Convergence Analysis for Particle Swarm Optimization: = Konvergenzanalyse für die Partikelschwarmoptimierung
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Erlangen
FAU University Press
2015
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| Series: | FAU Forschungen
Reihe B, Medizin, Naturwissenschaft, Technik ; 3 |
| Subjects: | |
| Online Access: | https://nbn-resolving.org/urn:nbn:de:bvb:29-opus4-61621 Volltext Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 214 S. Ill., graph. Darst. 240 mm x 170 mm |
| ISBN: | 9783944057309 |
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| 245 | 1 | 0 | |a Convergence Analysis for Particle Swarm Optimization |b = Konvergenzanalyse für die Partikelschwarmoptimierung |c Berthold Immanuel Schmitt |
| 246 | 1 | 1 | |a Konvergenzanalyse für die Partikelschwarmoptimierung |
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Record in the Search Index
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CONTENTS
1 INTRODUCTION AND CONTRIBUTION 1
1.1 CONTRIBUTIONS 2
1.2 OVERVIEW 6
2 PARTICLE SWARM OPTIMIZATION: STATE OF THE ART 9
2.1 APPLICATIONS OF PARTICLE SWARM OPTIMIZATION 10
2.2 THE CLASSICAL PARTICLE SWARM OPTIMIZATION ALGORITHM . 12
2.3 VARIANTS OF PARTICLE SWARM OPTIMIZATION 16
2.3.1 NEIGHBORHOOD TOPOLOGIES 16
2.3.2 CONSTRAINTS AND BOUND HANDLING 21
2.3.3 VARIANTS OF THE MOVEMENT EQUATIONS 25
2.4 MULTI-OBJECTIVE PARTICLE SWARM OPTIMIZATION 31
2.4.1 MULTI-OBJECTIVE BLACK BOX OPTIMIZATION 31
2.4.2 PSO FOR MULTI-OBJECTIVE BLACK BOX OPTIMIZATION . . 33
2.5 PARTICLE SWARM OPTIMIZATION FOR DISCRETE PROBLEMS 36
2.6 THEORETICAL RESULTS ABOUT PARTICLE SWARM OPTIMIZATION . 38
2.7 OTHER NATURE-INSPIRED META-HEURISTICS 41
2.7.1 EVOLUTIONARY ALGORITHMS 41
2.7.2 ANT ALGORITHMS 45
3 PSO AS A
STOCHASTIC PROCESS 49
3.1 BASICS OF PROBABILITY THEORY 50
3.1.1 PROBABILITY SPACE, RANDOM VARIABLES, STOCHASTIC PRO
CESSES AND CONDITIONAL EXPECTATION 50
3.1.2 MEASURABILITY 58
3.2 (NO) FREE LUNCH AND LEBESGUE'S DIFFERENTIATION THEOREM . . 60
3.3 DRIFT THEORY 61
3.3.1 CLASSICAL DRIFT THEORY 62
3.3.2 DRIFT THEORY FOR CONTINUOUS SEARCH SPACES 63
3.4 THE PSO MODEL 71
XI
HTTP://D-NB.INFO/1070397512
CONTENTS
3.5 DISCUSSION OF PREVIOUS RESULTS 74
3.5.1 NEGATIVE RESULTS 74
3.5.2 CONVERGENCE ANALYSIS 77
4 CONVERGENCE OF 1-DIMENSIONAL PSO 81
4.1 PARTICLE SWARM OPTIMIZATION ALMOST SURELY FINDS LOCAL OPTIMA 81
4.1.1 PROOF OF CONVERGENCE TOWARDS A LOCAL OPTIMUM . 84
4.1.2 EXPERIMENTAL SETUP 93
4.1.3 EXPERIMENTAL RESULTS ON THE POTENTIAL GAIN 94
4.2 PROOF OF LINEAR CONVERGENCE TIME 96
4.2.1 MEASURING THE DISTANCE TO OPTIMALITY 96
4.2.2 LOWER BOUNDS FOR THE DECREASE OF THE DISTANCE MEASURE 101
4.2.3 PUTTING THINGS TOGETHER 137
5 CONVERGENCE FOR MULTIDIMENSIONAL PROBLEMS 145
5.1 DETERMINING FURTHER BAD EVENTS 146
5.1.1 HIGH POTENTIAL IN AT LEAST ONE DIMENSION: A BAD EVENT 147
5.1.2 LOW POTENTIAL IN EVERY DIMENSION: A BAD EVENT . . 151
5.1.3 IMBALANCED POTENTIALS: A FATAL EVENT 156
5.2 MODIFIED PARTICLE SWARM OPTIMIZATION ALMOST SURELY FINDS
LOCAL OPTIMA 175
5.3 EXPERIMENTAL RESULTS WITH A STANDARD IMPLEMENTATION . . . 180
5.3.1 THE PROBLEM OF IMBALANCED POTENTIALS ON STANDARD
BENCHMARKS 180
5.3.2 AVOIDING IMBALANCED CONVERGENCE 182
5.3.3 DIFFERENTIABILITY 183
5.3.4 IMPACT OF THE MODIFICATION 186
6 CONCLUSION 189
BIBLIOGRAPHY 191
