Abstract
The large-step Markov chain (LSMC) approach is the most effective known heuristic for large symmetric TSP instances; cf. recent results of [Martin, Otto and Felten, 1991] and [Johnson, 1990]. In this paper, we examine relationships among (i) the underlying local optimization engine within the LSMC approach, (ii) the “kick move” perturbation that is applied between successive local search descents, and (iii) the resulting LSMC solution quality. We find that the traditional “double-bridge” kick move is not necessarily optimum: stronger local optimization engines (e.g., Lin-Kernighan) are best matched with stronger kick moves. We also propose use of an adaptive temperature schedule to allow escape from deep basins of attraction; the resulting hierarchical LSMC variant outperforms traditional LSMC implementations that use uniformly zero temperatures. Finally, a population-based LSMC variant is studied, wherein multiple solution paths can interact to achieve improved solution quality.
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References
Aldous, D. and U. Vazirani, “'Go with the winners' algorithms,” Proc. IEEE Symp. on Foundations of Computer Science, pages 492–501, 1994.
Applegate, D. L., July 1995, Personal Communication.
Applegate, D. L., R. Bixby, V. Chvatal and W. Cook, “Finding cuts in the TSP (a preliminary report),” Technical Report} No. 95–05, Center for Discrete Mathematics and Theoretical Computer Science, 19
Baum, E. B., “Iterated descent: A better algorithm for local search in combinatorial optimization problems,” Manuscript, 1986a.
Baum, E. B., “Towards practical 'neural' computation for combinatorial optimization problems,” Neural Networks for Computing, AIP Conference Proceedings, page 151, 1986b.
Bentley, J. L., “K-d trees for semidynamic point sets,” Proc. ACM Symp. on Computational Geometry, pages 187–197, June 1990.
Bentley, J. L., “Fast algorithms for geometric traveling salesman problems,” ORSA Journal on Computing, 4(4):387–411, 1992.
Boese, K. D., “Cost versus distance in the traveling salesman problem,” Technical Report TR-950018, UCLA CS Department, 1995.
Boese, K. D., A. B. Kahng, and S. Muddu, “A new adaptive multi-start technique for combinatorial global optimizations,” Operations Research Letters, 16(2):101–113, 1994.
Fogel, L. J., A. J. Owens, and M. J.Walsh, Artificial Intelligence Through Simulated Evolution, JohnWiley, 1966.
Garey, M. R. and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman, New York, 1979.
Glover, F., “Heuristics for integer programming using surrogate constraints,” Decision Sciences, 8:156–166, 1977.
Glover, F., “Tabu search and adaptive memory programming-advances, applications and challenges,” In R. Barr, R. Helgason, and J. Kennington, editors, Interfaces in Computer Science and Operations Research, pages 1–75, Kluwer Academic Publishers, 1996.
Glover, F. and M. Laguna, “Tabu search,” In C. Reeves, editor, Modern Heuristic Techniques for Combinatorial Problems, pages 70–141. Blackwell Scientific Publishing, Oxford, 1993.
Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, MA, 1989.
Johnson, D. S., “Local optimization and the traveling salesman problem,” Proc. 17th Intl. Colloquium on Automata, Languages and Programming, pages 446–460, 1990.
Johnson, D. S. and L. A. McGeoch, “The traveling salesman problem: A case study in local optimization,” In E. H. L. Aarts and J. K. Lenstra, editors, Local Search Algorithms. Wiley and Sons, New York, 1997.
Lawler, E. L., J. K. Lenstra, A. Rinnooy-Kan, and D. Shmoys, The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Wiley, Chichester, 1985.
Lin, S. and B. W. Kernighan, “An effective heuristics algorithm for the traveling-salesman problem,” Operations Research, 31:498–516, 1973.
Martin, O. and S. W. Otto, “Combining simulated annealing with local search heuristics,” In G. Laporte, I. H. Osman, and P. L. Hammer, editors, Annals of Operations Research, volume 63, pages 57–75. 1996.
Martin, O., S.W. Otto, and E.W. Felten, “Large-step markov chains for the traveling salesman problem,” Complex Systems, 5(3):299–326, June 1991.
Martin, O., S. W. Otto, and E. W. Felten, “Large-step markov chains for the TSP incorporating local search heuristics,” Operations Research Letters, 11(4):219–224, 1992.
Mühlenbein, H., M. Georges-Schleuter, and O. Krämer, “Evolution algorithms in combinatorial optimization,” Parallel Computing, 7:65–85, 1988.
Ulder, N. L. J., E. H. L. Aarts, H.-J. Bandelt, P. J. M. van Laarhoven, and E. Pesch, “Genetic local search algorithms for the traveling salesman problem,” Proc. Parallel Problem Solving from Nature, pages 109–116, 1990.
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Hong, I., Kahng, A.B. & Moon, BR. Improved Large-Step Markov Chain Variants for the Symmetric TSP. Journal of Heuristics 3, 63–81 (1997). https://doi.org/10.1023/A:1009624916728
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DOI: https://doi.org/10.1023/A:1009624916728