The linear ordering problem: exact and heuristic methods in combinatorial optimization
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Series: | Applied mathematical sciences
175 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 171 S. Ill., graph. Darst. |
| ISBN: | 3642167284 9783642167287 |
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| 100 | 1 | |a Martí, Rafael |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The linear ordering problem |b exact and heuristic methods in combinatorial optimization |c Rafael Martí ; Gerhard Reinelt |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
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Record in the Search Index
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IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 BASIC DEFINITIONS 1
1.2 APPLICATIONS OF THE LINEAR ORDERING PROBLEM 3
1.2.1 EQUIVALENT GRAPH PROBLEMS 3
1.2.2 RELATED GRAPH PROBLEMS 4
1.2.3 AGGREGATION OF INDIVIDUAL PREFERENCES 4
1.2.4 BINARY CHOICE PROBABILITIES 5
1.2.5 TRIANGULATION OF INPUT-OUTPUT TABLES 5
1.2.6 OPTIMAL WEIGHTED ANCESTRY RELATIONSHIPS 6
1.2.7 RANKING IN SPORTS TOURNAMENTS 6
1.2.8 CORRUPTION PERCEPTION 7
1.2.9 CROSSING MINIMIZATION 8
1.2.10 LINEAR ORDERING WITH QUADRATIC OBJECTIVE FUNCTION 8 1.2.11
SCHEDULING WITH PRECEDENCES 9
1.2.12 LINEAR ORDERING WITH CUMULATIVE COSTS 9
1.2.13 COUPLED TASK PROBLEM 9
1.2.14 TARGET VISITATION PROBLEM 10
1.3 BENCHMARK PROBLEMS 10
1.3.1 DATA FORMAT 10
1.3.2 INPUT-OUTPUT MATRICES 12
1.3.3 RANDOMLY GENERATED INSTANCES A (TYPE 1) 13
1.3.4 RANDOMLY GENERATED INSTANCES A (TYPE 2) 13
1.3.5 RANDOMLY GENERATED INSTANCES B 13
1.3.6 SGB INSTANCES 13
1.3.7 INSTANCES OF SCHIAVINOTTO AND STUETZTE 14
1.3.8 INSTANCES OF MITCHELL AND BORCHERS 14
1.3.9 FURTHER SPECIAL INSTANCES 14
2 HEURISTIC METHODS 17
2.1 INTRODUCTION 17
2.1.1 ASSESSING THE QUALITY OF HEURISTICS 19
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1007313870
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
2.2 CONSTRUCTION HEURISTICS 21
2.2.1 THE METHOD OF CHENERY AND WATANABE 21
2.2.2 HEURISTICS OF AUJAC & MASSON 22
2.2.3 HEURISTICS OF BECKER 22
2.2.4 BEST INSERTION 23
2.3 LOCAL SEARCH 25
2.3.1 INSERTION 26
2.3.2 THE HEURISTIC OF CHANAS & KOBYLANSKI 27
2.3.3 FC-OPT 27
2.3.4 KERNIGHAN-LIN TYPE IMPROVEMENT 27
2.3.5 LOCAL ENUMERATION 29
2.4 MULTI-START PROCEDURES 30
2.4.1 VARIANTS OF MULTI-START 31
2.4.2 EXPERIMENTS WITH THE LOP 33
META-HEURISTICS 41
3.1 INTRODUCTION 41
3.2 GRASP 43
3.2.1 CONSTRUCTION PHASE 44
3.2.2 IMPROVEMENT PHASE 48
3.3 TABU SEARCH 50
3.3.1 SHORT TERM MEMORY 51
3.3.2 LONG TERM MEMORY 53
3.4 SIMULATED ANNEALING 56
3.5 VARIABLE NEIGHBORHOOD SEARCH 60
3.5.1 VARIABLE NEIGHBORHOOD DESCENT 61
3.5.2 RESTRICTED VARIABLE NEIGHBORHOOD SEARCH 61
3.5.3 BASIC VARIABLE NEIGHBORHOOD SEARCH 62
3.5.4 FREQUENCY VARIABLE NEIGHBORHOOD SEARCH 62
3.5.5 HYBRID VARIABLE NEIGHBORHOOD SEARCH 63
3.6 SCATTER SEARCH 66
3.6.1 REFERENCE SET CREATION 70
3.6.2 REFERENCE SET UPDATE 71
3.6.3 REFERENCE SET REBUILD 73
3.7 GENETIC ALGORITHMS 77
3.8 EMPIRICAL COMPARISON 82
BRANCH-AND-BOUND 85
4.1 INTRODUCTION 85
4.2 BRANCH-AND-BOUND WITH PARTIAL ORDERINGS 87
4.3 LEXICOGRAPHIC SEARCH 89
4.4 EXTENSION OF LEXICOGRAPHIC SEARCH TO BRANCH-AND-BOUND 89 4.5
BRANCH-AND-BOUND WITH LAGRANGIAN RELAXATION 91
IMAGE 3
CONTENTS XI
5 BRANCH-AND-CUT 95
5.1 INTEGER PROGRAMMING 95
5.2 CUTTING PLANE ALGORITHMS 97
5.3 BRANCH-AND-CUT WITH 3-DICYCLE CUTS 100
5.3.1 SOLVING THE 3-DIYCLE RELAXATION 101
5.3.2 AN LP BASED HEURISTIC 102
5.3.3 COMPUTATIONAL RESULTS WITH 3-DICYCLES 102
5.4 GENERATION OF FURTHER CUTS 104
5.4.1 CHVATAL-GOMORY CUTS 104
5.4.2 MAXIMALLY VIOLATED MOD-A: CUTS 105
5.4.3 MOD-2 CUTS 107
5.5 IMPLEMENTATION OF BRANCH-AND-CUT 107
5.5.1 INITIALIZATION 108
5.5.2 ACTIVE VARIABLES 109
5.5.3 LOCAL UPPER BOUND 109
5.5.4 BRANCHING 109
5.5.5 FIXING AND SETTING OF VARIABLES 109
5.5.6 LOGICAL IMPLICATIONS 110
5.5.7 SELECTION OF NODES 110
5.5.8 LOWER BOUNDS I LL
5.5.9 SEPARATION I LL
5.5.10 ELIMINATION OF CONSTRAINTS I LL