AUTHOR'S OWN PUBLICATIONS 209
ACRONYMS 211
INDEX 213
XII |
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| physical | XII, 214 S. Ill., graph. Darst. 240 mm x 170 mm |
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| publishDate | 2015 |
| publishDateSearch | 2015 |
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| series2 | FAU Forschungen : Reihe B, Medizin, Naturwissenschaft, Technik |
| spelling | Schmitt, Berthold Immanuel Verfasser aut Convergence Analysis for Particle Swarm Optimization = Konvergenzanalyse für die Partikelschwarmoptimierung Berthold Immanuel Schmitt Konvergenzanalyse für die Partikelschwarmoptimierung Erlangen FAU University Press 2015 XII, 214 S. Ill., graph. Darst. 240 mm x 170 mm txt rdacontent n rdamedia nc rdacarrier FAU Forschungen : Reihe B, Medizin, Naturwissenschaft, Technik 3 Zugl.: Erlangen-Nürnberg, Univ., Diss., 2015 Konvergenz (DE-588)4032326-2 gnd rswk-swf Partikel-Schwarm-Optimierung (DE-588)7658941-9 gnd rswk-swf Partikel-Schwarm-Optimierung (DE-588)4113937-9 Hochschulschrift gnd-content Partikel-Schwarm-Optimierung (DE-588)7658941-9 s Konvergenz (DE-588)4032326-2 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:29-opus4-61621 FAU Forschungen Reihe B, Medizin, Naturwissenschaft, Technik ; 3 (DE-604)BV041959107 3 https://nbn-resolving.org/urn:nbn:de:bvb:29-opus4-61621 Resolving-System https://open.fau.de/handle/openfau/6162 kostenfrei Volltext X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=5227175&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028029512&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schmitt, Berthold Immanuel Convergence Analysis for Particle Swarm Optimization = Konvergenzanalyse für die Partikelschwarmoptimierung FAU Forschungen Konvergenz (DE-588)4032326-2 gnd Partikel-Schwarm-Optimierung (DE-588)7658941-9 gnd |
| subject_GND | (DE-588)4032326-2 (DE-588)7658941-9 (DE-588)4113937-9 |
| title | Convergence Analysis for Particle Swarm Optimization = Konvergenzanalyse für die Partikelschwarmoptimierung |
| title_alt | Konvergenzanalyse für die Partikelschwarmoptimierung |
| title_auth | Convergence Analysis for Particle Swarm Optimization = Konvergenzanalyse für die Partikelschwarmoptimierung |
| title_exact_search | Convergence Analysis for Particle Swarm Optimization = Konvergenzanalyse für die Partikelschwarmoptimierung |
| title_full | Convergence Analysis for Particle Swarm Optimization = Konvergenzanalyse für die Partikelschwarmoptimierung Berthold Immanuel Schmitt |
| title_fullStr | Convergence Analysis for Particle Swarm Optimization = Konvergenzanalyse für die Partikelschwarmoptimierung Berthold Immanuel Schmitt |
| title_full_unstemmed | Convergence Analysis for Particle Swarm Optimization = Konvergenzanalyse für die Partikelschwarmoptimierung Berthold Immanuel Schmitt |
| title_short | Convergence Analysis for Particle Swarm Optimization |
| title_sort | convergence analysis for particle swarm optimization konvergenzanalyse fur die partikelschwarmoptimierung |
| title_sub | = Konvergenzanalyse für die Partikelschwarmoptimierung |
| topic | Konvergenz (DE-588)4032326-2 gnd Partikel-Schwarm-Optimierung (DE-588)7658941-9 gnd |
| topic_facet | Konvergenz Partikel-Schwarm-Optimierung Hochschulschrift |
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