Robustness concepts for knapsack and network design problems under data uncertainty: Gamma-, multi-band, submodular, and recoverable robustness
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Göttingen
Cuvillier
2013
|
| Ausgabe: | 1. Aufl. |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XII, 237 S. graph. Darst. 21 cm |
| ISBN: | 9783954045938 |
Internformat
MARC
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| 245 | 1 | 0 | |a Robustness concepts for knapsack and network design problems under data uncertainty |b Gamma-, multi-band, submodular, and recoverable robustness |c Manuel Kutschka |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a Göttingen |b Cuvillier |c 2013 | |
| 300 | |a XII, 237 S. |b graph. Darst. |c 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 502 | |a Zugl.: Aachen, Univ., Diss., 2013 | ||
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Datensatz im Suchindex
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| adam_text |
CONTENTS
Abstract
■»
Zusammenfassung
v
Danksagung
vii
Contents
"x
Introduction
1
I Concepts
5
1
Mathematical preliminaries
7
1.1
Basics
. 7
1.2
The knapsack problem
. 14
1.3
The capacitated network design problem
. 20
1.4
Applications in telecommunication
. 27
2
Optimization under data uncertainty
35
2.1
Stochastic optimization
. 36
2.2
Robust optimization
. 37
2.2.1
Uncertainty sets
. 38
2.2.2
Tractability of robust optimization problems
. 41
2.3
Multi-stage optimization under data uncertainty
. 42
2.3.1
Multi-stage stochastic optimization
. 43
2.3.2
Multi-stage robust optimization
. 43
3
Robustness concepts
45
3.1
T-robustness
. 45
3.1.1
The concept of
Г
-robustness
.
46
3.1.2
The T-robust counterpart
. 48
3.1.3
Probabilistic analysis and feasibility guarantees
. 50
ix
Contents
_
3.2
Multi-band robustness
. 51
3.2.1
The concept of multi-band robustness
. 52
3.2.2
The multi-band robust counterpart
. 55
3.2.3
Probabilistic analysis
. 57
3.3
Submodular
robustness
. 57
3.3.1
The concept of
submodular
robustness
. 58
3.3.2
The
submodular
robust counterpart
. 59
3.3.3
Submodular
functions:
Г-
and multi-band robustness
. 60
3.4
Recoverable robustness
. 61
3.4.1
The concept of recoverable robustness
. 62
3.4.2
The recoverable robust counterpart
. 63
3.5
Evaluation of robustness
. 64
II Robust Knapsack Problems
69
4
The
Г
-robust
knapsack problem
71
4.1
Formulations
. 72
4.2
Polyhedral study
. 73
4.2.1
Basic characteristics
. 73
4.2.2
Valid inequalities
. 74
4.3
Algorithms
. 76
4.3.1
Separation of violated
Г
-robust
(extended) cover inequalities
. 76
4.3.2
Solving the P-RKP
. 78
5
The multi-band robust knapsack problem
79
5.1
Formulations
. 80
5.2
Polyhedral study
. 81
5.2.1
Basic characteristics
. 81
5.2.2
Valid inequalities
. 82
5.3
Algorithms
. 83
5.3.1
Separation of multi-band robust strengthened extended cover in¬
equalities
. 84
6
The submodular knapsack problem
85
6.1
Formulations
. 86
6.2
Polyhedral study
. 87
6.2.1
Basic characteristics
. 87
6.2.2
Valid inequalities
. 87
7
The recoverable robust knapsack problem
95
7.1
Formulations
. 97
7.2
Polyhedral study
. 102
7.2.1
Basic characteristics
. 103
Contents
7.2.2
Valid inequalities
.105
7.3
Algorithms
.
ПІ
7 3.1
Solving the Maximum Weight Set Problem
.
