and conferences. Basic assignment problem ? Quadratic assignment problem

- Multicriteria assignment problem

? ? Multicriteria Generalized quadratic assignment assignment problem @ problem @

? ? Generalized quadratic assignment problem

@ R @

? Multicriteria generalized assignment problem

? ? Multicriteria generalized quadratic assignment problem

Figure 18.2 Family of assignment-like problems

18.4 Lectures and Projects The following lecture plan is examined: Part 1. General introduction. 1.1. Introduction. Decision cycle. Basic search strategies. 1.2. Computational complexity. Kinds of algorithms and algorithm systems. 1.3. Main methods (branch-and-bound method, dynamic programming, local optimization, approximation schemes, evolutionary optimization). 1.4. Algorithm frameworks as model management (selection, modiﬁcation, design). Basic structures of solving frameworks (e.g., series, parallel, seriesparallel, multi-layer, multi-agent). Algorithm systems. 1.5. Architecture of DSSs, knowledge-based systems. Examples. Part 2. Basic combinatorial optimization problems and corresponding problem families. 2.1. Scheduling problems. Applications. 2.2. Knapsack-like problems. Applications.

18 Applied Combinatorial Optimization

203

2.3. Assignment and allocation problems. Applications (personnel assignment, facility allocation, information allocation, channel assignment, task assignment). 2.4. Traveling salesman problem. Applications (routing, scheduling, machine design, etc.). 2.5. Basic bin-packing problem and algorithms. (e.g., multidimensional bin-packing problem, bin-packing problem with composite bins). Applications. 2.6. Packing problems. Covering problems. Applications. 2.7. Clique and graph coloring problems. Applications. 2.8. Basic network design problems (spanning tree problem, routing problems, minimal Steiner tree problem). Applications. Table 18.1 Layers of of educational framework Layer/phase

Contents

Assignments/projects

1. General system Applied decision cycle, search strategies, outline complexity, main algorithmic methods (branch-and-bound, dynamic programming, local optimization, etc.) system architecture 1. Simple assignments 2. Basic families Problem families and projects (problem (scheduling, knapsack, of formulations, combinatorial assignment/allocation, optimization multicriteria selection, traveling salesman design of algorithms) problems problem, bin-packing 2. Preparation of problem, clique, etc. surveys on problems and algorithms 1. Repositories of 3. Composite Team projects (analysis problems combinatorial optimization of applied problems 2. Intersections of problems problems formulations, design of 3. Applied frameworks model framework, design of problems (network of solving schemes, design, function tes- design of algorithms) ting, timetabling, etc. 4. Preparation of Preparation of Presentation at reports/articles materials seminars/conferences

Part 3. Composite problems and real-world applications. 3.1. Repositories of problem families. Examples (scheduling, allocation, etc.). Intersection of problem families (TSP and scheduling, knapsack problem and scheduling, packing and scheduling, etc.). 3.2. Composite solving frameworks. Examples. 3.3. Timetabling problems. Applications.

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3.4. Dynamical allocation problems. Matching problem, multiple-matching problem. Applications (multistage allocation; multiple target track-to-track assignment in monitoring systems, etc.). 3.5. Composite network design problems (multiple routing problem, facilities allocation, etc.). Applications. 3.6. Design of multi-product systems and reconﬁgurable systems. 3.7. System life cycle and application of combinatorial problems. The prospective topics for individual assignments and projects are the following: formulation of problems (ordering, scheduling, selection, allocation, composition); combinatorial optimization problems on networks; multicriteria selection and combinatorial synthesis; surveys on problems and/or algorithms (algorithm schemes); formulation of composite combinatorial optimization problems; and design of algorithms/algorithm schemes. The above-mentioned topics can be considered at levels of simple projects and complex applied projects, including special application domains on the basis of student suggestions (e.g., joint multidisciplinary student teams, which will include students from diﬀerent disciplines).

