The traveling salesman problem and its variations:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
2002
|
| Series: | Combinatorial optimization
12 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 761-806) and index |
| Physical Description: | XVIII, 830 S. Ill., grah. Darst. |
| ISBN: | 1402006640 |
Staff View
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| 245 | 1 | 0 | |a The traveling salesman problem and its variations |c ed. by Gregory Gutin ... |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 2002 | |
| 300 | |a XVIII, 830 S. |b Ill., grah. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Combinatorial optimization |v 12 | |
| 500 | |a Includes bibliographical references (p. 761-806) and index | ||
| 650 | 7 | |a Handelsreizigersprobleem |2 gtt | |
| 650 | 4 | |a Optimisation combinatoire | |
| 650 | 4 | |a Problèmes de tournées | |
| 650 | 4 | |a Traveling-salesman problem | |
| 650 | 4 | |a Combinatorial optimization | |
| 650 | 0 | 7 | |a Travelling-salesman-Problem |0 (DE-588)4185966-2 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Gutin, Gregory Z. |d 1957- |e Sonstige |0 (DE-588)142715557 |4 oth | |
| 830 | 0 | |a Combinatorial optimization |v 12 |w (DE-604)BV012009079 |9 12 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xi
Contributing Authors xv
1
The Traveling Salesman Problem: Applications, Formulations 1
and Variations
Abraham P. Punnen
1.1 Introduction 1
1.2 Simple Variations of the TSP 7
1.3 Applications of TSP 9
1.4 Alternative representations of the TSP 15
1.5 Matrix Transformations 23
1.6 More Variations of the TSP 24
2
Polyhedral Theory and Branch and Cut Algorithms for 29
the Symmetric TSP
Denis Naddef
2.1 Introduction 29
2.2 Integer linear programming models 30
2.3 STSP polytope and relaxations 35
2.4 The graphical relaxation Framework 44
2.5 The Comb inequalities 58
2.6 The Star and Path inequalities 62
2.7 The Clique Tree and Bipartition inequalities C7
2.8 The Ladder inequalities 71
2.9 A general approach to some TSP valid inequalities 73
2.10 A unifying family oi inequalities 77
2.11 Domino inequalities 78
2.12 Other inequalities 81
2.13 The separation problem 82
2.14 Greedy heuristic for minimum cut 84
2.15 Graph associated to a vector x* E Mf 85
2.16 Heuristics for Comb Separation 86
2.17 Separation of multi handle inequalities 94
2.18 Separation outside the template paradigm 100
2.19 Branch and Cut implementation of the STSP 105
2.20 Computational results 113
2.21 Conclusion 114
vi THE TRAVELING SALESMAN PROBLEM AND ITS VARIATIONS
3
Polyhedral Theory for the Asymmetric Traveling Salesman Problem 117
Egon Balas and Matteo Fischetti
3.1 Introduction 117
3.2 Basic ATS inequalities 120
3.3 The monotone ATS polytope 128
3.4 Facet lifting procedures 133
3.5 Equivalence of inequalities and canonical forms 142
3.6 Odd closed alternating trail inequalities 145
3.7 Source destination inequalities 150
3.8 Lifted cycle inequalities 155
4
Exact Methods for the Asymmetric Traveling Salesman Problem 169
Matteo Fischetti, Andrea Lodi and Paolo Toth
4.1 Introduction 169
4.2 ,4P Based Branch and Bound Methods 172
4.3 An Additive Branch and Bound Method 176
4.4 A Branch and Cut Approach 181
4.5 Computational Experiments 194
5
Approximation Algorithms for Geometric TSP 207
Sanjeev Arora
5.1 Background on Approximation 208
5.2 Introduction to the Algorithm 209
5.3 Simpler Algorithm 214
5.4 Better Algorithm 215
5.5 Faster Algorithm 219
5.6 Generalizations to other Problems 220
6
Exponential Neighborhoods and Domination Analysis for the TSP 223
Gregory Gutin, Anders Yeo and Alexei Zverovitch
6.1 Introduction, Terminology and Notation 223
6.2 Exponential Neighborhoods 228
6.3 Upper Bounds for Neighborhood Size 237
6.4 Diameters of Neighborhood Structure Digraphs 240
6.5 Domination Analysis 244
6.6 Further Research 254
7
Probabilistic Analysis of the TSP 257
A. M. Frieze and J. E. Yukich
7.1 Introduction 257
7.2 Hamiltonian Cycles in Random Graphs 259
7.3 Traveling Salesman Problem: Independent Model 274
7.4 Euclidean Traveling Salesman Problem 282
8
Local Search and Metaheuristics ^9
Cesar Rego and Fred Glover
8.1 Background on Heuristic Methods 309
Contents vii
8.2 Improvement Methods 313
8.3 Tabu Search 345
8.4 Recent Unconventional Evolutionary Methods 355
8.5 Conclusions and Research Opportunities 367
9
Experimental Analysis of Heuristics for the STSP 369
David S. Johnson and Lyle A. McGeoch
9.1 Introduction 369
9.2 DIMACS STSP Implementation Challenge 371
9.3 Heuristics and Results 381
9.4 Conclusions and Further Research 438
10
Experimental Analysis of Heuristics for the ATSP 445
David S. Johnson, Gregory Gutin, Lyle A. McGeoch, Anders Yeo, Weixiong
Zhang and Alexei Zverovitch
10.1 Introduction 446
10.2 Methodology 447
10.3 Heuristics 457
10.4 Results 463
10.5 Conclusions and Further Research 486
11
Polynomially Solvable Cases of the TSP 489
Santosh N. Kabadi
11.1 Introduction 489
11.2 Constant TSP and its generalizations 489
