Multiple criteria optimization : state of the art annotated bibliographic surveys

519 Pages·2002·6.57 MB·English

by  Ehrgott

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
eBookISBN: 0-306-48107-3
Print ISBN: 1-4020-7128-0
©2003 Kluwer Academic Publishers
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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
DataEnvelopment 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
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List of Figures
1.1 The set ofefficient 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