MULTIPLE CRITERIA OPTIMIZATION: STATE OF THE ART ANNOTATED BIBLIOGRAPHIC SURVEYS INTERNATIONAL SERIES IN OPERATIONS RESEARCH & MANAGEMENT SCIENCE Frederick S. Hillier, Series Editor Stanford University Ho, T.-H. & Tang, C. S. / PRODUCT VARIETY MANAGEMENT El-Taha, M. & Stidham , S. / SAMPLE-PATH ANALYSIS OF QUEUEING SYSTEMS Miettinen, K. M. / NONLINEAR MULTIOBJECTIVE OPTIMIZATION Chao, H. & Huntington, H. G. / DESIGNING COMPETITIVE ELECTRICITY MARKETS Weglarz, J. / PROJECT SCHEDULING: Recent Models, Algorithms & Applications Sahin, I. & Polatoglu, H. / QUALITY, WARRANTY AND PREVENTIVE MAINTENANCE Tavares, L. V. / ADVANCED MODELS FOR PROJECT MANAGEMENT Tayur, S., Ganeshan, R. & Magazine, M. / QUANTITATIVE MODELING FOR SUPPLY CHAIN MANAGEMENT Weyant, J./ ENERGY AND ENVIRONMENTAL POLICY MODELING Shanthikumar, J.G. & Sumita, U./APPLIED PROBABILITY AND STOCHASTIC PROCESSES Liu, B. & Esogbue, A.O. / DECISION CRITERIA AND OPTIMAL INVENTORY PROCESSES Gal, T., Stewart, T.J., Hanne, T. / MULTICRITERIA DECISION MAKING: Advances in MCDM Models, Algorithms, Theory, and Applications Fox, B. L./ STRATEGIES FOR QUASI-MONTE CARLO Hall, R.W. / HANDBOOK OF TRANSPORTATION SCIENCE Grassman, W.K./ COMPUTATIONAL PROBABILITY Pomerol, J-C. & Barba-Romero, S. / MULTICRITERION DECISION IN MANAGEMENT Axsäter, S. / INVENTORY CONTROL Wolkowicz, H., Saigal, R., Vandenberghe, L./ HANDBOOK OF SEMI-DEFINITE PROGRAMMING: Theory, Algorithms, and Applications Hobbs, B. F. & Meier, P. / ENERGY DECISIONS AND THE ENVIRONMENT: A Guide to the Use of Multicriteria Methods Dar-El, E./ HUMAN LEARNING: From Learning Curves to Learning Organizations Armstrong, J. S./ PRINCIPLES OF FORECASTING: A Handbook for Researchers and Practitioners Balsamo, S., Personé, V., Onvural, R./ ANALYSIS OF QUEUEING NETWORKS WITH BLOCKING Bouyssou, D. et al/ EVALUATION AND DECISION MODELS: A Critical Perspective Hanne, T./ INTELLIGENT STRATEGIES FOR META MULTIPLE CRITERIA DECISION MAKING Saaty, T. & Vargas, L./ MODELS, METHODS, CONCEPTS & APPLICATIONS OF THE ANALYTIC HIERARCHY PROCESS Chatterjee, K. & Samuelson, W./ GAME THEORY AND BUSINESS APPLICATIONS Hobbs, B. et al/ THE NEXT GENERATION OF ELECTRIC POWER UNIT COMMITMENT MODELS Vanderbei, R.J./ LINEAR PROGRAMMING: Foundations and Extensions, 2nd Ed. Kimms, A./ MATHEMATICAL PROGRAMMING AND FINANCIAL OBJECTIVES FOR SCHEDULING PROJECTS Baptiste, P., Le Pape, C. & Nuijten, W./ CONSTRAINT-BASED SCHEDULING Feinberg, E. & Shwartz, A./ HANDBOOK OF MARKOV DECISION PROCESSES: Methods and Applications Ramík, J. & Vlach, M. / GENERALIZED CONCAVITY IN FUZZY OPTIMIZATION AND DECISION ANALYSIS Song, J. & Yao, D. / SUPPLY CHAIN STRUCTURES: Coordination, Information and Optimization Kozan, E. & Ohuchi, A./ OPERATIONS RESEARCH/ MANAGEMENT SCIENCE AT WORK Bouyssou et al/ AIDING DECISIONS WITH MULTIPLE CRITERIA : Essays in Honor of Bernard Roy Cox, Louis Anthony, Jr./ RISK ANALYSIS: Foundations, Models and Methods Dror, M., L’Ecuyer, P. & Szidarovszky, F. / MODELING UNCERTAINTY: An Examination of Stochastic Theory, Methods, and Applications Dokuchaev, N./ DYNAMIC PORTFOLIO STRATEGIES: