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The Undirected m -Peripatetic Salesman Problem: Polyhedral Results and New Algorithms

Author

Listed:
  • Éric Duchenne

    (LAMIH, Université de Valenciennes et du Hainaut-Cambresis, 59313 Valenciennes Cedex 9, France)

  • Gilbert Laporte

    (Centre de Recherche sur les Transports, HEC Montréal, Montreal, Quebec, Canada H3T 2A7)

  • Frédéric Semet

    (LAMIH, Université de Valenciennes et du Hainaut-Cambresis, 59313 Valenciennes Cedex 9, France)

Abstract

In the m -peripatetic salesman problem ( m -PSP), the aim is to determine m edge disjoint Hamiltonian cycles of minimum total cost on a graph. This article introduces new valid inequalities and polyhedral results for the m -PSP. An improved 2-index branch-and-cut algorithm is developed. Tests performed on randomly generated and TSPLIB Euclidean instances indicate that this algorithm can solve instances with more than double the size of what was previously achievable.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:5:p:949-965
    DOI: 10.1287/opre.1070.0387
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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.
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    6. 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.
    7. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
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    Cited by:

    1. Keskin, Burcu B. & Li, Shirley (Rong) & Steil, Dana & Spiller, Sarah, 2012. "Analysis of an integrated maximum covering and patrol routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 215-232.
    2. TALARICO, Luca & SÖRENSEN, Kenneth & SPRINGAEL, Johan, 2013. "The k-dissimilar vehicle routing problem," Working Papers 2013029, University of Antwerp, Faculty of Business and Economics.
    3. 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.

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