Multi-Objective Optimization Book

	Foreword
	Preface
1	Prologue	1
1.1	Single and Multi-Objective Optimization	2
1.2	Two Approaches to Multi-Objective Optimization	4
1.3	Why Evolutionary?	7
1.4	Rise of Multi-Objective Evolutionary Algorithms	8
2	Multi-Objective Optimization	13
2.1	Multi-Objective Optimization Problem	13
2.2	Principles of Multi-Objective Optimization	16
2.3	Difference with Single-Objective Optimization	23
2.4	Dominance and Pareto-Optimality	25
2.5	Optimality Conditions	44
3	Classical Methods	47
3.1	Weighted Sum Method	48
3.2	[epsilon]-Constraint Method	55
3.3	Weight Metric Methods	58
3.4	Benson's Method	64
3.5	Value Function Method	65
3.6	Goal Programming Methods	67
3.7	Interactive Methods	72
3.8	Review of Classical Methods	72
4	Evolutionary Algorithms	77
4.1	Difficulties with Classical Optimization Algorithms	77
4.2	Genetic Algorithms	80
4.3	Evolution Strategies	129
4.4	Evolutionary Programming (EP)	138
4.5	Genetic Programming (GP)	140
4.6	Multi-Modal Function Optimization	143
5	Non-Elitist Multi-Objective Evolutionary Algorithms	161
5.1	Motivation for Finding Multiple Pareto-Optimal Solutions	162
5.2	Early Suggestions	164
5.3	Example Problems	166
5.4	Vector Evaluated Genetic Algorithm	169
5.5	Vector-Optimized Evolution Strategy	178
5.6	Weight-Based Genetic Algorithm	179
5.7	Random Weighted GA	190
5.8	Multiple Objective Genetic Algorithm	190
5.9	Non-Dominated Sorting Genetic Algorithm	199
5.10	Niched-Pareto Genetic Algorithm	208
5.11	Predator-Prey Evolution Strategy	213
5.12	Other Methods	220
6	Elitist Multi-Objective Evolutionary Algorithms	227
6.1	Rudolph's Elitist Multi-Objective Evolutionary Algorithm	228
6.2	Elitist Non-Dominated Sorting Genetic Algorithm	233
6.3	Distance-Based Pareto Genetic Algorithm	241
6.4	Strength Pareto Evolutionary Algorithm	249
6.5	Thermodynamical Genetic Algorithm	258
6.6	Pareto-Archived Evolution Strategy	260
6.7	Multi-Objective Messy Genetic Algorithm	267
6.8	Other Elitist Multi-Objective Evolutionary Algorithms	270
7	Constrained Multi-Objective Evolutionary Algorithms	275
7.1	An Example Problem	276
7.2	Ignoring Infeasible Solutions	277
7.3	Penalty Function Approach	277
7.4	Jimenez-Verdegay-Gomez-Skarmeta's Method	283
7.5	Constrained Tournament Method	287
7.6	Ray-Tai-Seow's Method	294
8	Salient Issues of Multi-Objective Evolutionary Algorithms	301
8.1	Illustrative Representation of Non-Dominated Solutions	302
8.2	Performance Metrics	306
8.3	Test Problem Design	324
8.4	Comparison of Multi-Objective Evolutionary Algorithms	361
8.5	Objective Versus Decision-Space Niching	373
8.6	Searching for Preferred Solutions	375
8.7	Exploiting Multi-Objective Evolutionary Optimization	386
8.8	Scaling Issues	400
8.9	Convergence Issues	405
8.10	Controlling Elitism	412
8.11	Multi-Objective Scheduling Algorithms	418
9	Applications of Multi-Objective Evolutionary Algorithms	429
9.1	An Overview of Different Applications	430
9.2	Mechanical Component Design	432
9.3	Truss-Structure Design	437
9.4	Microwave Absorber Design	442
9.5	Low-Thrust Spacecraft Trajectory Optimization	444
9.6	A Hybrid MOEA for Engineering Shape Design	448
10	Epilogue	463
	References	471
	Index	491