5.5.11 CONSTRAINT POOL I LL
5.5.12 PRICING I LL
5.5.13 INFEASIBLE LPS 112
5.5.14 ADDITION OF VARIABLES 112
5.6 SOME COMPUTATIONAL RESULTS 113
6 THE LINEAR ORDERING POLYTOPE 117
6.1 POLYHEDRAL COMBINATORICS AND BASIC RESULTS 117
6.2 FACETS OF THE LINEAR ORDERING POLYTOPE 120
6.3 COMPUTATION OF COMPLETE DESCRIPTIONS 126
6.4 DIFFERENCES BETWEEN FACETS 130
6.5 SEPARATION OF SMALL FACETS 135
6.6 COMPUTATIONAL EXPERIMENTS WITH SMALL FACETS 139
6.6.1 COMPARISON OF HEURISTICS 139
6.6.2 CUTTING PLANE SELECTION 139
6.6.3 NUMBER OF CLASSES TAKEN INTO ACCOUNT 140
6.6.4 FACET SELECTION 141
6.7 LOCAL CUTS AND TARGET CUTS 141
7 FURTHER ASPECTS 145
7.1 APPROXIMATIVE ALGORITHMS 145
7.2 INTEGRALITY GAPS OF LP RELAXATIONS 146
7.3 DEGREE OF LINEARITY 146
7.4 SEMIDEFINITE RELAXATIONS 150
IMAGE 4
XII CONTENTS
7.5 CONTEXT INDEPENDENT SOLVERS 151
7.6 DIFFICULTY OF LOP INSTANCES 153
7.7 SPARSE PROBLEMS 155
7.8 A SIMPLE DUAL HEURISTIC 156
7.9 FUTURE RESEARCH 158
REFERENCES 163
INDEX 169 |
| any_adam_object | 1 |
| author | Martí, Rafael Reinelt, Gerhard |
| author_GND | (DE-588)101987113X |
| author_facet | Martí, Rafael Reinelt, Gerhard |
| author_role | aut aut |
| author_sort | Martí, Rafael |
| author_variant | r m rm g r gr |
| building | Verbundindex |
| bvnumber | BV037211851 |
| classification_rvk | SK 890 |
| ctrlnum | (OCoLC)706965437 (DE-599)DNB1007313870 |
| dewey-full | 519.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.64 |
| dewey-search | 519.64 |
| dewey-sort | 3519.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| spelling | Martí, Rafael Verfasser aut The linear ordering problem exact and heuristic methods in combinatorial optimization Rafael Martí ; Gerhard Reinelt Berlin [u.a.] Springer 2011 XII, 171 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 175 Kombinatorische Optimierung (DE-588)4031826-6 gnd rswk-swf Lineares Ordnungsproblem (DE-588)4120676-9 gnd rswk-swf Kombinatorische Optimierung (DE-588)4031826-6 s Lineares Ordnungsproblem (DE-588)4120676-9 s DE-604 Reinelt, Gerhard Verfasser (DE-588)101987113X aut Erscheint auch als Online-Ausgabe 978-3-642-16729-4 Applied mathematical sciences 175 (DE-604)BV000005274 175 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3544046&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=021125889&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Martí, Rafael Reinelt, Gerhard The linear ordering problem exact and heuristic methods in combinatorial optimization Applied mathematical sciences Kombinatorische Optimierung (DE-588)4031826-6 gnd Lineares Ordnungsproblem (DE-588)4120676-9 gnd |
| subject_GND | (DE-588)4031826-6 (DE-588)4120676-9 |
| title | The linear ordering problem exact and heuristic methods in combinatorial optimization |
| title_auth | The linear ordering problem exact and heuristic methods in combinatorial optimization |
| title_exact_search | The linear ordering problem exact and heuristic methods in combinatorial optimization |
| title_full | The linear ordering problem exact and heuristic methods in combinatorial optimization Rafael Martí ; Gerhard Reinelt |
| title_fullStr | The linear ordering problem exact and heuristic methods in combinatorial optimization Rafael Martí ; Gerhard Reinelt |
| title_full_unstemmed | The linear ordering problem exact and heuristic methods in combinatorial optimization Rafael Martí ; Gerhard Reinelt |
| title_short | The linear ordering problem |
| title_sort | the linear ordering problem exact and heuristic methods in combinatorial optimization |
| title_sub | exact and heuristic methods in combinatorial optimization |
| topic | Kombinatorische Optimierung (DE-588)4031826-6 gnd Lineares Ordnungsproblem (DE-588)4120676-9 gnd |
| topic_facet | Kombinatorische Optimierung Lineares Ordnungsproblem |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3544046&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021125889&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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