11.3 The Gilmore Gomory TSP (GG TSP) 494
11.4 GG Scheme: a generalization of Gilmore Gomory scheme for
GG TSP 506
11.5 Minimum cost connected directed pseudograph problem with
node deficiency requirements (MCNDP) 539
11.6 Solvable cases of geometric TSP 547
11.7 Generalized graphical TSP 560
11.8 Solvable classes of TSP on specially structured graphs 564
11.9 Classes of TSP with known compact polyhedral representation 566
11.10 Other solvable cases and related results 576
12
The Maximum TSP 585
Alexander Barvinok , Edward. Kh. Gimndi and Anatoliy I. Scrriyukov
12.1 Introduction 585
12.2 Hardness Results 588
12.3 Preliminaries: Factors and Matc hings 589
12.4 MAX TSP with General Non Negative Weights 590
12.5 The Symmetric MAX TSP 591
12.6 The Scmimetrie MAX TSP 595
12.7 The Metric MAX TSP 597
12.8 TSP with Warehouses 598
12.9 MAX TSP in a Space with a Polyhedral Norm 600
12.10 MAX TSP in a Normed Space 602
viii THE TRAVELING SALESMAN PROBLEM AND ITS VARIATIONS
12.11 Probabilistic Analysis of Heuristics 605
13
The Generalized Traveling Salesman and Orienteering Problems 609
Matteo Fischetti, Juan JoseSalazar Gonzalez and Paolo Toth
13.1 Introduction 609
13.2 The Generalized Traveling Salesman Problem 617
13.3 The Orienteering Problem 642
14
The Prize Collecting Traveling Salesman Problem 663
and Its Applications
Egon Balas
14.1 Introduction 663
14.2 An Application 664
14.3 Polyhedral Considerations 667
14.4 Lifting the Facets of the ATS Polytope 668
14.5 Primitive Inequalities from the ATSP 671
14.6 Cloning and Clique Lifting for the PCTSP. 680
14.7 A Projection: The Cycle Polytope 686
15
The Bottleneck TSP 697
Santosh N. Kabadi and Abraham P. Punnen
15.1 Introduction 697
15.2 Exact Algorithms 699
15.3 Approximation Algorithms 705
15.4 Polynomially Solvable Cases of BTSP 714
15.5 Variations of the Bottleneck TSP 734
16
TSP Software 737
Andrea Lodi and Abraham P. Punnen
16.1 Introduction 737
16.2 Exact algorithms for TSP 739
16.3 Approximation Algorithms for TSP 741
16.4 Java Applets 745
16.5 Variations of the TSP 745
16.6 Other Related Problems and General Purpose Codes 747
Appendix: A. Sets, Graphs and Permutations 7^0
Gregory Gutin
A .i Sets 750
A .2 Graphs 750
A .3 Permutations 753
Appendix: B. Computational Complexity 754
Abraham P. Punnen
B .l Introduction 754
B .2 Basic Complexity Results 756
B .3 Complexity and Approximation 758
Contents lx
References 761
List of Figures 807
List of Tables 813
Index 8i?
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| indexdate | 2024-07-09T19:03:19Z |
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| isbn | 1402006640 |
| language | English |
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| physical | XVIII, 830 S. Ill., grah. Darst. |
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| series | Combinatorial optimization |
| series2 | Combinatorial optimization |
| spelling | The traveling salesman problem and its variations ed. by Gregory Gutin ... Dordrecht [u.a.] Kluwer 2002 XVIII, 830 S. Ill., grah. Darst. txt rdacontent n rdamedia nc rdacarrier Combinatorial optimization 12 Includes bibliographical references (p. 761-806) and index Handelsreizigersprobleem gtt Optimisation combinatoire Problèmes de tournées Traveling-salesman problem Combinatorial optimization Travelling-salesman-Problem (DE-588)4185966-2 gnd rswk-swf Travelling-salesman-Problem (DE-588)4185966-2 s DE-604 Gutin, Gregory Z. 1957- Sonstige (DE-588)142715557 oth Combinatorial optimization 12 (DE-604)BV012009079 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009890571&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The traveling salesman problem and its variations Combinatorial optimization Handelsreizigersprobleem gtt Optimisation combinatoire Problèmes de tournées Traveling-salesman problem Combinatorial optimization Travelling-salesman-Problem (DE-588)4185966-2 gnd |
| subject_GND | (DE-588)4185966-2 |
| title | The traveling salesman problem and its variations |
| title_auth | The traveling salesman problem and its variations |
| title_exact_search | The traveling salesman problem and its variations |
| title_full | The traveling salesman problem and its variations ed. by Gregory Gutin ... |
| title_fullStr | The traveling salesman problem and its variations ed. by Gregory Gutin ... |
| title_full_unstemmed | The traveling salesman problem and its variations ed. by Gregory Gutin ... |
| title_short | The traveling salesman problem and its variations |
| title_sort | the traveling salesman problem and its variations |
| topic | Handelsreizigersprobleem gtt Optimisation combinatoire Problèmes de tournées Traveling-salesman problem Combinatorial optimization Travelling-salesman-Problem (DE-588)4185966-2 gnd |
| topic_facet | Handelsreizigersprobleem Optimisation combinatoire Problèmes de tournées Traveling-salesman problem Combinatorial optimization Travelling-salesman-Problem |
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