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Some Examples of Difficult Traveling Salesman Problems

Author

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  • C. H. Papadimitriou

    (Harvard University, Cambridge, Massachusetts)

  • K. Steiglitz

    (Princeton University, Princeton, New Jersey)

Abstract

We construct instances of the symmetric traveling salesman problem with n = 8 k cities that have the following property: There is exactly one optimal tour with cost n , and there are 2 k −1 ( k − 1)! tours that are next-best, have arbitrarily large cost, and cannot be improved by changing fewer than 3 k edges. Thus, there are many local optima with arbitrarily high cost. It appears that local search algorithms are ineffective when applied to these problems. Even more catastrophic examples are available in the non-symmetric case.

Suggested Citation

  • C. H. Papadimitriou & K. Steiglitz, 1978. "Some Examples of Difficult Traveling Salesman Problems," Operations Research, INFORMS, vol. 26(3), pages 434-443, June.
    • Handle: RePEc:inm:oropre:v:26:y:1978:i:3:p:434-443
    DOI: 10.1287/opre.26.3.434
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    Cited by:

    1. Lenstra, J. K. & Rinnooy Kan, A. H. G., 1979. "Complexity Of Vehicle Routing And Scheduling Problems," Econometric Institute Archives 272191, Erasmus University Rotterdam.
    2. Helsgaun, Keld, 2000. "An effective implementation of the Lin-Kernighan traveling salesman heuristic," European Journal of Operational Research, Elsevier, vol. 126(1), pages 106-130, October.

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