Tetsuzo TaninoTamaki TanakaMasahiro Inuiguchi

Multi-Objective Programmingand Goal Programming

Theory and Applications

With 77 Figuresand 48 Tables

Springer

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Contents

PART I: Invited Papers 1Multiple Objective Combinatorial Optimization — A Tutorial . 3Matthias Ehrgott, Xavier Gandibleux1 Importance in Practice 32 Definitions 43 Characteristics of MOCO Problems 44 Exact Solution Methods 55 Heuristic Solution Methods 86 Directions of Research and Resources 12References 13

Analysis of Trends in Distance Metric Optimisation Modellingfor Operational Research and Soft Computing 19D. F. Jones, M. Tamiz1 Introduction 192 Distance Metric Optimisation and Meta Heuristic Methods 203 Distance Metric Optimisation and the Analytical Hierarchy Process 214 Distance Metric Optimisation and Data Mining 225 Some Further Observations on Goal Programming Modelling Practice 226 Conclusions 23References 23

MOP/GP Approaches to Data Mining 27Hirotaka Nakayama1 Introduction 272 Multisurface Method (MSM) 283 Goal Programming Approaches to Pattern Classification 294 Revision of MSM by MOP/GP 305 Support Vector Machine 316 Concluding Remarks 34References 34

Computational Investigations Evidencing Multiple Objectivesin Portfolio Optimization 35Ralph E. Steuer, Yue Qi1 Introduction 352 Different Perspectives 383 Computational Investigations 404 Concluding Remarks 42References 43

VIII

Behavioral Aspects of Decision Analysis with Application toPublic Sectors 45Hiroyuki Tamura1 Introduction 452 Behavioral Models to Resolve Expected Utility Paradoxes 453 Behavioral Models to Resolve Restrictions of Additive/Utility In-

dependence in Consensus Formation Process 494 Concluding Remarks 54References 54

Optimization Models for Planning Future Energy Systems inUrban Areas 57Kiichiro Tsuji1 Introduction 572 Optimization Problems in Integrated Energy Service System 583 Energy System Optimization for Specific Area 594 Optimization of DHC System[5] 615 Optimization of Electric Power Distribution Network[6] 626 Concluding Remarks 63References 64

Multiple Objective Decision Making in Past, Present, and Fu-ture 65Gwo-Hshiung Tzeng1 Introduction 652 Fuzzy Multiple Objectives Linear Programming 673 Fuzzy Goal Programming 674 Fuzzy Goal and Fuzzy Constraint Programming 685 Two Phase Approach for Solving FMOLP Problem 696 Goal Programming with Achievement Functions 707 Multiple Objective Programming with DEA 718 De Novo Programming Method in MODM 739 Summary 74References 75

Dynamic Multiple Goals Optimization in Behavior Mechanism 77P. L. Yu, C. Y. ChiangLin1 Introduction 782 Goal Setting and State Evaluation 793 Charge Structures and Attention Allocation 814 Least Resistance Principle 825 Information Input 826 Conclusion 83References 83

PART II: General Papers - Theory 85

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An Example-Based Learning Approach to Multi-Objective Pro-gramming 87Masami Amano, Hiroyuki Okano1 Introduction 872 Our Learning Approach 883 Numerical Experiments 904 Concluding Remarks 92References 92

Support Vector Machines using Multi Objective Programming 93Takeshi Asada, Hirotaka Nakayama1 Principle of SVM 932 Multi Objective Programming formulation 943 Application to Stock Investment problem 974 Conclusion 97References 98

On the Decomposition of DEA Inefficiency 99Yao Chen, Hiroshi Morita, Joe Zhu1 Introduction 992 Scale and Congestion Components 1003 Conclusion 104References 104

An Approach for Determining DEA Efficiency Bounds 105Yao Chen, Hiroshi Morita, Joe Zhu1 Introduction 1052 Determination of the Lower Bounds 106References 110

An Extended Approach of Multicriteria Optimization for MODMProblems I l lHua-Kai Chiou, Gwo-Hshiung Tzeng1 Introduction I l l2 The Multicriteria Metric for Compromise Ranking Methods 1123 The Extended Compromise Ranking Approach 1134 Illustrative Example 1145 Conclusion 116References 116

The Method of Elastic Constraints for Multiobjective Com-binatorial Optimization and its Application in Airline CrewScheduling 117Matthias Ehrgott, David M. Ryan1 Multiobjective Combinatorial Optimization 1172 The Method of Elastic Constraints 118

