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A Multilevel Approach to the Travelling Salesman Problem

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  • Chris Walshaw

    (Computing and Mathematical Sciences, University of Greenwich, Old Royal Naval College, Greenwich, London, SE10 9LS, United Kingdom)

Abstract

We motivate, derive, and implement a multilevel approach to the travelling salesman problem. The resulting algorithm progressively coarsens the problem, initialises a tour, and then employs either the Lin-Kernighan (LK) or the Chained Lin-Kernighan (CLK) algorithm to refine the solution on each of the coarsened problems in reverse order. In experiments on a well-established test suite of 80 problem instances we found multilevel configurations that either improved the tour quality by over 25% as compared to the standard CLK algorithm using the same amount of execution time, or that achieved approximately the same tour quality over seven times more rapidly. Moreover, the multilevel variants seem to optimise far better the more clustered instances with which the LK and CLK algorithms have the most difficulties.

Suggested Citation

  • Chris Walshaw, 2002. "A Multilevel Approach to the Travelling Salesman Problem," Operations Research, INFORMS, vol. 50(5), pages 862-877, October.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:5:p:862-877
    DOI: 10.1287/opre.50.5.862.373
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    References listed on IDEAS

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    1. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
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    Cited by:

    1. Yuichi Nagata & Shigenobu Kobayashi, 2013. "A Powerful Genetic Algorithm Using Edge Assembly Crossover for the Traveling Salesman Problem," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 346-363, May.
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    3. Shengbin Wang & Weizhen Rao & Yuan Hong, 2020. "A distance matrix based algorithm for solving the traveling salesman problem," Operational Research, Springer, vol. 20(3), pages 1505-1542, September.

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