Quantitative Methods and Empirical Rules for Incomplete Information Sarker, R., Mohammadian, M. & Yao, X./ EVOLUTIONARY OPTIMIZATION Demeulemeester, R. & Herroelen, W./ PROJECT SCHEDULING: A Research Handbook Gazis, D.C. / TRAFFIC THEORY Zhu/ QUANTITATIVE MODELS FOR PERFORMANCE EVALUATION AND BENCHMARKING MULTIPLE CRITERIA OPTIMIZATION: STATE OF THE ART ANNOTATED BIBLIOGRAPHIC SURVEYS Edited by MATTHIAS EHRGOTT University of Auckland XAVIER GANDIBLEUX Université de Valenciennes KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: 0-306-48107-3 Print ISBN: 1-4020-7128-0 ©2003 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2002 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://kluweronline.com and Kluwer's eBookstore at: http://ebooks.kluweronline.com Contents List of Figures ix List of Tables xi Preface xiii Ralph E. Steuer Introduction xv Matthias Ehrgott, Xavier Gandibleux References xviii 1 Theory of Vector Optimization 1 Christiane Tammer, Alfred Göpfert 1.1 Solution Concepts 1 1.2 Optimality Conditions 13 1.3 Duality 24 1.4 Vector Variational Inequalities and Vector Equilibria 34 1.5 Multicriteria Fractional Programming 36 1.6 Multicriteria Control Problems 42 References 46 2 Nonlinear Multiobjective Programming 71 Tetsuzo Tanino, Hun Kuk 2.1 Introduction 72 2.2 Solution Concepts 73 2.3 Scalarization and Optimality Conditions 76 2.4 Stability and Sensitivity Analysis 80 2.5 Duality 81 2.6 Vector Variational Inequalities 86 2.7 Concluding Remarks 89 References 89 vi MULTIPLE CRITERIA OPTIMIZATION 3 Goal Programming in the Period 1990-2000 129 Dylan F. Jones, Mehrdad Tamiz 3.1 Introduction 129 3.2 Details of Literature Review 133 3.3 Classification of GP Extension Articles 136 3.4 Integration and Combination of Goal Programming with Other Techniques 140 3.5 Conclusion and Comment 144 References 148 4 Fuzzy Multiobjective and Multilevel Optimization 171 Masatoshi Sakawa 4.1 Fuzzy Decision 172 4.2 Multiobjective Programming and Solution Concepts 178 4.3 Interactive Multiobjective Programming 179 4.4 Fuzzy Multiobjective Linear Programming 183 4.5 Interactive Fuzzy Multiobjective Linear Programming 186 4.6 Interactive Fuzzy Multiobjective Linear Programming with Fuzzy Parameters 193 4.7 Related Works and Applications 203 4.8 Interactive Fuzzy Two-level Linear Programming 204 4.9 Interactive Fuzzy Two-level Linear Programming with Fuzzy Parameters 212 References 217 5 Interactive Nonlinear Multiobjective Procedures 227 Kaisa Miettinen 5.1 Introduction 227 5.2 Concepts 228 5.3 Methods 231 5.4 Comparing the Methods 253 5.5 Conclusions 254 References 256 6 Evolutionary Algorithms and Multiple Objective Optimization 277 Carlos A. Coello Coello, Carlos E. Mariano Romero 6.1 Introduction 278 6.2 Definitions 279 6.3 Notions of Evolutionary Algorithms 280 6.4 Classifying Techniques 281 6.5 Non-Pareto Techniques 281 6.6 Pareto-Based Techniques 291 6.7 Recent Approaches 298 6.8 Diversity 302 6.9 Test Functions 305 6.10 Metrics 306 6.11 Applications 308 6.12 Future Research Paths 309 6.13 Summary 311 References 312 Contents vii 7 Data