18.5 Textbooks In the main, the course is oriented to the usage of special course materials (lectures, assignments, etc.). Basic additional kinds of textbooks are: (1) combinatorial optimization (e.g. [281, 450, 477, 551, 634, 703, 732, 889]); (2) general system approaches (e.g. [565, 849]); (3) system design [119, 409, 464, 497, 505]; and (4) integrated sources, including books on combinatorial optimization (a mix of combinatorial optimization and real-world applications, e.g. in network design) [196, 497, 579, 713].

18.6 Summary In this chapter, the new reference point for education in combinatorial optimization with orientation to applied specialists is described. Here, basic families of combinatorial optimization problems are considered as a fundamental for the educational process. The prospective realization of the suggested course can be considered for students in various applied disciplines (e.g., engineering, computer science, management, social and organizational science).

Conclusion

This book addresses the author’s approach to composite systems, relevant composite systems decisions, and support procedures required. Evidently, successful modeling the complex composite (modular) systems and design of composite systems decisions are based on multidisciplinary expertise, experience, and thinking. The author hopes that the theoretical models and applied examples described in the book will be useful for readers as follows: 1. to learn and understand the problems in the ﬁeld of composite systems decisions; 2. to accumulate many case studies in the ﬁeld of composite systems decisions; 3. to organize some information and knowledge bases in the ﬁeld of composite systems decisions; and 4. to extend the models and examples above from our book to obtain new advances models and new real-world applications.

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About the Author

Dr Mark Sh. Levin received the M.S. degree in Radioengineering from Moscow Technological University for Communication and Informatics (1970), the M.S. degree in Mathematics from M.V. Lomonosov Moscow State University (1975), the Ph.D. degree in Systems Analysis and Combinatorial Optimization from the Institute for Systems Analysis of the Russian Academy of Sciences (1982). From 1970 to 1983 he was with Moscow R & D organizations as an Engineer, a Senior Engineer, and Head of Laboratory (algorithms for air-traﬃc control, software & information engineering for government and industry, management and decision support systems). After that he conducted his (mainly independent) research projects as a Researcher (Senior Researcher, Leading Researcher, Independent Researcher, Visiting Researcher/Scholar) in Russia (Research Institute for Normalization in Machine-Building, the Russian Academy of Sciences), Japan (The University of Aizu), Canada (University of Ottawa, University of Toronto), and Israel (Ofakim Center of Technology, The Ariel College, The Ben-Gurion University). Now, Dr Levin is with the Institute for Information Transmission Problems of the Russian Academy of Sciences (Moscow) as a Senior Scientiﬁc Researcher. Dr Levin has multiyear experience in advanced development and in leadership roles for advanced systems development projects.

Index

Ackoﬀ, R.L., 6 additive function, 48 admissible morphological scheme, 40 Advanced beginner (rookie), 23 agglomerative algorithm, 196 aggregation for preference relations, 155 aggregation method for multistage design, 104 AHP, 8, 10, 22, 47, 48, 96, 97, 195 algebraic logic, 48 algorithm framework, 26, 27, 200, 201 algorithm scheme, 5, 27, 200, 201, 204 algorithm system, 5, 25, 26, 200–202 algorithmic state machine (ASM), 55 alignment problem, 195 allocation of modularity, 90 allocation problem, 195, 199, 203, 204 Altshuller, G.S., 4, 66 analytic hierarchy process, 8 And–Or tree, 16, 31, 37, 65, 67, 143, 177, 178 any-time algorithm, 23 approaches for complex systems design, 37 approaches for revelation of system bottlenecks, 56 approximation, 169 approximation scheme, 200, 202 architecture of representations, 14 Artobolevsky, I.I., 33 assignment problem, 89, 195, 203 associative thinking, 186, 187 axiomatic design, 34 big diﬀerence, 162 bin-packing problem, 203

