Multiobjective optimization: principles and case studies
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
[2004]
|
| Series: | Decision engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 293 Seiten Illustrationen |
| ISBN: | 9783642072833 9783662088838 3540401822 9783540401827 |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Forewords 1
Hard Optimization 1
Metaheuristics 2
Source of efficiency of metaheuristics 3
Extensions of metaheuristics 4
General classification of mono objective optimization methods 5
Multiobjective optimization 7
Structure of the book 9
Reading advices 11
Acknowledgments 11
Part I Principles of multiobjective optimization methods
1 Introduction: multiobjective optimization and domination 15
1.1 What is a multiobjective optimization problem ? 15
1.2 Vocabulary and definitions 16
1.3 Classification of optimization problems 17
1.4 Multiobjective optimization 18
1.5 Multiplicity of solutions 18
1.6 Domination 19
1.6.1 Introduction and definitions 19
1.6.2 Example 22
1.6.3 Sizing of a beam 25
1.6.3.1 Full beam with a square section 25
1.6.3.2 Hollow beam with a square section 27
1.7 Illustration of the reason for using multiobjective optimization 27
1.8 Relations derived from domination 30
1.8.1 Introduction 30
1.8.2 Lexicographic optimality 32
1.8.3 Extremal optimality 32
1.8.4 Maximal optimality 33
1.8.5 Cone optimality 34
1.8.6 a domination 36
1.8.7 Domination in the Geoffrion sense 37
1.8.8 Conclusion 38
VI Contents
1.9 Tradeoff surface 38
1.10 Convexity 39
1.11 Representation of a tradeoff surface 41
1.12 Solution methods of multiobjective optimization problems 42
1.13 Annotated bibliography 43
2 Scalar methods 45
2.1 The weighted sum of objective functions method 45
2.2 Keeney Raiffa method 51
2.3 Distance to a reference objective method 52
2.4 Compromise method 55
2.5 Hybrid methods 60
2.6 Goal attainment method 61
2.7 Goal programming method 66
2.8 Lexicographic method 67
2.9 Proper equality constraints method 68
2.10 Proper inequality constraints method 72
2.11 Lin Tabak algorithm 73
2.12 Lin Giesy algorithm 74
2.13 Annotated bibliography 75
3 Interactive methods 77
3.1 Introduction 77
3.2 Surrogate worth tradeoff method 77
3.3 Fandel method 80
3.4 STEP method 86
3.5 Jahn method 88
3.6 Geoffrion method 92
3.7 Simplex method 94
3.8 Annotated bibliography 98
4 Fuzzy methods 99
4.1 Introduction to fuzzy logic 99
4.1.1 Drawing a parallel with classical logic 99
4.1.2 Membership function 100
4.2 Sakawa method 102
4.3 Reardon method 106
5 Multiobjective methods using metaheuristics 109
5.1 What is a metaheuristic ? 109
5.2 Task decomposition in optimization 109
5.3 General concepts 110
5.4 Simulated annealing Ill
5.4.1 PASA (Pareto archived simulated annealing) method 112
5.4.2 MOSA (Multiple objective simulated annealing) method 114
5.5 Tabu search 118
5.6 Genetic algorithms 119
5.7 Multiobjective optimization and genetic algorithms 122
5.7.1 A nonaggregative method 124
5.7.2 The aggregative methods 125
5.8 Annotated bibliography 133
Contents VII
6 Decision aid methods 135
6.1 Introduction 135
6.2 Definitions 137
6.2.1 Order and equivalence relations 137
6.2.2 Preference relations 138
6.2.3 Definition of a criterion 139
6.2.4 Analysis 139
6.3 Various methods 139
6.3.1 Introduction 140
6.3.1.1 Notation 140
6.3.1.2 The representation 140
6.3.2 The ELECTRE I method 142
6.3.3 The ELECTRE IS method 149
6.3.4 The ELECTRE II method 150
6.3.5 The ELECTRE III method 157
6.3.6 The ELECTRE IV method 164
6.3.7 The ELECTRE TRI method 166
6.3.8 The PROMETHEE I method 169
6.3.9 The PROMETHEE II method 173
6.4 Annotated bibliography 173
Part II Evaluation of methods, and criteria for choice of method
7 Performance measurement 177
7.1 Introduction 177
7.2 Error ratio 178
7.3 Generational distance 180
7.4 The STDGD metric 181
7.5 Maximal error with respect to the tradeoff surface 182
7.6 Hyperarea and hyperarea ratio 184
7.7 Spacing metric 186
7.8 The HRS metric 188
7.9 Overall nondominated vector generation metric 188
7.10 Progress measure 189
7.11 Generational nondominated vector generation metric 190
7.12 Nondominated vector addition 190
7.13 Waves metric 191
7.14 Zitzler metrics 192
7.14.1 The relative metrics 192
7.14.2 The absolute metrics 194
7.15 Laumanns metric 195
7.16 Annotated bibliography 196
VIII Contents
8 Test functions for multiobjective optimization methods 197
8.1 Introduction 197
8.2 The Deb test problems 197
8.2.1 The nonconvex Deb function 198
8.2.2 The discontinuous Deb function 200
8.2.3 The multifrontal Deb function 201
8.2.4 The nonuniform Deb function 202
8.3 The Hanne test problems 203
8.3.1 The linear Hanne function 203
8.3.2 The convex Hanne function 205
8.3.3 The nonconvex Hanne function 208
8.3.4 The discontinuous Hanne function 209
8.3.5 The Hanne function with several efficiency areas 211
8.4 Annotated bibliography 211
9 An attempt to classify multiobjective optimization methods 213
