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The undirected m-Capacitated Peripatetic Salesman Problem

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  • Duchenne, Éric
  • Laporte, Gilbert
  • Semet, Frédéric

Abstract

In the m-Capacitated Peripatetic Salesman Problem (m-CPSP) the aim is to determine m Hamiltonian cycles of minimal total cost on a graph, such that all the edges are traversed less than the value of their capacity. This article introduces three formulations for the m-CPSP. Two branch-and-cut algorithms and one branch-and-price algorithm are developed. Tests performed on randomly generated and on TSPLIB Euclidean instances indicate that the branch-and-price algorithm can solve instances with more than twice the size of what is achievable with the branch-and-cut algorithms.

Suggested Citation

  • Duchenne, Éric & Laporte, Gilbert & Semet, Frédéric, 2012. "The undirected m-Capacitated Peripatetic Salesman Problem," European Journal of Operational Research, Elsevier, vol. 223(3), pages 637-643.
    • Handle: RePEc:eee:ejores:v:223:y:2012:i:3:p:637-643
    DOI: 10.1016/j.ejor.2012.07.022
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    References listed on IDEAS

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    1. Duchenne, Eric & Laporte, Gilbert & Semet, Frederic, 2005. "Branch-and-cut algorithms for the undirected m-Peripatetic Salesman Problem," European Journal of Operational Research, Elsevier, vol. 162(3), pages 700-712, May.
    2. Asef-Vaziri, Ardavan & Laporte, Gilbert, 2005. "Loop based facility planning and material handling," European Journal of Operational Research, Elsevier, vol. 164(1), pages 1-11, July.
    3. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    4. Laurel Lindner-Dutton & Rajan Batta & Mark H. Karwan, 1991. "Equitable Sequencing of a Given Set of Hazardous Materials Shipments," Transportation Science, INFORMS, vol. 25(2), pages 124-137, May.
    5. De Kort, Jeroen B. J. M., 1993. "A branch and bound algorithm for symmetric 2-Peripatetic Salesman Problems," European Journal of Operational Research, Elsevier, vol. 70(2), pages 229-243, October.
    6. Matteo Fischetti & Juan José Salazar González & Paolo Toth, 1997. "A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem," Operations Research, INFORMS, vol. 45(3), pages 378-394, June.
    7. Éric Duchenne & Gilbert Laporte & Frédéric Semet, 2007. "The Undirected m -Peripatetic Salesman Problem: Polyhedral Results and New Algorithms," Operations Research, INFORMS, vol. 55(5), pages 949-965, October.
    8. Plastria, Frank, 2002. "Formulating logical implications in combinatorial optimisation," European Journal of Operational Research, Elsevier, vol. 140(2), pages 338-353, July.
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