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A tabu search for the design of capacitated rooted survivable planar networks

Author

Listed:
  • Alain Hertz

    (Polytechnique and GERAD)

  • Thomas Ridremont

    (Polytechnique and GERAD
    ENSTA ParisTech and CEDRIC-CNAM)

Abstract

Consider a rooted directed graph G with a subset of vertices called terminals, where each arc has a positive integer capacity and a non-negative cost. For a given positive integer k, we say that G is k-survivable if every of its subgraphs obtained by removing at most k arcs admits a feasible flow that routes one unit of flow from the root to every terminal. We aim at determining a k-survivable subgraph of G of minimum total cost. We focus on the case where the input graph G is planar and propose a tabu search algorithm whose main procedure takes advantage of planar graph duality properties. In particular, we prove that it is possible to test the k-survivability of a planar graph by solving a series of shortest path problems. Experiments indicate that the proposed tabu search algorithm produces optimal solutions in a very short computing time, when these are known.

Suggested Citation

  • Alain Hertz & Thomas Ridremont, 2020. "A tabu search for the design of capacitated rooted survivable planar networks," Journal of Heuristics, Springer, vol. 26(6), pages 829-850, December.
    • Handle: RePEc:spr:joheur:v:26:y:2020:i:6:d:10.1007_s10732-020-09453-x
    DOI: 10.1007/s10732-020-09453-x
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    References listed on IDEAS

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    1. Geir Dahl & Mechthild Stoer, 1998. "A Cutting Plane Algorithm for Multicommodity Survivable Network Design Problems," INFORMS Journal on Computing, INFORMS, vol. 10(1), pages 1-11, February.
    2. Quentin Botton & Bernard Fortz & Luis Gouveia & Michael Poss, 2013. "Benders Decomposition for the Hop-Constrained Survivable Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 13-26, February.
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