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The Traveling Salesman Problem and Its Variations : Combinatorial Optimization - Gregory Gutin

The Traveling Salesman Problem and Its Variations

Combinatorial Optimization

By: Gregory Gutin (Editor), Abraham P. Punnen (Editor)

Hardcover Published: May 2002
ISBN: 9781402006647
Number Of Pages: 830

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Preface. Contributing Authors. 1. The Traveling Salesman Problem: Applications, Formulations and Variations; A.P. Punnen. 2. Polyhedral Theory and Branch-and-Cut Algorithms for the Symmetric TSP; D. Naddef. 3. Polyhedral Theory for the Asymmetric Traveling Salesman Problem; E. Balas, M. Fischetti. 4. Exact Methods for the Asymmetric Traveling Salesman Problem M. Fischetti, et al. 5. Approximation Algorithms for Geometric TSP; S. Arora. 6. Exponential Neighborhoods and Domination Analysis for the TSP; G. Gutin, et al. 7. Probabilistic Analysis of the TSP; A.M. Frieze, J.E. Yukich. 8. Local Search and Metaheuristics; C. Rego, F. Glover. 9. Experimental Analysis of Heuristics for the STSP; D.S. Johnson, L.A. McGeoch. 10. Experimental Analysis of Heuristics for the ATSP; D.S. Johnson, et al. 11. Polynomially Solvable Cases of the TSP; S.N. Kabadi. 12. The Maximum TSP; A. Barvinok, et al. 13. The Generalized Traveling Salesman and Orienteering Problems; M. Fischetti, et al. 14. The Prize Collecting Traveling Salesman Problem and Its Applications; E. Balas. 15. The Bottleneck TSP; S.N. Kabadi, A.P. Punnen. 16. TSP Software; A. Lodi, A.P. Punnen. Appendix A: Sets, Graphs and Permutations. Appendix B: Computational Complexity. References. List of Figures. List of Tables. Index.

