Evolutionary Multi-objective Optimization in Uncertain Environments: Issues and Algorithms

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Springer Science & Business Media, Mar 9, 2009 - Computers - 271 pages
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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.

 

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Contents

Introduction
1
111 Totally Conflicting Nonconflicting and Partially Conflicting Multiobjective Problems
2
112 Pareto Dominance and Optimality
3
113 Multiobjective Optimization Goals
5
121 MOEA Framework
6
122 Basic MOEA Components
8
123 Benchmark Problems
16
124 Performance Metrics
18
553 Dynamic Nondominated Sorting Genetic Algorithm II
142
554 Dynamic Multiobjective Evolutionary Algorithm Based on an Orthogonal Design
144
555 Dynamic Queuing Multiobjective Optimizer
146
556 Multiobjective Immune Algorithm
148
56 Conclusion
152
A Coevolutionary Paradigm for Dynamic MultiObjective Optimization
153
61 Competition Cooperation and CompetitiveCooperation in Coevolution
154
612 Cooperative Coevolution
155

13 Empirical Analysis and Performance Assessment Adequacy for EMO Techniques
21
132 Systematic Design for Empirical Assessment
25
133 Survey on Experimental Specifications
31
134 Conceptualizing Empirical Adequacy
33
135 Case Studies
36
14 Overview of This Book
38
15 Conclusion
39
Evolving Solution Sets in the Presence of Noise
41
Noisy Evolutionary Multiobjective Optimization
42
21 Noisy Multiobjective Optimization Problems
44
22 Performance Metrics for Noisy Multiobjective Optimization
45
23 Empirical Results of Noise Impact
46
231 General MOEA Behavior under Different Noise Levels
47
232 MOEA Behavior in the Objective Space
50
233 MOEA Behavior in Decision Space
53
24 Conclusion
54
Handling Noise in Evolutionary Multiobjective Optimization
55
31 Estimate Strength Pareto Evolutionary Algorithm
56
32 MultiObjective Probabilistic Selection Evolutionary Algorithm
60
33 Noise Tolerant Strength Pareto Evolutionary Algorithm
63
34 Modified Nondominated Sorting Genetic Algorithm II
65
35 Multiobjective Evolutionary Algorithm for Epistemic Uncertainty
67
36 IndicatorBased Evolutionary Algorithm for Multiobjective Optimization
70
37 MultiObjective Evolutionary Algorithm with Robust Features
72
38 Comparative Study
80
39 Effects of the Proposed Features
92
310 Further Examination
97
311 Conclusion
98
Handling Noise in Evolutionary Neural Network Design
101
41 Singular Value Decomposition for ANN Design
102
412 Actual Rank of Hidden Neuron Matrix
103
413 Estimating the Threshold
106
414 MoorePenrose Generalized Pseudoinverse
107
422 Multiobjective Fitness Evaluation
108
423 VariableLength Representation for ANN Structure
109
425 MicroHybrid Genetic Algorithm
112
43 Experimental Study
114
432 Analysis of HMOEN Performance
116
44 Conclusion
121
Tracking Dynamic Multiobjective Landscapes
122
Dynamic Evolutionary Multiobjective Optimization
125
51 Dynamic Multiobjective Optimization Problems
126
53 Dynamic Multiobjective Test Problems
128
531 TLK2 Dynamic Test Function
129
532 FDA Dynamic Test Functions
130
533 dMOP Test Functions
131
534 DSW Test Functions
133
555 JS Test Functions
134
54 Performance Metrics for Dynamic Multiobjective Optimization
135
542 Time Averaging Static Performance Measures
136
55 Evolutionary Dynamic Optimization Techniques
138
552 DirectionalBased Dynamic Evolutionary Multiobjective Optimization Algorithm
141
613 CompetitiveCooperative Coevolution
158
62 Applying CompetitiveCooperation Coevolution for Multiobjective Optimization
160
621 Cooperative Mechanism
161
622 Competitive Mechanism
162
623 Implementation
164
63 Adapting COEA for Dynamic Multiobjective Optimization
165
632 Handling Outdated Archived Solutions
167
64 Static Environment Empirical Study
168
642 Effects of the Competitive Mechanism
172
643 Effects of Different Competition Schemes
174
65 Dynamic Environment Empirical Study
177
652 Effects of Stochastic Competitors
182
66 Conclusion
185
Evolving Robust Solution Sets
186
Robust Evolutionary Multiobjective Optimization
189
72 Robust Measures
190
73 Robust Optimization Problems
191
74 Robust Continuous Multiobjective Test Problem Design
192
742 Empirical Analysis of Existing Benchmark Features
194
75 Robust Continuous Multiobjective Test Problem Design
197
751 Basic Landscape Generation
199
752 Changing the Decision Space
202
754 Example of a Robust Multiobjective Test Suite
203
76 Vehicle Routing Problem with Stochastic Demand
207
761 Problem Features
208
762 Problem Formulation
210
77 Conclusion
211
Evolving Robust Solutions in MultiObjective Optimization
212
81 Evolutionary Robust Optimization Techniques
214
812 Multiobjective Approach
215
813 Robust MultiObjective Optimization Evolutionary Algorithm
216
82 Empirical Analysis
219
823 Evaluating VRPSD Test Problems
225
83 Conclusion
227
Evolving Robust Routes
229
92 Hybrid Evolutionary MultiObjective Optimization
230
921 VariableLength Chromosome
231
922 Local Search Exploitation
232
924 Multimode Mutation
233
925 Route Simulation Method
235
926 Computing Budget
236
927 Algorithmic Flow of HMOEA
237
93 Simulation Results and Analysis
238
931 Performance of Hybrid Local Search
239
932 Comparison with a Deterministic Approach
241
933 Effects of Sample Size H
244
934 Effects of M
246
94 Conclusion
247
Final Thoughts
248
References
253
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