Ill
7 3.2
Separation of violated recoverable robust extended cover inequalities
112
7 3.3
Solving the RRKP: an approach using robustness cuts
.117
8
Computational studies
121
8.1
Instances
.122
8 2
Robustness parameters
.123
8^3
Results for the k,£/D-RRKP
.123
8.4
Results for the k/T-RRKP
.126
III Robust Network Design Problems
135
9
The
Г
-robust
network design problem
137
9.1
Formulations
. 139
9.2
Polyhedral study
. 143
9.2.1
Basic characteristics
. 144
9.2.2
Cutset-based inequalities
. 145
9.2.3
Г
-robust
arc residual capacity inequalities
. 156
9.2.4
Г
-robust
metric inequalities
. 160
9.3
Algorithms
. 165
9.3.1
Separation of cutset-based inequalities
. 165
9.3.2
Separation of
Г
-robust
arc residual capacity inequalities
. 167
9.3.3
Separation of
Г
-robust
metric inequalities
. 170
10
The multi-band robust network design problem
175
10.1
Formulations
. 176
10.2
Polyhedral study
. 179
10.2.1
Basic characteristics
. 180
10.2.2
Cutset-based inequalities
. 181
10.3
Algorithms
. 185
10.3.1
Separation of multi-band robust cutset inequalities
. 185
10.3.2
Separation of multi-band robust length inequalities
. 186
11
Computational studies
189
11.1
Instances
. 189
11.2
Robustness parameters
. 193
11.3
Comparison of formulations
. 194
11.4
Strength of valid inequalities
. 196
11.5
Speed-up of the compact link flow formulation
. 199
11.6
Speed-up of the capacity formulation
. 201
11.7
Handling large instances using the capacity formulation
. 203
Xl
Contents
11.8
Quality of
optimal robust
network designs
.205
Conclusions
209
List of
Tables
213
List of
Figures
215
Bibliography
217
Index
231
About the author
237
Xli |
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| dewey-raw | 519.77 |
| dewey-search | 519.77 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Aufl. |
| format | Thesis Book |
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| spelling | Kutschka, Manuel Verfasser (DE-588)1045998850 aut Robustness concepts for knapsack and network design problems under data uncertainty Gamma-, multi-band, submodular, and recoverable robustness Manuel Kutschka 1. Aufl. Göttingen Cuvillier 2013 XII, 237 S. graph. Darst. 21 cm txt rdacontent n rdamedia nc rdacarrier Zugl.: Aachen, Univ., Diss., 2013 Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 gnd rswk-swf Robustheit (DE-588)4126481-2 gnd rswk-swf Rucksackproblem (DE-588)4178600-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 s Robustheit (DE-588)4126481-2 s Rucksackproblem (DE-588)4178600-2 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4557914&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027266595&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kutschka, Manuel Robustness concepts for knapsack and network design problems under data uncertainty Gamma-, multi-band, submodular, and recoverable robustness Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 gnd Robustheit (DE-588)4126481-2 gnd Rucksackproblem (DE-588)4178600-2 gnd |
| subject_GND | (DE-588)4156566-6 (DE-588)4126481-2 (DE-588)4178600-2 (DE-588)4113937-9 |
| title | Robustness concepts for knapsack and network design problems under data uncertainty Gamma-, multi-band, submodular, and recoverable robustness |
| title_auth | Robustness concepts for knapsack and network design problems under data uncertainty Gamma-, multi-band, submodular, and recoverable robustness |
| title_exact_search | Robustness concepts for knapsack and network design problems under data uncertainty Gamma-, multi-band, submodular, and recoverable robustness |
| title_full | Robustness concepts for knapsack and network design problems under data uncertainty Gamma-, multi-band, submodular, and recoverable robustness Manuel Kutschka |
| title_fullStr | Robustness concepts for knapsack and network design problems under data uncertainty Gamma-, multi-band, submodular, and recoverable robustness Manuel Kutschka |
| title_full_unstemmed | Robustness concepts for knapsack and network design problems under data uncertainty Gamma-, multi-band, submodular, and recoverable robustness Manuel Kutschka |
| title_short | Robustness concepts for knapsack and network design problems under data uncertainty |
| title_sort | robustness concepts for knapsack and network design problems under data uncertainty gamma multi band submodular and recoverable robustness |
| title_sub | Gamma-, multi-band, submodular, and recoverable robustness |
| topic | Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 gnd Robustheit (DE-588)4126481-2 gnd Rucksackproblem (DE-588)4178600-2 gnd |
| topic_facet | Gemischt-ganzzahlige Optimierung Robustheit Rucksackproblem Hochschulschrift |
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