Cover image for Evolutionary multi-objective optimization in uncertain environments : issues and algorithms
Title:
Evolutionary multi-objective optimization in uncertain environments : issues and algorithms
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Series:
Studies in computational intelligence, 186

Studies in computational intelligence ; 186
Publication Information:
Berlin : Springer, 2009
Physical Description:
xi, 271 p. : ill. (some col.) ; 25 cm.
ISBN:
9783540959755
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30000010201723 QA402.5 G63 2009 Open Access Book Book
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Summary

Summary

Evolutionary algorithms are sophisticated search methods that have been found to be very efficient and effective in solving complex real-world multi-objective problems where conventional optimization tools fail to work well. Despite the tremendous amount of work done in the development of these algorithms in the past decade, many researchers assume that the optimization problems are deterministic and uncertainties are rarely examined.

The primary motivation of this book is to provide a comprehensive introduction on the design and application of evolutionary algorithms for multi-objective optimization in the presence of uncertainties. In this book, we hope to expose the readers to a range of optimization issues and concepts, and to encourage a greater degree of appreciation of evolutionary computation techniques and the exploration of new ideas that can better handle uncertainties. "Evolutionary Multi-Objective Optimization in Uncertain Environments: Issues and Algorithms" is intended for a wide readership and will be a valuable reference for engineers, researchers, senior undergraduates and graduate students who are interested in the areas of evolutionary multi-objective optimization and uncertainties.