Envelopment Analysis in Multicriteria Decision Making 333 Hirotaka Nakayama, Masao Arakawa, Ye Boon Yun 7.1 Introduction 334 7.2 Data Envelopment Analysis 335 7.32 Basic DEA Models 337 7.4 GDEA Based on Parametric Domination Structure 343 7.5 GDEA Based on Production Possibility 347 7.6 Comparison between GDEA and DEA Models 353 7.7 GDEA for Multiple Criteria Decision Making 357 7.8 Conclusions 364 References 365 8 Multiobjective Combinatorial Optimization 369 Matthias Ehrgott, Xavier Gandibleux 8.1 Introduction 370 8.2 Multiple Objective Combinatorial Optimization Problems 371 8.3 Properties of MOCO Problems 373 8.4 Solution Methods for MOCO Problems 376 8.5 Classification of the Literature 388 8.6 Annotation of the Literature Problem by Problem 389 8.7 Open Questions and Conclusions 404 References 407 9 Multicriteria Scheduling Problems 445 Vincent T'Kindt, Jean-Charles Billaut 9.1 Scheduling Theory 446 9.2 Overview of Multicriteria Optimization Theory 451 9.3 Solving Multicriteria Scheduling Problems 454 9.4 Complexity Results 458 9.5 Single Machine Problems 465 9.6 Parallel Machines Problems 475 9.7 Shop Problems 479 References 482 Index 493 This page intentionally left blank List of Figures 1.1 The set of efficient elements of a vector-valued loca- tion problem with the maximum norm. 34 4.1 Membership function and characteristic function. 173 4.2 Fuzzy number. 174 4.3 set of fuzzy number 175 4.4 Fuzzy decision, convex fuzzy decision, and product fuzzy decision. 177 4.5 Graphical interpretation of minimax method. 181 4.6 Linear membership function. 184 4.7 Fuzzy min membership function. 187 4.8 Fuzzy max membership function. 188 4.9 Fuzzy equal membership function. 188 4.10 Linear membership function. 208 4.11 Flowchart of interactive fuzzy two-level programming. 213 5.1 Visual illustrations in WWW-NIMBUS. 255 6.1 Scheme of VEGA’s selection mechanism. It is as- sumed that the population size is N and that there are M objective functions. 284 6.2 Example of cooperative and non-cooperative game solutions. 290 6.3 Flowchart of the Nondominated Sorting Genetic Al- gorithm (NSGA). 294 6.4 Diagram that illustrates the way in which the micro- GA for multiobjetive optimization works. 300 7.1 CCR efficient frontier and production possibility set generated by the CCR model from the observed data. 339 7.2 BCC efficient frontier and production possibility set generated by the BCC model from the observed data. 341 7.3 FDH efficient frontier and production possibility set generated by the FDH model from the observed data. 344 x MULTIPLE CRITERIA OPTIMIZATION 7.4 Efficient frontier generated by GDEA model with 347 7.5 Efficient frontier generated by GDEA model with 347 7.6 Efficient frontier generated by model with 348 7.7 Efficient frontier generated by model with and 352 7.8 Efficient frontier generated by model with and 353 7.9 Efficient frontier generated by model with and non-fixed 353 7.10 Ranking method. 358 7.11 GA with DEA method. 359 7.12 Geometric interpretation of in (P). 361 7.13 Results to the Example 1 (from left to right, 10, 20, 30 generations,