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A Heuristic Approach to Solving Travelling Salesman Problems

Author

Listed:
  • Robert L. Karg

    (National Tube Division, U.S. Steel and Duquesne University)

  • Gerald L. Thompson

    (Graduate School of Industrial Administration, Carnegie Institute of Technology)

Abstract

A code for solving travelling salesman problem employing heuristic ideas is described. Acyclic permutations of the cities are constructed by first choosing two cities at random for a permutation of length two, putting the remaining cities in a random list and then inserting cities from the list in the partially constructed permutations so that they add least to the length of the partial tour. A second heuristic idea used in the code is that of breaking up the problem into convex, or almost convex sub-problems and employing the above-mentioned heuristic on these subproblems. Numerical experience with the code is described as well as weaknesses and strengths of the method.

Suggested Citation

  • Robert L. Karg & Gerald L. Thompson, 1964. "A Heuristic Approach to Solving Travelling Salesman Problems," Management Science, INFORMS, vol. 10(2), pages 225-248, January.
    • Handle: RePEc:inm:ormnsc:v:10:y:1964:i:2:p:225-248
    DOI: 10.1287/mnsc.10.2.225
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    Citations

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    Cited by:

    1. Ferretti, Ivan & Zanoni, Simone & Zavanella, Lucio, 2006. "Production-inventory scheduling using Ant System metaheuristic," International Journal of Production Economics, Elsevier, vol. 104(2), pages 317-326, December.
    2. Gilbert Laporte & Jorge Riera-Ledesma & Juan-José Salazar-González, 2003. "A Branch-and-Cut Algorithm for the Undirected Traveling Purchaser Problem," Operations Research, INFORMS, vol. 51(6), pages 940-951, December.
    3. Dillmann, Roland & Becker, Burkhard & Beckefeld, Volker, 1996. "Practical aspects of route planning for magazine and newspaper wholesalers," European Journal of Operational Research, Elsevier, vol. 90(1), pages 1-12, April.
    4. Ozgur, C. O. & Brown, J. R., 1995. "A two-stage traveling salesman procedure for the single machine sequence-dependent scheduling problem," Omega, Elsevier, vol. 23(2), pages 205-219, April.
    5. C P Keller & M F Goodchild, 1988. "The Multiobjective Vending Problem: A Generalization of the Travelling Salesman Problem," Environment and Planning B, , vol. 15(4), pages 447-460, December.
    6. Rego, Cesar, 2001. "Technical note on the paper "An empirical study of a new metaheuristic for the traveling salesman problem" (by Shigeru Tsubakitani, James R. Evans, European Journal of Operational Research 1," European Journal of Operational Research, Elsevier, vol. 129(2), pages 456-459, March.
    7. Roy E. Marsten, 1972. "An Algorithm for Finding Almost All Of The Medians of a Network," Discussion Papers 23, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Manerba, Daniele & Mansini, Renata & Riera-Ledesma, Jorge, 2017. "The Traveling Purchaser Problem and its variants," European Journal of Operational Research, Elsevier, vol. 259(1), pages 1-18.
    9. Biskup, Dirk & Herrmann, Jan & Gupta, Jatinder N.D., 2008. "Scheduling identical parallel machines to minimize total tardiness," International Journal of Production Economics, Elsevier, vol. 115(1), pages 134-142, September.
    10. Tsubakitani, Shigeru & Evans, James R., 1998. "An empirical study of a new metaheuristic for the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 104(1), pages 113-128, January.
    11. Chandrasekharan Rajendran & Dipak Chaudhuri, 1990. "Heuristic algorithms for continuous flow‐shop problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 695-705, October.

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