3 Bicriteria Airline Crew Scheduling: Cost and Robustness 1194 Numerical Results 1215 Conclusion 121References 122

Some Evaluations Based on DEA with Interval Data 123Tornoe Entani, Hideo Tanaka1 Introduction 1232 Relative Efficiency Value 1243 Approximations of Relative Efficiency Value with Interval Data . . . . 1254 Numerical Example 1275 Conclusion 127References 128

Possibility and Necessity Measures in Dominance-based RoughSet Approach 129Salvatore Greco, Masahiro Inuiguchi, Roman Slowiriski1 Introduction 1292 Possibility and Necessity Measures 1303 Approximations by Means of Fuzzy Dominance Relations 1324 Conclusion 134References 134

Simplex Coding Genetic Algorithm for the Global Optimiza-tion of Nonlinear Functions 135Abdel-Rahman Hedar, Masao Fukushima1 Introduction 1352 Description of SCGA 1363 Experimental Results 1384 Conclusion 139References 140

On Min imax and Maximin Values in Multicriteria Games . . . . 141Masakazu Higuchi, Tamaki Tanaka1 Introduction 1412 Multicriteria Two-person Zero-sum Game 1413 Coincidence Condition 144References 146

Backtrack Beam Search for Multiobjective Scheduling Prob-lem 147Naoya Honda1 Introduction 1472 Problem Formulation 1483 Search Method 1484 Numerical Experiments 151

XI

5 Conclusion 152References 152

Cones to Aid Decision Making in Multicriteria Programming . 153Brian J. Hunt, Margaret M. Wiecek1 Introduction 1532 Problem Formulation 1543 Pointed and Non-Pointed Cones in Multicriteria Programming 1544 Decision Making with Polyhedral Cones 1565 Example 1576 Conclusion 158References 158

Efficiency in Solution Generation Based on Extreme Ray Gen-eration Method for Multiple Objective Linear Programming.. 159Masaaki Ida1 Introduction 1592 Cone Representation and Efficiency Test 1603 Efficient Solution Generation Algorithm 1614 Numerical Example 1635 Conclusion 164References 164

Robust Efficient Basis of Interval Multiple Criteria and Mul-tiple Constraint Level Linear Programming 165Masaaki Ida1 Introduction 1652 Multiple Criteria and Multiple Constraint Level Linear Programming 1663 Interval Coefficient Problem 1674 Main Results 1685 Conclusion 169References 169

An Interactive Satisficing Method through the Variance Mini-mization Model for Fuzzy Random Multiobjective Linear Pro-gramming Problems 171Hideki Katagiri, Masatoshi Sakawa, Shuuji Ohsaki1 Introduction 1712 Formulation 1723 Interactive Decision Making Using the Variance Minimization Model

Based on a Possibility Measure 1744 Conclusion 176References 176

XII

On Saddle Points of Multiobjective Functions 177Kenji Kimura, El Mostafa Kalmoun, Tamaki Tanaka1 Introduction 1772 Preliminary and Terminology 1773 Existense Results of Cone Saddle Points 178References 181

An Application of Fuzzy Multiobjective Programming to FuzzyAHP 183Hiroaki Kuwano1 Introduction 1832 Preliminaries 1843 Subjective Evaluation 1854 A Numerical Example 1875 Conclusions 188References 189

On Affine Vector Variational Inequality 191Gue Myung Lee, Kwang Baik Lee1 Introduction and Preliminaries 1912 Main Result 192References 194

Graphical Illustration of Pareto Optimal Solutions 197Kaisa Miettinen1 Introduction 1972 Graphical Illustration 1983 Discussion 2014 Conclusions 201References 202

An Efficiency Evaluation Model for Company System Orga-nization 203Takashi Namatame, Hiroaki Tanimoto, Toshikazu Yamaguchi1 Introduction 2032 Characteristics of the Company System Organization 2033 Evaluation Model 2044 Example 2075 Conclusion 208References 208

Stackelberg Solutions to Two-Level Linear Programming Prob-lems with Random Variable Coefficients 209Ichiro Nishizaki, Masatoshi Sakawa, Kosuke Koto, Hideki Katagiri1 Introduction 209

XIII

2 Two-level Linear Programming Problems with Random VariableCoefficients 209

3 A Numerical Example 213References 214

On Inherited Propert ies for Vector-Valued Mult i funct ions . . . . 215Shogo Nishizawa, Tamaki Tanaka, Pando Gr. Georgiev1 Introduction 2152 Inherited Properties of Convexity 2163 Inherited Properties of Semicontinuity 2184 Conclusions 219References 220

Multicriteria Expansion of a Competence Set Using GeneticAlgorithm 221Serafim Opricovic, Gwo-Hshiung Tzeng1 Introduction 2212 Multicriteria Expansion of a Competence Set 2223 Multicriteria Genetic Algorithm 2224 Illustrative Example 2245 Conclusion 226References 226

