The quadratic assignment problem: theory and algorithms
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1998
|
| Schriftenreihe: | Combinatorial optimization
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 287 S. |
| ISBN: | 0792348788 |
Internformat
MARC
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| 245 | 1 | 0 | |a The quadratic assignment problem |b theory and algorithms |c by Eranda Çela |
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| 300 | |a XV, 287 S. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
PREFACE ix
LIST OF FIGURES xiii
LIST OF TABLES Xv
1 PROBLEM STATEMENT AND COMPLEXITY
ASPECTS 1
1.1 Problem Statement 2
1.2 Applications 3
1.3 Two alternative formulations of the QAP 5
1.4 Linearizations 7
1.4.1 Kaufman and Broeckx linearization 8
1.4.2 Frieze and Yadegar linearization 9
1.4.3 Padberg and Rijal linearization 10
1.5 Computational complexity aspects 17
1.5.1 The complexity of optimally and approximately solving
QAPs 17
1.5.2 The complexity of local search 22
2 EXACT ALGORITHMS AND LOWER BOUNDS 27
2.1 Lower bounds 28
2.1.1 The bound of Gilmore Lawler and other Gilmore Lawler
like bounds 28
2.1.2 Eigenvalue related lower bounds 38
2.1.3 Bounding techniques based on reformulations 43
2.1.4 Bounds based on linear programming relaxations 46
v
2.1.5 Bounds based on semidefinite relaxations 50
2.1.6 Improving bounds by means of decompositions 57
2.1.7 Bounding techniques: Conclusions 60
2.2 Branch and Bound approaches 62
2.3 Cutting plane methods 65
2.3.1 Traditional cutting planes 65
2.3.2 Polyhedral cutting planes 69
3 HEURISTICS AND ASYMPTOTIC BEHAVIOR 73
3.1 Construction and limited enumeration methods 74
3.2 Improvement methods 77
3.3 Tabu search algorithms 79
3.4 Simulates annealing approaches 82
3.5 Genetic Algorithms 87
3.6 Greedy randomized adaptive search 90
3.7 QAP instances with known optimal solutions 92
3.8 Asymptotic behavior 100
3.8.1 On the asymptotic behavior of some combinatorial opti¬
mization problems 101
3.8.2 On the asymptotic behavior of the QAP 104
4 QAPS ON SPECIALLY STRUCTURED
MATRICES 107
4.1 Definitions and notations 108
4.2 The cones of Monge like matrices 113
4.2.1 The cone of Monge matrices 115
4.2.2 The cone of graded Anti Monge matrices 118
4.2.3 The cone of Kalmanson matrices 121
4.2.4 The cone structure and the QAP 123
4.3 Simple polynomially solvable cases of the QAP 124
4.4 QAPs with Monge like matrices 130
4.5 QAPs with circulant and small bandwidth matrices 140
4.5.1 Two easy QAPs with circulant and bandwidth k ma¬
trices 141
4.5.2 Special cases of the taxonomy problem 150
5 TWO MORE RESTRICTED VERSIONS OF THE
QAP 159
5.1 Polynomially solvable cases of the Anti Monge Toeplitz QAP 160
5.1.1 Benevolent Toeplitz matrices 160
5.1.2 The Anti Monge Toeplitz QAP with a benevolent matrix 163
5.1.3 The Anti Monge Toeplitz QAP with a periodic Toeplitz
matrix 171
5.1.4 Symmetric Toeplitz matrices with small bandwidth 176
5.2 The Anti Monge Toeplitz QAP: Applications 183
5.2.1 The turbine problem 183
5.2.2 The TSP on symmetric Monge matrices 185
5.2.3 Data arrangement in a linear storage medium 186
5.3 The Kalmanson Toeplitz QAP 187
5.4 Permuted polynomially solvable cases 189
5.5 Open problems and conclusions 192
6 QAPS ARISING AS OPTIMIZATION
PROBLEMS IN GRAPHS 195
6.1 QAPs related to placement problems 196
6.2 Special cases related to the feedback arc set problem 199
6.3 QAPs arising from packing problems in graphs 206
6.4 Special cases of the GQAP 214
7 ON THE BIQUADRATIC ASSIGNMENT
PROBLEM (BIQAP) 223
7.1 An application of the BiQAP arising in the VLSI synthesis 224
7.2 Different formulations for the BiQAP 228
7.3 Bounds for the BiQAP 232
7.4 BiQAPs with known optimal solution 235
7.5 The asymptotic behavior of the BiQAP 238
7.6 Heuristics for BiQAPs 241
7.6.1 Deterministic improvement methods 241
7.6.2 Simulated annealing algorithms 242
7.6.3 Tabu search approaches 244
7.6.4 Greedy randomized adaptive search for the BiQAP 245
7.7 On computational results 245
7.8 Conclusions and open questions 247
REFERENCES 251
NOTATION INDEX 271
SUBJECT INDEX 279
|
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| id | DE-604.BV011994592 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:19:52Z |
| institution | BVB |
| isbn | 0792348788 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008117522 |
| oclc_num | 439757031 |
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| physical | XV, 287 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Kluwer Acad. Publ. |
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| series | Combinatorial optimization |
| series2 | Combinatorial optimization |
| spelling | Çela, Eranda Verfasser aut The quadratic assignment problem theory and algorithms by Eranda Çela Dordrecht [u.a.] Kluwer Acad. Publ. 1998 XV, 287 S. txt rdacontent n rdamedia nc rdacarrier Combinatorial optimization 1 Quadratische Optimierung (DE-588)4130555-3 gnd rswk-swf Quadratisches Zuordnungsproblem (DE-588)4621707-1 gnd rswk-swf Quadratische Optimierung (DE-588)4130555-3 s DE-604 Quadratisches Zuordnungsproblem (DE-588)4621707-1 s Combinatorial optimization 1 (DE-604)BV012009079 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008117522&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Çela, Eranda The quadratic assignment problem theory and algorithms Combinatorial optimization Quadratische Optimierung (DE-588)4130555-3 gnd Quadratisches Zuordnungsproblem (DE-588)4621707-1 gnd |
| subject_GND | (DE-588)4130555-3 (DE-588)4621707-1 |
| title | The quadratic assignment problem theory and algorithms |
| title_auth | The quadratic assignment problem theory and algorithms |
| title_exact_search | The quadratic assignment problem theory and algorithms |
| title_full | The quadratic assignment problem theory and algorithms by Eranda Çela |
| title_fullStr | The quadratic assignment problem theory and algorithms by Eranda Çela |
| title_full_unstemmed | The quadratic assignment problem theory and algorithms by Eranda Çela |
| title_short | The quadratic assignment problem |
| title_sort | the quadratic assignment problem theory and algorithms |
| title_sub | theory and algorithms |
| topic | Quadratische Optimierung (DE-588)4130555-3 gnd Quadratisches Zuordnungsproblem (DE-588)4621707-1 gnd |
| topic_facet | Quadratische Optimierung Quadratisches Zuordnungsproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008117522&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012009079 |
| work_keys_str_mv | AT celaeranda thequadraticassignmentproblemtheoryandalgorithms |