binary relation over change operations, 69 binary relations, 119, 120 bipartite matching, 199 Bottom-up framework, 39 branch-and-bound method, 202 Brown, D.C., 7 CAD, 55 CAD/CAM, 54, 183 CAL Expert System, 16 Cambridge Engineering Centre, 16 CASE, 95, 96 case-based reasoning, 37 Chandrasekaran, B., 7 CIM, 54 classiﬁcation formulae for multi-product system, 85 classiﬁcation of specialists, 23 clique problem, 195, 203 clustering, 34, 35, 196 CODE4, 16 Colbourn, C.J., 199 colored Petri nets, 56 combinatorial design spaces, 17 combinatorial evolution, 65, 74, 104 combinatorial synthesis, 38, 110, 123, 124, 204 combinatorial thinking, 188 common modules in multi-product system, 77 common part of digraphs, 155, 160 common part of two digraphs, 156 common subgraph, 156 communication operator, 173 communication skill, 187

250

Index

compatibility among software modules, 97 component-based software development, 96 component-based system design, 8, 37 component-based systems, 33 composable systems, 5, 37, 65, 66 composite decision, 14, 39–41, 45, 54, 57, 59, 62–64, 76, 100, 102, 104, 106, 116, 117, 124, 125, 127, 128, 134, 135, 138, 139, 141, 142, 152, 154, 160, 168, 173–175 composite decision with redundancy, 102 composite packaged software, 95 composite scale, 34 composite system trajectory, 54 composite systems, 5, 8–11, 14, 38, 41, 47, 50, 54, 57, 65, 66, 69, 74, 77, 84, 104, 106, 107, 109, 122, 123, 185, 196, 202 composition, 34, 95 composition problem, 40, 106 computer aided support environments (CASE), 95 concept lattices, 14, 17 conceptual design, 14, 31, 43, 47, 55, 185, 193 conceptual knowledge, 16 conceptual knowledge systems, 17 concrete macrotechnology, 123 concurrent engineering, 54, 184, 186, 193 conﬁguration management, 32, 75, 97 conﬁguration of buildings, 110 Conklin, J., 14 consensus, 155 constraint-based space-decreasing methods, 24 contradiction in common part of digraphs, 157 coordination of two digraphs, 156 course on applied combinatorial optimization, 199 course on design of systems, 193 covering problem, 76, 195, 199, 203 creative levels, 4 criteria for medical treatment, 136 criteria for software, 98 critical path problem, 199 data envelopment analysis DEA, 47

DBMS, 98, 186 decision cycle, 5, 8, 184, 186, 187, 200, 201 decision maker, 22 decision support systems, 11 decision-aiding methodology, 18 decision-based design, 37 decision-making framework, 20, 21 decision-making paradigm, 18, 195 decomposable system, 41, 65, 66 decomposition, 8, 33, 34, 184 DELPHY, 10 Demster–Shafer theory, 142 Denning, P.J., 23, 65 design ﬂow, 36 design framework, 6, 86, 194, 197 design morphology, 38, 63, 124, 128 design of life cycle, 53, 54 design spaces, 18 design strategy, 78, 79, 82 design structure matrix, 34 Designer’s Electronic Guidebook, 16 discrete space of system excellence, 42, 47, 50, 52, 80, 100, 139, 140 dissimilarity, 155–157, 167 distributed hypermedia system for managing knowledge in organizations (KMS), 16 divide and conquer, 33 Dixon, J.R., 36 domain expert, 5, 15, 22, 31, 37 domain factual knowledge (DFK), 7 domain-independent engineering, 185, 187 DSS COMBI PC, 10, 17, 48, 125 DSS for hierarchical engineering design SED, 17 DSSs, 11, 18, 19, 71, 97, 98, 142, 143, 186, 200, 202 dynamic programming, 24, 33, 41, 42, 161, 202 ELECTRE, 22, 196 ellipsoid method, 24, 195 engineering concept spaces, 14, 17, 18, 51, 186 engineering databases, 31, 51 engineering design spaces, 194 engineering experience, 33, 74 engineering history bases, 14, 17, 51, 67 engineering style, 193, 199