Comparing DEA and MCDM Method 227Serafim Opricovic, Gwo-Hshiung Tzeng1 Introduction 2272 Comparison of DEA and VIKOR ; 2283 Numerical Experiment 2304 Conclusions 232References 232

Linear Coordination Method for Multi-Objective Problems . . . 233Busaba Phruksaphanrat, Ario Ohsato1 Introduction 2332 Lexicographic Models 2343 Efficient Linear Coordination Method Based on Convex Cone Con-

cept 2354 Numerical Example 2355 Conclusions 238References 238

Experimental Analysis for Rational Decision Making by As-piration Level AHP 239Kouichi Taji, Junsuke Suzuki, Satoru Takahashi, Hiroyuki Tamura1 Introduction 2392 Irrational Ranking 240

XIV

3 Cause and Several Revisions 2414 Experimental Analysis 2425 Conclusion 244References 244

Choquet Integral Type DEA 245Eiichiro Takahagi1 Introduction 2452 Fuzzy Measure Choquet Integral Model 2453 CCR Model (Notations) 2464 Choquet Integral Type DEA (Maximum Model) 2465 Choquet Integral Type DEA(Average Model) 2476 Numerical Examples 2487 Conclusions 250References 250

Interactive Procedures in Hierarchical Dynamic Goal Pro-gramming 251T. Trzaskalik1 Discrete Multi-Objective Dynamic Programming Problem 2512 Goal Programming Approach 2523 Hierarchical Goal Programming Approach 2534 Numerical Example 254References 256

Solution Concepts for Coalitional Games in Constructing Net-works 257Masayo Tsurumi, Tetsuzo Tanino, Masahiro Inuiguchi1 Introduction 2572 Games in Constructing Networks 2583 Conventional Solution Concepts 2594 A New Concept of Demand Operations 2615 Conclusion 262References 262

Multi-Objective Facility Location Problems in CompetitiveEnvironments 263Takeshi Uno, Hiroaki Ishii, Seiji Saito, Shigehiro Osumi1 Introduction 2632 Medianoid Problem with Single Objective 2643 Medianoid Problem with Multi-Objective 2654 Algorithm for Competitive Facility Location Problems 2665 Numerical Experiments 2666 Conclusions 268References 268

XV

Solving Portfolio Problems Based on Meta-Controled Boltz-mann Machine 269Junzo Watada, Teruyuki Watanabe1 Introduction 2692 Portfolio Selection Problem 2703 Energy Functions for Meta-controlled Boltzmann Machine 2704 Numerical Example 2725 Concluding Remarks 273References 273

Tradeoff Directions and Dominance Sets 275Petra Weidner1 Introduction 2752 Tradeoff Concepts 2763 A Scalarization Using Widened Dominance Sets 2784 Calculation of Tradeoffs 279References 280

A Soft Margin Algorithm Controlling Tolerance Directly 281Min Yoon, Hirotaka Nakayama, Yeboon Yun1 Introduction 2812 Error Bound for Soft Margin Algorithms 2813 The Proposed Method 2834 Conclusion 285References 286

An Analysis of Expected Utility Based on Fuzzy Interval Data 289Shin-ichi Yoshikawa, Tetsuji Okuda1 Introduction 2892 Fuzzy Interval Data and Membership Functions 2903 Expected Utility Using Fuzzy Interval Data 2904 The Value of Fuzzy Information 2915 The Amount of Fuzzy Information /ij 2926 Numerical Example 2937 Conclusions 294

On Analyzing the Stability of Discrete Descriptor Systems viaGeneralized Lyapunov Equations 295Qingling Zhang, James Lam, Liqian Zhang1 Introduction 2952 Preliminaries 2963 Asymptotic Stability 298References 300

XVI

Solving DEA via Excel 301Joe Zhu1 Introduction 3012 DEA Spreadsheets 3023 Conclusions 306References 306

PART III: General Papers - Applications 307

Planning and Scheduling Staff Duties by Goal Programming.. 309Sydney CK Chu, Christina SY Yuen1 Introduction 3092 Goal Programming Models 3113 A Concluding Remark 314References 315

An Interactive Approach to Fuzzy-based Robust Design 317Hideo Fujimoto, Yu Tao, Satoko Yamakawa1 Introduction 3172 Proposed Approach 3183 Pressure Vessel Design Problem 3214 Conclusions 323References 324

A Hybrid Genetic Algorithm for solving a capacity ConstrainedTruckload Transportation with crashed customer 325Sangheon Han, Yoshio Tabata1 Introduction 3252 The Vehicle Routing Problem; The Case of Crashed Customers 3263 A hybrid methodology for Vehicle Routing Problem 3284 Numerical Example and Discussions 3305 Conclusions and Recommendations 330References 331