Table of Contents

1 Introductionp. 1
1.1 Multi-objective Optimizationp. 1
1.1.1 Totally Conflicting, Non-conflicting, and Partially Conflicting Multi-objective Problemsp. 2
1.1.2 Pareto Dominance and Optimalityp. 3
1.1.3 Multi-objective Optimization Goalsp. 5
1.2 Evolutionary Multi-objective Optimizationp. 5
1.2.1 MOEA Frameworkp. 6
1.2.2 Basic MOEA Componentsp. 8
1.2.3 Benchmark Problemsp. 16
1.2.4 Performance Metricsp. 18
1.3 Empirical Analysis and Performance Assessment Adequacy for EMO Techniquesp. 21
1.3.1 Preliminary Discussionsp. 21
1.3.2 Systematic Design for Empirical Assessmentp. 25
1.3.3 Survey on Experimental Specificationsp. 31
1.3.4 Conceptualizing Empirical Adequacyp. 33
1.3.5 Case Studiesp. 36
1.4 Overview of This Bookp. 38
1.5 Conclusionp. 39
Part I Evolving Solution Sets in the Presence of Noise
2 Noisy Eyolutionary Multi-objective Optimizationp. 43
2.1 Noisy Multi-objective Optimization Problemsp. 44
2.2 Performance Metrics for Noisy Multi-objective Optimizationp. 45
2.3 Empirical Results of Noise Impactp. 46
2.3.1 General MOEA Behavior under Different Noise Levelsp. 47
2.3.2 MOEA Behavior in the Objective Spacep. 50
2.3.3 MOEA Behavior in Decision Spacep. 53
2.4 Conclusionp. 54
3 Handling Noise in Evolutionary Multi-objective Optimizationp. 55
3.1 Estimate Strength Pareto Evolutionary Algorithmp. 56
3.2 Multi-Objective Probabilistic Selection Evolutionary Algorithmp. 60
3.3 Noise Tolerant Strength Pareto Evolutionary Algorithmp. 63
3.4 Modified Non-dominated Sorting Genetic Algorithm IIp. 65
3.5 Multi-objective Evolutionary Algorithm for Epistemic Uncertaintyp. 67
3.6 Indicator-Based Evolutionary Algorithm for Multi-objective Optimizationp. 70
3.7 Multi-Objective Evolutionary Algorithm with Robust Featuresp. 72
3.8 Comparative Studyp. 80
3.9 Effects of the Proposed Featuresp. 92
3.10 Further Examinationp. 97
3.11 Conclusionp. 98
4 Handling Noise in Evolutionary Neural Network Designp. 101
4.1 Singular Value Decomposition for ANN Designp. 102
4.1.1 Rank-Revealing Decompositionp. 102
4.1.2 Actual Rank of Hidden Neuron Matrixp. 103
4.1.3 Estimating the Thresholdp. 106
4.1.4 Moore-Penrose Generalized Pseudoinversep. 107
4.2 Hybrid Multi-Objective Evolutionary Neural Networksp. 107
4.2.1 Algorithmic Flow of HMOENp. 107
4.2.2 Multi-Objective Fitness Evaluationp. 108
4.2.3 Variable-Length Representation for ANN Structurep. 109
4.2.4 SVD-Based Architectural Recombinationp. 109
4.2.5 Micro-Hybrid Genetic Algorithmp. 112
4.3 Experimental Studyp. 114
4.3.1 Experimental Setupp. 114
4.3.2 Analysis of HMOEN Performancep. 116
4.4 Conclusionp. 121
Part II Tracking Dynamic Multi-objective Landscapes
5 Dynamic Evolutionary Multi-objective Optimizationp. 125
5.1 Dynamic Multi-objective Optimization Problemsp. 126
5.2 Dynamic Multi-objective Problem Categorizationp. 126
5.3 Dynamic Multi-objective Test Problemsp. 128
5.3.1 TLK2 Dynamic Test Functionp. 129
5.3.2 FDA Dynamic Test Functionsp. 130
5.3.3 dMOP Test Functionsp. 131
5.3.4 DSW Test Functionsp. 133
5.3.5 JS Test Functionsp. 134
5.4 Performance Metrics for Dynamic Multi-objective Optimizationp. 135
5.4.1 Illustrating Performance Using Static Performance Measuresp. 135
5.4.2 Time Averaging Static Performance Measuresp. 136
5.5 Evolutionary Dynamic Optimization Techniquesp. 138
5.5.1 Design Issuesp. 138
5.5.2 Directional-Based Dynamic Evolutionary Multi-objective Optimization Algorithmp. 141
5.5.3 Dynamic Non-dominated Sorting Genetic Algorithm IIp. 142
5.5.4 Dynamic Multi-objective Evolutionary Algorithm Based on an Orthogonal Designp. 144
5.5.5 Dynamic Queuing Multi-objective Optimizerp. 146
5.5.6 Multi-objective Immune Algorithmp. 148
5.6 Conclusionp. 152
6 A Coevolutionary Paradigm for Dynamic Multi-Objective Optimizationp. 153
6.1 Competition, Cooperation, and Competitive-Cooperation in Coevolutionp. 154
6.1.1 Competitive Coevolutionp. 154
6.1.2 Cooperative Coevolutionp. 155
6.1.3 Competitive-Cooperative Coevolutionp. 158
6.2 Applying Competitive-Cooperation Coevolution for Multi-objective Optimizationp. 160
6.2.1 Cooperative Mechanismp. 161
6.2.2 Competitive Mechanismp. 162
6.2.3 Implementationp. 164
6.3 Adapting COEA for Dynamic Multi-objective Optimizationp. 165
6.3.1 Introducing Diversity via Stochastic Competitorsp. 165
6.3.2 Handling Outdated Archived Solutionsp. 167
6.4 Static Environment Empirical Studyp. 168
6.4.1 Comparative Study of COEAp. 168
6.4.2 Effects of the Competitive Mechanismp. 172
6.4.3 Effects of Different Competition Schemesp. 174
6.5 Dynamic Environment Empirical Studyp. 177
6.5.1 Comparative Studyp. 177
6.5.2 Effects of Stochastic Competitorsp. 182
6.5.3 Effects of Temporal Memoryp. 182
6.6 Conclusionp. 185
Part III Evolving Robust Solution Sets
7 Robust Evolutionary Multi-objective Optimizationp. 189
7.1 Robust Multi-objective Optimization Problemsp. 189
7.2 Robust Measuresp. 190
7.3 Robust Optimization Problemsp. 191
7.4 Robust Continuous Multi-objective Test Problem Designp. 192
7.4.1 Robust Multi-objective Problem Categorizationp. 192
7.4.2 Empirical Analysis of Existing Benchmark Featuresp. 194
7.5 Robust Continuous Multi-objective Test Problem Designp. 197
7.5.1 Basic Landscape Generationp. 199
7.5.2 Changing the Decision Spacep. 202
7.5.3 Changing the Solution Spacep. 202
7.5.4 Example of a Robust Multi-objective Test Suitep. 203
7.6 Vehicle Routing Problem with Stochastic Demandp. 207
7.6.1 Problem Featuresp. 208
7.6.2 Problem Formulationp. 210
7.7 Conclusionp. 211
8 Evolving Robust Solutions in Multi-Objective Optimizationp. 213
8.1 Evolutionary Robust Optimization Techniquesp. 214
8.1.1 Single-Objective Approachp. 214
8.1.2 Multi-objective Approachp. 215
8.1.3 Robust Multi-Objective Optimization Evolutionary Algorithmp. 216
8.2 Empirical Analysisp. 219
8.2.1 Fitness Inheritance for Robust Optimizationp. 219
8.2.2 Evaluating GTCO Test Suitep. 219
8.2.3 Evaluating VRPSD Test Problemsp. 225
8.3 Conclusionp. 227
9 Evolving Robust Routesp. 229
9.1 Overview of Existing Worksp. 229
9.2 Hybrid Evolutionary Multi-Objective Optimizationp. 230
9.2.1 Variable-Length Chromosomep. 231
9.2.2 Local Search Exploitationp. 232
9.2.3 Route-Exchange Crossoverp. 232
9.2.4 Multi-mode Mutationp. 233
9.2.5 Route Simulation Methodp. 235
9.2.6 Computing Budgetp. 236
9.2.7 Algorithmic Flow of HMOEAp. 237
9.3 Simulation Results and Analysisp. 238
9.3.1 Performance of Hybrid Local Searchp. 239
9.3.2 Comparison with a Deterministic Approachp. 241
9.3.3 Effects of Sample Size, Hp. 244
9.3.4 Effects of Mp. 246
9.4 Conclusionp. 247
10 Final Thoughtsp. 249
Referencesp. 253