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An Algorithm for the Traveling Salesman Problem

Author

Listed:
  • John D. C. Little

    (Massachusetts Institute of Technology)

  • Katta G. Murty

    (Indian Statistical Institute)

  • Dura W. Sweeney

    (International Business Machines Corporation)

  • Caroline Karel

    (Case Institute of Technology)

Abstract

A “branch and bound” algorithm is presented for solving the traveling salesman problem. The set of all tours (feasible solutions) is broken up into increasingly small subsets by a procedure called branching. For each subset a lower bound on the length of the tours therein is calculated. Eventually, a subset is found that contains a single tour whose length is less than or equal to some lower bound for every tour. The motivation of the branching and the calculation of the lower bounds are based on ideas frequently used in solving assignment problems. Computationally, the algorithm extends the size of problem that can reasonably be solved without using methods special to the particular problem.

Suggested Citation

  • John D. C. Little & Katta G. Murty & Dura W. Sweeney & Caroline Karel, 1963. "An Algorithm for the Traveling Salesman Problem," Operations Research, INFORMS, vol. 11(6), pages 972-989, December.
    • Handle: RePEc:inm:oropre:v:11:y:1963:i:6:p:972-989
    DOI: 10.1287/opre.11.6.972
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