A Multi-Objective Programming Approach for Evaluating Agri-Environmental Policy 333Kiyotada Hayashi1 Introduction 3332 Mathematical Programming Approach to Agri-Environmental Prob-

lems 3343 Possibility of Integrated Evaluation 3354 Concluding Remarks 337References 338

XVII

Improve the Shipping Performance of Build-to-ORder (BTO)Product in Semiconductor Wafer Manufacturing 339Shao-Chung Hsu, Chen-Yuan Peng, Chia-Hung Wu1 Introduction 3392 The Yield Forecast Model 3413 Computational Simulation 3424 An Empirical Case and the Application 3435 Conclusion and Future Work 344References 345

Competence Set Expansion for Obtaining Scheduling Plans inIntelligent Transportation Security Systems 347Yi-Chung Hu, Yu-Jing Chiu, Chin-Mi Chen, Gwo-Hshiung Tzeng1 Introduction 3472 Competence Set Expansion 3483 A Relationship-Based Method 3494 Generate Learning Sequences 3505 Empirical Results 3516 Conclusions 351References 352

DEA for Evaluating the Current-period and Cross-period Ef-ficiency of Taiwan's Upgraded Technical Institutes 353Li-Chen Liu, Chuan Lee, Gwo-Hshiung Tzeng1 Introduction 3532 The Selection of School Objects and Variables for Performance Eval-

uation 3543 Building the Performance Model 3554 Emperical Study: Taiwan's 38 Upgraded Technical Institutes 3575 Conclusions 359References 359

Using DEA of REM and EAM for Efficiency Assessment ofTechnology Institutes Upgraded from Junior Colleges: TheCase in Taiwan 361Li-Chen Liu, Chuan Lee, Gwo-Hshiung Tzeng1 Introduction 3612 Selection of Variables and Samples for Efficiency Assessment 3623 Measure of Assessment Model 3624 Analysis and Conclusion for the Results of Case Study 3655 Conclusions 366References 366

XVIII

The Comprehensive Financial Risk Management in a Bank —Stochastic Goal Programming Optimization 367Jerzy Michnik1 Introduction 3672 Model Formulation 3683 The Exemplary Model and Computational Tests 3714 Conclusions 372References 372

The Effectiveness of the Balanced Scorecard Framework forE-Commerce 373Jamshed J. Mistry, B. K. Pathak1 Introduction 3732 Background and Significance 3743 Methodology 3754 Results 376References 379

A Study of Variance of Locational Price in a Deregulated Gen-eration Market 381Jin-Tang Peng, Chen-Fu Chien1 Introduction 3812 Proposed Market Mechanism 3823 Scenario and Simulation Analysis 3844 Discussion and Conclusion 386References 386

Pseudo-Criterion Approaches to Evaluating Alternatives inMangrove Forests Management 389Santha Chenayah Ramu, Eiji Takeda1 Introduction 3892 Ternary Comparison Method (TCM) 3903 Pseudo-Criterion Approaches to Mangrove Forests Management . . . 3904 Concluding Remarks 394References 394

Energy-Environment-Cost Tradeoffs in Planning Energy Sys-tems for an Urban Area 395Hideharu Sugihara, Kiichiro Tsuji1 Introduction 3952 Definitions of Energy System Alternatives 3953 Formulation of Multi-objective Optimization Model 3974 Tradeoff Analyses 3995 Conclusion 400Reference 400

XIX

DEA Approach to the Allocation of Various TV Commercialsto Dayparts 403Katsuaki Tanaka, Eiji Takeda1 Introduction 4032 DEA Approach to the Allocation of Various TV Commercials to

Dayparts 4043 Concluding Remarks 406References 406

Analyzing Alternative Strategies of Semiconductor Final Test-ing 409Hung-Ju Wang, Chen-Fu Chien, Chung-Jen Kuo1 Introduction 4092 Research Framework 4093 An Empirical Study 4114 Conclusion 414References 414

A Discrete-Time European Options Model under Uncertaintyin Financial Engineering 415Yuji Yoshida1 Introduction 4152 Fuzzy Stochastic Processes 4163 European Options in Uncertain Environment 4164 The Expected Price of European Options 419References 420

Multipurpose Decision-Making in House Plan by Using AHP . 421Bingjiang Zhang, Hui Liang, Tamaki Tanaka1 Introduction 4212 Housing Planing Model by AHP 4213 Comprehensive Evaluation for the House of Room Arrangements . . . 4234 Algorithm 4255 Conclusion and Remarks 426References 426