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

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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.

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Acknowledgements

This work was done with the support of the Gaspard Monge Program for Optimization and operations research (PGMO) http://www.fondation-hadamard.fr/fr/pgmo.

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Authors and Affiliations

  1. Polytechnique and GERAD, Montréal, Canada

    Alain Hertz & Thomas Ridremont

  2. ENSTA ParisTech and CEDRIC-CNAM, Paris, France

    Thomas Ridremont

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  1. Alain Hertz
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  2. Thomas Ridremont
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Correspondence to Alain Hertz.

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Hertz, A., Ridremont, T. A tabu search for the design of capacitated rooted survivable planar networks. J Heuristics 26, 829–850 (2020). https://doi.org/10.1007/s10732-020-09453-x

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  • DOI: https://doi.org/10.1007/s10732-020-09453-x

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