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A Generalized Insertion Heuristic for the Traveling Salesman Problem with Time Windows

Author

Listed:
  • Michel Gendreau

    (Université de Montrél, Montréal, Québec, Canada)

  • Alain Hertz

    (École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland)

  • Gilbert Laporte

    (École des Hautes Études Commerciales, Montreál, Québec, Canada)

  • Mihnea Stan

    (Delta Technology, Atlanta, Georgia)

Abstract

This article describes a generalized insertion heuristic for the Traveling Salesman Problem with Time Windows in which the objective is the minimization of travel times. The algorithm gradually builds a route by inserting at each step a vertex in its neighbourhood on the current route, and performing a local reoptimization. This is done while checking the feasibility of the remaining part of the route. Backtracking is sometimes necessary. Once a feasible route has been determined, an attempt is made to improve it by applying a post-optimization phase based on the successive removal and reinsertion of all vertices. Tests performed on 375 instances indicate that the proposed heuristic compares very well with alternative methods and very often produces optimal or near-optimal solutions.

Suggested Citation

  • Michel Gendreau & Alain Hertz & Gilbert Laporte & Mihnea Stan, 1998. "A Generalized Insertion Heuristic for the Traveling Salesman Problem with Time Windows," Operations Research, INFORMS, vol. 46(3), pages 330-335, June.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:3:p:330-335
    DOI: 10.1287/opre.46.3.330
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    References listed on IDEAS

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    1. Martin Desrochers & Jacques Desrosiers & Marius Solomon, 1992. "A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 40(2), pages 342-354, April.
    2. A. W. J. Kolen & A. H. G. Rinnooy Kan & H. W. J. M. Trienekens, 1987. "Vehicle Routing with Time Windows," Operations Research, INFORMS, vol. 35(2), pages 266-273, April.
    3. Yvan Dumas & Jacques Desrosiers & Eric Gelinas & Marius M. Solomon, 1995. "An Optimal Algorithm for the Traveling Salesman Problem with Time Windows," Operations Research, INFORMS, vol. 43(2), pages 367-371, April.
    4. Harilaos N. Psaraftis, 1980. "A Dynamic Programming Solution to the Single Vehicle Many-to-Many Immediate Request Dial-a-Ride Problem," Transportation Science, INFORMS, vol. 14(2), pages 130-154, May.
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