Index enumerative algorithm, 40 Ershov, A.P., 3 evaluating concepts for software quality, 97 evaluation approaches, 47 evolution process, 10, 32, 65, 66, 68–71, 73, 74, 96, 104 evolutionary design, 37 evolutionary multiobjective optimization, 37 evolutionary optimization, 38, 202 evolutionary synthesis, 36, 38 exchange operations, 68 Expert (virtuoso), 23 expert judgment, 56, 97, 109, 127, 132, 139, 142, 147, 155, 174 expert system, 37, 47, 48, 96, 98, 142 expert system R1/MICON, 37 facilities allocation, 204 family of algorithms, 201 family of assignment-like problems, 201, 202 family of combinatorial optimization problems, 200, 202, 204 family of models, 201 feasible morphological scheme, 40 ﬁnite automata, 37 ﬂow graph representation (FGR), 32 ﬂows problems, 199 FMS, 54 formal methods for design, 37 frame of political administration, 178 framework of systems engineering education, 189 functions of political administration, 177 game theory, 199 general engineering, 183, 191 general problem-solving cycle, 6 global creative decision, 5 global optimization, 37, 194 goals of modularity, 33 gradient-like methods, 24 grammars, 31 grammatical design, 37 graph coloring problem, 195, 199, 203 graph edit distance, 155, 171 graph-dynamics, 74 greedy algorithm, 24 group decision making, 8, 199

251

hard technology, 54 heuristic, 25, 34, 42, 157, 200 hierarchical hypertext system (HHS), 16, 18 hierarchical morphological approach, 38, 176, 177, 179 hierarchical morphological multicriteria design, 5 hierarchical morphological space of operations (HMSO), 42 hierarchical solving process, 8 hierarchical system design, 37 high dissimilarity, 167 high-level system design methods, 55 HMMD, 5, 9, 10, 17, 24, 36–40, 50, 54, 57, 60, 64, 66, 69–71, 77, 82, 91, 95, 97, 103, 104, 106, 109, 128, 143, 145, 154, 173, 194–197 HMSO, 42, 43 hybrid methods, 38 hypergraph, 156, 167 immunoassay technology, 145, 153, 154 improvement, 10, 14, 24, 25, 38, 39, 41, 54, 56, 57, 67, 74, 95, 100, 102, 104, 106–111, 113, 119, 120, 122, 140, 141, 179, 185 improvement actions, 38, 45, 54, 100, 105, 108, 109, 111–113, 118, 120, 121, 128, 141, 179 improvement actions for buildings, 111 improvement of medical plan, 141 improvement operations for buildings, 118 improvement plan, 56, 108, 179 improvement process, 56, 120, 122, 141 improvement process for buildings, 120 improvement search strategy, 24 improvement strategy, 24, 25, 120 improvement trajectory, 67 information design model (EDM) for engineering design, 16 information model for cooperative product development SHARED, 17 integrated intelligent design and manufacturing system, 54 integrated product and process design, 54 integrated software, 98 integration tables, 47, 48, 50, 113, 196

252

Index

intellectual capital, 14, 22 intellectual decision, 5 intersection of problem families, 203 Jackson approach to software development (JSD), 96 JIT, 54 K-exchange operation, 68 KADS technology, 15, 143 kinds of evolution, 65 kinds of platforms, 76 kinds of political administration, 177 kinds of requirements, 55 kinds of scales, 34 knapsack problem, 70, 109, 120, 161, 195, 196, 201, 203 knapsack-like problem, 96, 157, 196, 202 knowledge acquisition, 15, 16, 37, 42, 43, 142, 143 knowledge acquisition activity matrix, 15 knowledge acquisition and representation language KARL, 16 knowledge engineer, 22 knowledge-based systems, 3, 20, 37, 142, 187, 200, 202 large design spaces, 17 largest common subgraph, 156 last mile problem, 173 lattices, 35, 42, 47 laws for evolution of software systems, 66 Legend, 23, 65 Lehman, M.M., 66 levels of system complexity, 32 life-cycle engineering, 35, 53, 59, 64, 193, 194, 197 life-cycle maintenance, 59 life-cycle management, 53 line graph representation (LGR), 32 linguistic geometry, 16, 122 local optimization, 24, 202 local quasi-creative decision, 5 M-Class model, 16 macroheuristic, 5, 40 maintenance, 57, 59, 64, 97, 194, 196, 197 maintenance framework, 57, 58