Prefacep. xi
Contributing Authorsp. xv
The Traveling Salesman Problem: Applications, Formulations and Variationsp. 1
Introductionp. 1
Simple Variations of the TSPp. 7
Applications of TSPp. 9
Alternative representations of the TSPp. 15
Matrix Transformationsp. 23
More Variations of the TSPp. 24
Polyhedral Theory and Branch-and-Cut Algorithms for the Symmetric TSPp. 29
Introductionp. 29
Integer linear programming modelsp. 30
STSP polytope and relaxationsp. 35
The graphical relaxation Frameworkp. 44
The Comb inequalitiesp. 58
The Star and Path inequalitiesp. 62
The Clique Tree and Bipartition inequalitiesp. 67
The Ladder inequalitiesp. 71
A general approach to some TSP valid inequalitiesp. 73
A unifying family of inequalitiesp. 77
Domino inequalitiesp. 78
Other inequalitiesp. 81
The separation problemp. 82
Greedy heuristic for minimum cutp. 84
Graph associated to a vector x* [set membership] R[superscript E]p. 85
Heuristics for Comb Separationp. 86
Separation of multi-handle inequalitiesp. 94
Separation outside the template paradigmp. 100
Branch-and-Cut implementation of the STSPp. 105
Computational resultsp. 113
Conclusionp. 114
Polyhedral Theory for the Asymmetric Traveling Salesman Problemp. 117
Introductionp. 117
Basic ATS inequalitiesp. 120
The monotone ATS polytopep. 128
Facet-lifting proceduresp. 133
Equivalence of inequalities and canonical formsp. 142
Odd closed alternating trail inequalitiesp. 145
Source-destination inequalitiesp. 150
Lifted cycle inequalitiesp. 155
Exact Methods for the Asymmetric Traveling Salesman Problemp. 169
Introductionp. 169
AP-Based Branch-and-Bound Methodsp. 172
An Additive Branch-and-Bound Methodp. 176
A Branch-and-Cut Approachp. 181
Computational Experimentsp. 194
Approximation Algorithms for Geometric TSPp. 207
Background on Approximationp. 208
Introduction to the Algorithmp. 209
Simpler Algorithmp. 214
Better Algorithmp. 215
Faster Algorithmp. 219
Generalizations to other Problemsp. 220
Exponential Neighborhoods and Domination Analysis for the TSPp. 223
Introduction, Terminology and Notationp. 223
Exponential Neighborhoodsp. 228
Upper Bounds for Neighborhood Sizep. 237
Diameters of Neighborhood Structure Digraphsp. 240
Domination Analysisp. 244
Further Researchp. 254
Probabilistic Analysis of the TSPp. 257
Introductionp. 257
Hamiltonian Cycles in Random Graphsp. 259
Traveling Salesman Problem: Independent Modelp. 274
Euclidean Traveling Salesman Problemp. 282
Local Search and Metaheuristicsp. 309
Background on Heuristic Methodsp. 309
Improvement Methodsp. 313
Tabu Searchp. 345
Recent Unconventional Evolutionary Methodsp. 355
Conclusions and Research Opportunitiesp. 367
Experimental Analysis of Heuristics for the STSPp. 369
Introductionp. 369
DIMACS STSP Implementation Challengep. 371
Heuristics and Resultsp. 381
Conclusions and Further Researchp. 438
Experimental Analysis of Heuristics for the ATSPp. 445
Introductionp. 446
Methodologyp. 447
Heuristicsp. 457
Resultsp. 463
Conclusions and Further Researchp. 486
Polynomially Solvable Cases of the TSPp. 489
Introductionp. 489
Constant TSP and its generalizationsp. 489
The Gilmore-Gomory TSP (GG-TSP)p. 494
GG Scheme: a generalization of Gilmore-Gomory scheme for GG-TSPp. 506
Minimum cost connected directed pseudograph problem with node deficiency requirements (MCNDP)p. 539
Solvable cases of geometric TSPp. 547
Generalized graphical TSPp. 560
Solvable classes of TSP on specially structured graphsp. 564
Classes of TSP with known compact polyhedral representationp. 566
Other solvable cases and related resultsp. 576
The Maximum TSPp. 585
Introductionp. 585
Hardness Resultsp. 588
Preliminaries: Factors and Matchingsp. 589
MAX TSP with General Non-Negative Weightsp. 590
The Symmetric MAX TSPp. 591
The Semimetric MAX TSPp. 595
The Metric MAX TSPp. 597
TSP with Warehousesp. 598
MAX TSP in a Space with a Polyhedral Normp. 600
MAX TSP in a Normed Spacep. 602
Probabilistic Analysis of Heuristicsp. 605
The Generalized Traveling Salesman and Orienteering Problemsp. 609
Introductionp. 609
The Generalized Traveling Salesman Problemp. 617
The Orienteering Problemp. 642
The Prize Collecting Traveling Salesman Problem and Its Applicationsp. 663
Introductionp. 663
An Applicationp. 664
Polyhedral Considerationsp. 667
Lifting the Facets of the ATS Polytopep. 668
Primitive Inequalities from the ATSPp. 671
Cloning and Clique Lifting for the PCTSPp. 680
A Projection: The Cycle Polytopep. 686
The Bottleneck TSPp. 697
Introductionp. 697
Exact Algorithmsp. 699
Approximation Algorithmsp. 705
Polynomially Solvable Cases of BTSPp. 714
Variations of the Bottleneck TSPp. 734
TSP Softwarep. 737
Introductionp. 737
Exact algorithms for TSPp. 739
Approximation Algorithms for TSPp. 741
Java Appletsp. 745
Variations of the TSPp. 745
Other Related Problems and General-Purpose Codesp. 747
Sets, Graphs and Permutationsp. 750
Setsp. 750
Graphsp. 750
Permutationsp. 753
Computational Complexityp. 754
Introductionp. 754
Basic Complexity Resultsp. 756
Complexity and Approximationp. 758
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9781402006647
ISBN-10: 1402006640
Series: Combinatorial Optimization
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 830
Published: May 2002
Publisher: Springer-Verlag New York Inc.
Country of Publication: NL
Dimensions (cm): 24.74 x 16.76  x 4.57
Weight (kg): 1.28

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