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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
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Searching... | 30000010201723 | QA402.5 G63 2009 | Open Access Book | Book | Searching... |
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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 Introduction | p. 1 |
1.1 Multi-objective Optimization | p. 1 |
1.1.1 Totally Conflicting, Non-conflicting, and Partially Conflicting Multi-objective Problems | p. 2 |
1.1.2 Pareto Dominance and Optimality | p. 3 |
1.1.3 Multi-objective Optimization Goals | p. 5 |
1.2 Evolutionary Multi-objective Optimization | p. 5 |
1.2.1 MOEA Framework | p. 6 |
1.2.2 Basic MOEA Components | p. 8 |
1.2.3 Benchmark Problems | p. 16 |
1.2.4 Performance Metrics | p. 18 |
1.3 Empirical Analysis and Performance Assessment Adequacy for EMO Techniques | p. 21 |
1.3.1 Preliminary Discussions | p. 21 |
1.3.2 Systematic Design for Empirical Assessment | p. 25 |
1.3.3 Survey on Experimental Specifications | p. 31 |
1.3.4 Conceptualizing Empirical Adequacy | p. 33 |
1.3.5 Case Studies | p. 36 |
1.4 Overview of This Book | p. 38 |
1.5 Conclusion | p. 39 |
Part I Evolving Solution Sets in the Presence of Noise | |
2 Noisy Eyolutionary Multi-objective Optimization | p. 43 |
2.1 Noisy Multi-objective Optimization Problems | p. 44 |
2.2 Performance Metrics for Noisy Multi-objective Optimization | p. 45 |
2.3 Empirical Results of Noise Impact | p. 46 |
2.3.1 General MOEA Behavior under Different Noise Levels | p. 47 |
2.3.2 MOEA Behavior in the Objective Space | p. 50 |
2.3.3 MOEA Behavior in Decision Space | p. 53 |
2.4 Conclusion | p. 54 |
3 Handling Noise in Evolutionary Multi-objective Optimization | p. 55 |
3.1 Estimate Strength Pareto Evolutionary Algorithm | p. 56 |
3.2 Multi-Objective Probabilistic Selection Evolutionary Algorithm | p. 60 |
3.3 Noise Tolerant Strength Pareto Evolutionary Algorithm | p. 63 |
3.4 Modified Non-dominated Sorting Genetic Algorithm II | p. 65 |
3.5 Multi-objective Evolutionary Algorithm for Epistemic Uncertainty | p. 67 |
3.6 Indicator-Based Evolutionary Algorithm for Multi-objective Optimization | p. 70 |
3.7 Multi-Objective Evolutionary Algorithm with Robust Features | p. 72 |
3.8 Comparative Study | p. 80 |
3.9 Effects of the Proposed Features | p. 92 |
3.10 Further Examination | p. 97 |
3.11 Conclusion | p. 98 |
4 Handling Noise in Evolutionary Neural Network Design | p. 101 |
4.1 Singular Value Decomposition for ANN Design | p. 102 |
4.1.1 Rank-Revealing Decomposition | p. 102 |
4.1.2 Actual Rank of Hidden Neuron Matrix | p. 103 |
4.1.3 Estimating the Threshold | p. 106 |
4.1.4 Moore-Penrose Generalized Pseudoinverse | p. 107 |
4.2 Hybrid Multi-Objective Evolutionary Neural Networks | p. 107 |
4.2.1 Algorithmic Flow of HMOEN | p. 107 |
4.2.2 Multi-Objective Fitness Evaluation | p. 108 |
4.2.3 Variable-Length Representation for ANN Structure | p. 109 |
4.2.4 SVD-Based Architectural Recombination | p. 109 |
4.2.5 Micro-Hybrid Genetic Algorithm | p. 112 |
4.3 Experimental Study | p. 114 |
4.3.1 Experimental Setup | p. 114 |
4.3.2 Analysis of HMOEN Performance | p. 116 |
4.4 Conclusion | p. 121 |
Part II Tracking Dynamic Multi-objective Landscapes | |
5 Dynamic Evolutionary Multi-objective Optimization | p. 125 |
5.1 Dynamic Multi-objective Optimization Problems | p. 126 |
5.2 Dynamic Multi-objective Problem Categorization | p. 126 |
5.3 Dynamic Multi-objective Test Problems | p. 128 |
5.3.1 TLK2 Dynamic Test Function | p. 129 |
5.3.2 FDA Dynamic Test Functions | p. 130 |
5.3.3 dMOP Test Functions | p. 131 |
5.3.4 DSW Test Functions | p. 133 |
5.3.5 JS Test Functions | p. 134 |
5.4 Performance Metrics for Dynamic Multi-objective Optimization | p. 135 |