maintenance of life cycle, 53 maintenance problems, 58 maintenance procedures, 57, 59 maintenance scheme, 58 management information systems, 11 management of life cycle, 54 Markov process, 199 Master, 23, 65 matching problem, 204 mathematical logic, 48 MatLab, 196 maximal substructure, 195 maximum agreement substructure, 155 maximum common subgraph, 171 maximum common substructure, 155 maximum dissimilarity, 156, 157 measurement problems, 35 mereology, 32 mereotopology, 32 metaheuristics, 26, 200 metrics, 155 minimal Steiner tree problem, 76, 195, 203 minimal superstructure, 195 minimum cost transformation, 155 Minsky, M., 14 MIS, 11, 186 modular architecture, 47, 77, 95 modular design, 8, 10, 36, 37, 43, 47, 95, 98, 104, 145, 194 modular systems, 5, 10, 33, 57–59, 96, 107 modularity, 33, 77, 87, 89, 184, 193, 195 monotone function, 48 morphological analysis, 8, 37, 194 morphological class, 40, 41 morphological clique, 40, 42, 84 morphological clique problem, 40, 42, 44, 47, 50, 66, 70, 71, 77, 90, 110, 121, 156, 160, 167, 169, 175 morphological design approach, 194, 197 morphological macroheuristic, 40 morphological scheme, 40, 60 morphological table, 147 multi-agent systems, 22 multi-algorithm framework, 27, 28 multi-attribute space, 47 multi-attribute utility analysis, 47, 48 multi-product systems, 75–77, 84, 91, 195, 204

Index multicriteria knapsack problem, 196 multicriteria ranking, 17, 22, 42, 57, 60, 70, 97, 110, 121, 196 multicriteria space, 35 multidisciplinarity, 184 multidisciplinary engineering spaces, 186 multidisciplinary optimization, 37, 195 multidisciplinary thinking, 184, 186, 187 multiobjective evolutionary optimization, 38 multiparameter space, 35, 48 multiple-choice problem, 70, 110, 121, 195, 196 multiple-valued logic, 48 multistage design, 10, 36, 38, 59, 64, 66, 95, 103, 106, 123, 128, 141, 194, 195 multistage evolution trajectory, 71 multistage knowledge acquisition, 16 Nemhauser, C.L., 26 nominal scale, 34 non-linear mixed integer programming, 37, 110, 194, 195 non-linear multiobjective optimization, 37 Novice (beginner), 23 ontology, 16, 17, 31 operations of traditional logic, 185 optimal system trajectories, 59 ordinal scale, 4, 34, 35, 39, 47, 48, 143, 147, 163, 196 organic hierarchy, 38 outranking techniques, 22, 195, 196 packing problem, 195, 201, 203 parallel method, 24 parameter space investigation (PSI), 24 Pareto-eﬀective decisions, 40, 45, 57, 60, 100, 104–106, 128, 159, 160, 195 Pareto-eﬀective points, 42, 45, 48, 100, 127, 139, 140, 196 Pareto-eﬀective solutions, 40, 116 Pareto-like approach, 47, 48 partitioning, 8, 33 partitioning–synthesis method, 24, 38 Petri nets, 10, 31 phases of literacy, 4 planning of life cycle, 53 planning of medical treatment, 135