9.1 Introduction 213
9.2 Mathematical classification of optimization methods 214
9.2.1 Introduction 214
9.2.2 The Ehrgott classification formula 214
9.2.3 Conclusion 216
9.3 Hierarchical classification of multiobjective optimization methods .... 216
9.3.1 Introduction 216
9.3.2 A hierarchical graph 217
9.3.2.1 A hierarchy for the treatment of a multiobjective
problem 217
9.3.2.2 A hierarchy for interactions 219
9.3.2.3 A hierarchy for optimization methods 220
9.3.2.4 How to use this hierarchy 221
9.3.3 Classification of some methods 222
9.3.4 How to choose a method 223
Part III Case studies
10 Case study 1: qualification of scientific software 229
10.1 Introduction 229
10.2 Description of the problem 229
10.3 To represent the tradeoff surface 231
10.4 Conclusion 233
11 Case study 2: study of the extension of a telecommunication
network 237
11.1 Network 237
11.2 Choice criteria 238
11.2.1 Parameter used to model the availability 238
11.2.2 Link between availability and cost 239
11.2.3 Costs 239
11.2.3.1 Investment costs 239
11.2.3.2 Maintenance/management costs 239
Contents IX
11.2.3.3 Costs related to economic activity of the network
(profitability and penalties) 240
11.3 Study of a network extension 240
11.3.1 Problem 240
11.3.2 Modeling 240
11.3.2.1 Variables 240
11.3.2.2 Criteria 241
11.3.2.3 Constraints 241
11.3.3 Necessary data 241
11.3.3.1 Fixed infrastructure of the network 241
11.3.3.2 Variable infrastructure of the network 241
11.3.3.3 Demand matrix 242
11.4 Method of solution 242
11.4.1 Definition of an admissible solution 243
11.4.2 Algorithm 243
11.4.2.1 Initialization 1: encoding 243
11.4.2.2 Initialization 2: construction of an initial solution .... 244
11.4.2.3 Evaluation 1: computation of the current solution .... 244
11.4.2.4 Evaluation 2: localization of the solution with respect
to the current Pareto frontier 246
11.4.2.5 Selection 246
11.4.2.6 Breeding 246
11.4.2.7 Stopping criterion 247
11.4.2.8 Global algorithm 248
11.5 Results 248
11.6 Conclusion 248
12 Case study 3: multicriteria decision tools to deal with bids 251
12.1 Introduction 251
12.2 First generation model 251
12.2.1 Goal of the model 251
12.2.2 The criteria of the first generation model 252
12.2.3 Evolution of the first generation model 254
12.3 Understanding the insufficiency of the first generation model 255
12.3.1 Examples of nondiscriminative criteria 256
12.3.2 Ineffective criteria due to the marking method 258
12.3.3 Criteria which are in fact constraints 259
12.4 Second generation model 260
12.4.1 Principle of the rebuilding of the model 261
12.4.2 Abandonment of the principle of the uniqueness of the model . 261
12.4.3 Architecture of the families of models 262
12.4.4 Criteria 262
12.4.5 Tuning of the model 264
12.4.6 Performance of the model 265
12.5 Conclusion 266
13 Conclusion 269
Conclusion 269
References 271
Index 291
|
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| indexdate | 2024-07-09T20:01:46Z |
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| spelling | Collette, Yann aut Optimisation multiobjectif Multiobjective optimization principles and case studies Yann Collette ; Patrick Siarry Berlin ; Heidelberg Springer [2004] © 2004 IX, 293 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Decision engineering Mehrkriterielle Optimierung Mehrkriterielle Optimierung (DE-588)4610682-0 gnd rswk-swf Mehrkriterielle Optimierung (DE-588)4610682-0 s DE-604 Siarry, Patrick 1952- (DE-588)112947321X aut Erscheint auch als Online-Ausgabe 978-3-662-08883-8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012961479&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Collette, Yann Siarry, Patrick 1952- Multiobjective optimization principles and case studies Mehrkriterielle Optimierung Mehrkriterielle Optimierung (DE-588)4610682-0 gnd |
| subject_GND | (DE-588)4610682-0 |
| title | Multiobjective optimization principles and case studies |
| title_alt | Optimisation multiobjectif |
| title_auth | Multiobjective optimization principles and case studies |
| title_exact_search | Multiobjective optimization principles and case studies |
| title_full | Multiobjective optimization principles and case studies Yann Collette ; Patrick Siarry |
| title_fullStr | Multiobjective optimization principles and case studies Yann Collette ; Patrick Siarry |
| title_full_unstemmed | Multiobjective optimization principles and case studies Yann Collette ; Patrick Siarry |
| title_short | Multiobjective optimization |
| title_sort | multiobjective optimization principles and case studies |
| title_sub | principles and case studies |
| topic | Mehrkriterielle Optimierung Mehrkriterielle Optimierung (DE-588)4610682-0 gnd |
| topic_facet | Mehrkriterielle Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012961479&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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