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Application of the out-of-kilter algorithm to the asymmetric traveling salesman problem

Author

Listed:
  • K Sang-Ho

    (Hanyang University, Sa-dong, Ansan)

  • G Young-Gun

    (Hanyang University, Sa-dong, Ansan)

  • K Maing-Kyu

    (Hanyang University, Sa-dong, Ansan)

Abstract

This paper presents a heuristic method that finds optimum or near-optimum solutions to the asymmetric traveling salesman problem. The method uses the out-of-kilter algorithm to search for a neighbourhood. When subtours are produced by a flow-augmenting path of the out-of-kilter algorithm, it patches them into a Hamiltonian cycle. It extends the neighbourhood space by exchanging an even number of arcs, and it also exchanges arcs by a non-sequential primary change. Instances from real applications were used to test the algorithm, along with randomly generated problems. The new heuristic algorithm produced optimum solutions for 16 out of 28 real-world instances from TSPLIB and other sources. Also, compared with four efficient heuristics, it produced the best solutions for all except six instances. It also produced relatively good solutions in reasonable times for 216 randomly generated instances from nine instance generators.

Suggested Citation

  • K Sang-Ho & G Young-Gun & K Maing-Kyu, 2003. "Application of the out-of-kilter algorithm to the asymmetric traveling salesman problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(10), pages 1085-1092, October.
    • Handle: RePEc:pal:jorsoc:v:54:y:2003:i:10:d:10.1057_palgrave.jors.2601614
    DOI: 10.1057/palgrave.jors.2601614
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    References listed on IDEAS

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    1. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    2. Paris-C. Kanellakis & Christos H. Papadimitriou, 1980. "Local Search for the Asymmetric Traveling Salesman Problem," Operations Research, INFORMS, vol. 28(5), pages 1086-1099, October.
    3. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    4. 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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