Combinatorial Optimization

By: A.P. Punnen (Editor), G. Gutin (Editor)

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Paperback | 18 May 2007

At a Glance

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852 Pages

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23.4 x 15.8 x 4.9

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This volume, which contains chapters written by reputable researchers, provides the state of the art in theory and algorithms for the traveling salesman problem (TSP). The book covers all important areas of study on TSP, including polyhedral theory for symmetric and asymmetric TSP, branch and bound, and branch and cut algorithms, probabilistic aspects of TSP, thorough computational analysis of heuristic and metaheuristic algorithms, theoretical analysis of approximation algorithms, including the emerging area of domination analysis of algorithms, discussion of TSP software and variations of TSP such as bottleneck TSP, generalized TSP, prize collecting TSP, maximizing TSP, orienteering problem, etc. This book is intended for researchers, practitioners, and academicians in mathematics, computer science, and operations research. It is appropriate as a reference work or as a main or supplemental textbook in graduate and senior undergraduate courses and projects.

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You Can Find This Book In

Non-Fiction Mathematics Combinatorics & Graph Theory Business & Management Sales & Marketing Computing & I.T.Computer Programming & Software Development Algorithms & Data Structures Optimisation Linear Programming Discrete Mathematics Databases

Data Capture & Analysis Applied Mathematics Operational Research Medicine Medicine in General Computer Science

Preface	p. xi
Contributing Authors	p. xv
The Traveling Salesman Problem: Applications, Formulations and Variations	p. 1
Introduction	p. 1
Simple Variations of the TSP	p. 7
Applications of TSP	p. 9
Alternative representations of the TSP	p. 15
Matrix Transformations	p. 23
More Variations of the TSP	p. 24
Polyhedral Theory and Branch-and-Cut Algorithms for the Symmetric TSP	p. 29
Introduction	p. 29
Integer linear programming models	p. 30
STSP polytope and relaxations	p. 35
The graphical relaxation Framework	p. 44
The Comb inequalities	p. 58
The Star and Path inequalities	p. 62
The Clique Tree and Bipartition inequalities	p. 67
The Ladder inequalities	p. 71
A general approach to some TSP valid inequalities	p. 73
A unifying family of inequalities	p. 77
Domino inequalities	p. 78
Other inequalities	p. 81
The separation problem	p. 82
Greedy heuristic for minimum cut	p. 84
Graph associated to a vector x [isin] R[superscript E]	p. 85
Heuristics for Comb Separation	p. 86
Separation of multi-handle inequalities	p. 94
Separation outside the template paradigm	p. 100
Branch-and-Cut implementation of the STSP	p. 105
Computational results	p. 113
Conclusion	p. 114
Polyhedral Theory for the Asymmetric Traveling Salesman Problem	p. 117
Introduction	p. 117
Basic ATS inequalities	p. 120
The monotone ATS polytope	p. 128
Facet-lifting procedures	p. 133
Equivalence of inequalities and canonical forms	p. 142
Odd closed alternating trail inequalities	p. 145
Source-destination inequalities	p. 150
Lifted cycle inequalities	p. 155
Exact Methods for the Asymmetric Traveling Salesman Problem	p. 169
Introduction	p. 169
AP-Based Branch-and-Bound Methods	p. 172
An Additive Branch-and-Bound Method	p. 176
A Branch-and-Cut Approach	p. 181
Computational Experiments	p. 194
Approximation Algorithms for Geometric TSP	p. 207
Background on Approximation	p. 208
Introduction to the Algorithm	p. 209
Simpler Algorithm	p. 214
Better Algorithm	p. 215
Faster Algorithm	p. 219
Generalizations to other Problems	p. 220
Exponential Neighborhoods and Domination Analysis for the TSP	p. 223
Introduction, Terminology and Notation	p. 223
Exponential Neighborhoods	p. 228
Upper Bounds for Neighborhood Size	p. 237
Diameters of Neighborhood Structure Digraphs	p. 240
Domination Analysis	p. 244
Further Research	p. 254
Probabilistic Analysis of the TSP	p. 257
Introduction	p. 257
Hamiltonian Cycles in Random Graphs	p. 259
Traveling Salesman Problem: Independent Model	p. 274
Euclidean Traveling Salesman Problem	p. 282
Local Search and Metaheuristics	p. 309
Background on Heuristic Methods	p. 309
Improvement Methods	p. 313
Tabu Search	p. 345
Recent Unconventional Evolutionary Methods	p. 355
Conclusions and Research Opportunities	p. 367
Experimental Analysis of Heuristics for the STSP	p. 369
Introduction	p. 369
DIMACS STSP Implementation Challenge	p. 371
Heuristics and Results	p. 381
Conclusions and Further Research	p. 438
Experimental Analysis of Heuristics for the ATSP	p. 445
Introduction	p. 446
Methodology	p. 447
Heuristics	p. 457
Results	p. 463
Conclusions and Further Research	p. 486
Polynomially Solvable Cases of the TSP	p. 489
Introduction	p. 489
Constant TSP and its generalizations	p. 489
The Gilmore-Gomory TSP (GG-TSP)	p. 494
GG Scheme: a generalization of Gilmore-Gomory scheme for GG-TSP	p. 506
Minimum cost connected directed pseudograph problem with node deficiency requirements (MCNDP)	p. 539
Solvable cases of geometric TSP	p. 547
Generalized graphical TSP	p. 560
Solvable classes of TSP on specially structured graphs	p. 564
Classes of TSP with known compact polyhedral representation	p. 566
Other solvable cases and related results	p. 576
The Maximum TSP	p. 585
Introduction	p. 585
Hardness Results	p. 588
Preliminaries: Factors and Matchings	p. 589
MAX TSP with General Non-Negative Weights	p. 590
The Symmetric MAX TSP	p. 591
The Semimetric MAX TSP	p. 595
The Metric MAX TSP	p. 597
TSP with Warehouses	p. 598
MAX TSP in a Space with a Polyhedral Norm	p. 600
MAX TSP in a Normed Space	p. 602
Probabilistic Analysis of Heuristics	p. 605
The Generalized Traveling Salesman and Orienteering Problems	p. 609
Introduction	p. 609
The Generalized Traveling Salesman Problem	p. 617
The Orienteering Problem	p. 642
The Prize Collecting Traveling Salesman Problem and Its Applications	p. 663
Introduction	p. 663
An Application	p. 664
Polyhedral Considerations	p. 667
Lifting the Facets of the ATS Polytope	p. 668
Primitive Inequalities from the ATSP	p. 671
Cloning and Clique Lifting for the PCTSP	p. 680
A Projection: The Cycle Polytope	p. 686
The Bottleneck TSP	p. 697
Introduction	p. 697
Exact Algorithms	p. 699
Approximation Algorithms	p. 705
Polynomially Solvable Cases of BTSP	p. 714
Variations of the Bottleneck TSP	p. 734
TSP Software	p. 737
Introduction	p. 737
Exact algorithms for TSP	p. 739
Approximation Algorithms for TSP	p. 741
Java Applets	p. 745
Variations of the TSP	p. 745
Other Related Problems and General-Purpose Codes	p. 747
Sets, Graphs and Permutations	p. 750
Sets	p. 750
Graphs	p. 750
Permutations	p. 753
Computational Complexity	p. 754
Introduction	p. 754
Basic Complexity Results	p. 756
Complexity and Approximation	p. 758
References	p. 761
List of Figures	p. 807
List of Tables	p. 813
Index	p. 817
Table of Contents provided by Ingram. All Rights Reserved.

Combinatorial Optimization

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