5.4.1 Illustrating Performance Using Static Performance Measures | p. 135 |
5.4.2 Time Averaging Static Performance Measures | p. 136 |
5.5 Evolutionary Dynamic Optimization Techniques | p. 138 |
5.5.1 Design Issues | p. 138 |
5.5.2 Directional-Based Dynamic Evolutionary Multi-objective Optimization Algorithm | p. 141 |
5.5.3 Dynamic Non-dominated Sorting Genetic Algorithm II | p. 142 |
5.5.4 Dynamic Multi-objective Evolutionary Algorithm Based on an Orthogonal Design | p. 144 |
5.5.5 Dynamic Queuing Multi-objective Optimizer | p. 146 |
5.5.6 Multi-objective Immune Algorithm | p. 148 |
5.6 Conclusion | p. 152 |
6 A Coevolutionary Paradigm for Dynamic Multi-Objective Optimization | p. 153 |
6.1 Competition, Cooperation, and Competitive-Cooperation in Coevolution | p. 154 |
6.1.1 Competitive Coevolution | p. 154 |
6.1.2 Cooperative Coevolution | p. 155 |
6.1.3 Competitive-Cooperative Coevolution | p. 158 |
6.2 Applying Competitive-Cooperation Coevolution for Multi-objective Optimization | p. 160 |
6.2.1 Cooperative Mechanism | p. 161 |
6.2.2 Competitive Mechanism | p. 162 |
6.2.3 Implementation | p. 164 |
6.3 Adapting COEA for Dynamic Multi-objective Optimization | p. 165 |
6.3.1 Introducing Diversity via Stochastic Competitors | p. 165 |
6.3.2 Handling Outdated Archived Solutions | p. 167 |
6.4 Static Environment Empirical Study | p. 168 |
6.4.1 Comparative Study of COEA | p. 168 |
6.4.2 Effects of the Competitive Mechanism | p. 172 |
6.4.3 Effects of Different Competition Schemes | p. 174 |
6.5 Dynamic Environment Empirical Study | p. 177 |
6.5.1 Comparative Study | p. 177 |
6.5.2 Effects of Stochastic Competitors | p. 182 |
6.5.3 Effects of Temporal Memory | p. 182 |
6.6 Conclusion | p. 185 |
Part III Evolving Robust Solution Sets | |
7 Robust Evolutionary Multi-objective Optimization | p. 189 |
7.1 Robust Multi-objective Optimization Problems | p. 189 |
7.2 Robust Measures | p. 190 |
7.3 Robust Optimization Problems | p. 191 |
7.4 Robust Continuous Multi-objective Test Problem Design | p. 192 |
7.4.1 Robust Multi-objective Problem Categorization | p. 192 |
7.4.2 Empirical Analysis of Existing Benchmark Features | p. 194 |
7.5 Robust Continuous Multi-objective Test Problem Design | p. 197 |
7.5.1 Basic Landscape Generation | p. 199 |
7.5.2 Changing the Decision Space | p. 202 |
7.5.3 Changing the Solution Space | p. 202 |
7.5.4 Example of a Robust Multi-objective Test Suite | p. 203 |
7.6 Vehicle Routing Problem with Stochastic Demand | p. 207 |
7.6.1 Problem Features | p. 208 |
7.6.2 Problem Formulation | p. 210 |
7.7 Conclusion | p. 211 |
8 Evolving Robust Solutions in Multi-Objective Optimization | p. 213 |
8.1 Evolutionary Robust Optimization Techniques | p. 214 |
8.1.1 Single-Objective Approach | p. 214 |
8.1.2 Multi-objective Approach | p. 215 |
8.1.3 Robust Multi-Objective Optimization Evolutionary Algorithm | p. 216 |
8.2 Empirical Analysis | p. 219 |
8.2.1 Fitness Inheritance for Robust Optimization | p. 219 |
8.2.2 Evaluating GTCO Test Suite | p. 219 |
8.2.3 Evaluating VRPSD Test Problems | p. 225 |
8.3 Conclusion | p. 227 |
9 Evolving Robust Routes | p. 229 |
9.1 Overview of Existing Works | p. 229 |
9.2 Hybrid Evolutionary Multi-Objective Optimization | p. 230 |
9.2.1 Variable-Length Chromosome | p. 231 |
9.2.2 Local Search Exploitation | p. 232 |
9.2.3 Route-Exchange Crossover | p. 232 |
9.2.4 Multi-mode Mutation | p. 233 |
9.2.5 Route Simulation Method | p. 235 |
9.2.6 Computing Budget | p. 236 |
9.2.7 Algorithmic Flow of HMOEA | p. 237 |
9.3 Simulation Results and Analysis | p. 238 |
9.3.1 Performance of Hybrid Local Search | p. 239 |
9.3.2 Comparison with a Deterministic Approach | p. 241 |
9.3.3 Effects of Sample Size, H | p. 244 |
9.3.4 Effects of M | p. 246 |
9.4 Conclusion | p. 247 |
10 Final Thoughts | p. 249 |
References | p. 253 |