Chained Lin-Kernighan for Large Traveling Salesman Problems

We discuss several issues that arise in the implementation of Martin, Otto, and Felten's Chained Lin-Kernighan heuristic for large-scale traveling salesman problems. Computational results are presented for TSPLIB instances ranging in size from 11,849 cities up to 85,900 cities; for each of these instances, solutions within 1% of the optimal value can routinely be found in under one CPU minute on a 300 MHz Pentium II workstation, and solutions within 0.5% of optimal can routinely be found in under ten CPU minutes. We also demonstrate the scalability of the heuristic, presenting results for randomly generated Euclidean instances having up to 25,000,000 cities. For the largest of these random instances, a tour within 1% of an estimate of the optimal value was obtained in under one CPU day on a 64-bit IBM RS6000 workstation.

[1]  David S. Johnson,et al.  Data structures for traveling salesmen , 1993, SODA '93.

[2]  Olivier C. Martin,et al.  Combining simulated annealing with local search heuristics , 1993, Ann. Oper. Res..

[3]  Richard M. Karp,et al.  The Traveling-Salesman Problem and Minimum Spanning Trees , 1970, Oper. Res..

[4]  David S. Johnson,et al.  Local Optimization and the Traveling Salesman Problem , 1990, ICALP.

[5]  R. Bland,et al.  Large travelling salesman problems arising from experiments in X-ray crystallography: A preliminary report on computation , 1989 .

[6]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[7]  G. Rinaldi,et al.  Chapter 4 The traveling salesman problem , 1995 .

[8]  R. Bixby,et al.  On the Solution of Traveling Salesman Problems , 1998 .

[9]  Jon Jouis Bentley,et al.  Fast Algorithms for Geometric Traveling Salesman Problems , 1992, INFORMS J. Comput..

[10]  Marek Chrobak,et al.  A Data Structure Useful for Finding Hamiltonian Cycles , 1990, Theor. Comput. Sci..

[11]  Edward W. Felten,et al.  Large-Step Markov Chains for the Traveling Salesman Problem , 1991, Complex Syst..

[12]  Steven Fortune,et al.  A sweepline algorithm for Voronoi diagrams , 1986, SCG '86.

[13]  Jukka Perttunen.  On the Significance of the Initial Solution in Travelling Salesman Heuristics , 1994 .

[14]  Keld Helsgaun,et al.  An effective implementation of the Lin-Kernighan traveling salesman heuristic , 2000, Eur. J. Oper. Res..

[15]  King-Tim Mak,et al.  A modified Lin-Kernighan traveling-salesman heuristic , 1993, Oper. Res. Lett..

[16]  Edward W. Felten,et al.  Large-step markov chains for the TSP incorporating local search heuristics , 1992, Oper. Res. Lett..

[17]  O. Bohigas,et al.  The random link approximation for the Euclidean traveling salesman problem , 1996, cond-mat/9607080.

[18]  Robert Bixby,et al.  On the Solution of Traveling Salesman , 1998 .

[19]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

[20]  Giovanni Manzini,et al.  Perturbation: An Efficient Technique for the Solution of Very Large Instances of the Euclidean TSP , 1996, INFORMS J. Comput..

[21]  Andrew B. Kahng,et al.  Improved Large-Step Markov Chain Variants for the Symmetric TSP , 1997, J. Heuristics.

[22]  D. Corneil,et al.  Efficient cluster compensation for lin-kernighan heuristics , 1999 .

[23]  David S. Johnson,et al.  Asymptotic experimental analysis for the Held-Karp traveling salesman bound , 1996, SODA '96.

[24]  Martin,et al.  Finite size and dimensional dependence in the Euclidean traveling salesman problem. , 1996, Physical review letters.

[25]  William J. Cook,et al.  Finding Tours in the TSP , 1999 .

[26]  Richard M. Karp,et al.  The traveling-salesman problem and minimum spanning trees: Part II , 1971, Math. Program..

[27]  Joseph F. Pekny,et al.  A Staged Primal-Dual Algorithm for Perfect b-Matching with Edge Capacities , 1995, INFORMS J. Comput..

[28]  Nicos Christofides.  Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem , 1976, Operations Research Forum.

[29]  Emile H. L. Aarts,et al.  Parallel Local Search and the Travelling Salesman Problem , 1992, Parallel Problem Solving from Nature.

[30]  J. Beardwood,et al.  The shortest path through many points , 1959, Mathematical Proceedings of the Cambridge Philosophical Society.

[31]  William J. Cook,et al.  TSP Cuts Which Do Not Conform to the Template Paradigm , 2000, Computational Combinatorial Optimization.

[32]  G. Reinelt.  The traveling salesman: computational solutions for TSP applications , 1994 .