253

political administration, 177–179 poset-like scale, 34, 47, 50, 132 potential graph representation (PGR), 32 preference relations, 155, 157, 170 preventive maintenance, 59, 107 principles of system analysis, 34 problem-solving cycle, 6 product family, 36, 53, 76, 91, 193, 201 product platform, 36, 53, 76, 91, 201 product portfolio, 76 product trajectory, 59–62, 64, 123 product trajectory design, 54 Professional (competent), 23 Professionals, 65 Proﬁcient professional (star), 23 PROforma approach, 143 Promethee, 22 properties of information technology, 13 proximity, 69 PSI, 37, 47, 194, 195 qualitative scale, 34 quantitative scale, 34, 35, 47, 48, 121 quasi-intellectual decision, 5 Ramil, J.F., 66 random method, 24 reconﬁgurable systems, 33, 75, 204 redesign, 10, 11, 38, 56, 66, 67, 69, 100, 107–113, 119–122, 135, 143, 185, 187, 195 redundancy of system components, 102 reengineering, 38, 56 region-approximation-based methods, 24 region-connection calculus, 32 repositories of problems, 203 requirements engineering, 31, 35, 55, 56, 97, 185, 196, 197 resistance graph representation (RGR), 32 revelation of system bottlenecks, 10, 38, 56, 57, 109, 194, 195 rotation distance, 155 routing problem, 199, 202–204 rules for development of technical systems, 66 Saaty, T.L., 10, 48 sandwich immunoassay, 145 Sawney, M.S., 76

254

Index

scale for creativity, 4 scheduling problems, 110, 195, 201–203 scientiﬁc style, 193, 199 search methodology, 24 search space, 24, 79, 194 search strategy, 24, 79, 200–202 Shakun model for evolutionary system design ESD, 67 Shannon, C.E., 5 Shenhar, A., 32 sign graph, 31 similarity, 155, 167 Simon, H.A., 18 Sobol, I.M., 24 soft description, 200 soft systems methodology for software development, 96 soft technology, 54 software conﬁguration management, 97 space of improvements, 57 space of models, 201 spanning tree, 24, 199 spanning tree problem, 195, 203 specialist’s proﬁle, 131 specialists in software engineering, 132 state charts, 31 state machine, 31 state-space search, 23 Statnikov, R.B., 24 STEPCLASS technique, 16 strong contradiction, 162 strong preference, 162, 164 structure of building, 110 structure of concrete macrotechnology, 124 structure of immunoassay technology, 153 structure of medical plan, 135 substructure, 69, 169 super substructure, 169 superstructure, 169 support of life cycle, 53 synthesis of ﬁnite automata, 37 system analysis, 34, 35, 50, 84, 107, 195–197 system architecture, 18, 47, 75, 185, 193, 200, 202 system change operations, 67, 195 system changes, 65–67, 69, 104, 194

system conﬁguration, 56, 67, 75, 76, 91 system design, 37, 38, 47, 51, 54, 55, 59, 186, 193–195, 197, 199, 204 system engineering education, 183 system evolution, 10, 14, 17, 32, 51, 59, 65–67, 69, 71, 74, 96, 104, 184, 186, 188, 190, 194 system for representing and using real-world knowledge NETL, 16 system hierarchy, 14, 15, 184 system improvement, 38, 56, 74, 106 system integration, 8, 35, 36, 38, 95, 106 system life cycle, 53, 185 system properties, 35, 38 system synthesis, 8, 35, 36, 38, 50, 95, 106, 186 system technological problems, 10, 195, 197 system thinking, 184 system trajectory, 54, 59, 129 system version spaces, 17, 18 system versions, 17, 18, 57, 69 system with redundancy, 102 technological strategy, 123, 124 technological trajectory, 67, 123 the ﬁrst literacy, 3 the second literacy, 3 the third literacy, 3 timetabling problems, 203 TQM, 54 trajectory design, 59, 63, 64, 123 trajectory method, 106, 141 trajectory method for multistage design, 104, 105 transitivity, 169 traveling salesman problem, 195, 199, 203 Trick, M.A., 26 Turing machine, 31 Turing, A., 31 utility function, 22, 48, 125, 195, 196 vector of system excellence, 40 version modeling, 32 weak contradiction, 162, 168 weak diﬀerence, 162, 169