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Benders decomposition for the hop-constrained survivable network design problem

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  • BOTTON, Quentin

    ()
    (Université catholique de Louvain, CESCM-LSM and CORE, B-1348 Louvain-la-Neuve, Belgium)

  • FORTZ, Bernard

    ()
    (GOM, Université Libre de Bruxelles, Belgium)

  • GOUVEIA, Luis

    ()
    (Universidade de Lisboa, DEIO, P-1749-016 Lisbon, Portugal)

  • POSS, Michael

    ()
    (GOM, Université Libre de Bruxelles, Belgium)

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    Abstract

    Given a graph with nonnegative edge weights and node pairs Q, we study the problem of constructing a minimum weight set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at most L edges between each pair in Q. Using the layered representation introduced by Gouveia (1998), we present a formulation for the problem valid for any K, L ≥ 1. We use a Benders decomposition method to efficiently handle the big number of variables and constraints. We show that our Benders cuts contain the constraints used by Huygens et al. to formulate the problem for L = 2,3,4, as well as new inequalities when L ≥ 5. While some recent works on Benders decomposition study the impact of the normalization constraint in the dual subproblem, we focus here on when to generate the Benders cuts. We present a thorough computational study of various branch-and-cut algorithms on a large set of instances including the real based instances from SNDlib. Our best branch-and-cut algorithm combined with an efficient heuristic is able to solve the instances significantly faster than CPLEX 12 on the extended formulation.

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    File URL: http://uclouvain.be/cps/ucl/doc/core/documents/coredp2011_37web.pdf
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    Bibliographic Info

    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2011037.

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    Date of creation: 01 Sep 2011
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    Handle: RePEc:cor:louvco:2011037

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    Related research

    Keywords: network design; survivability; hop-constraints; benders decomposition; branch-and-cut algorithms;

    References

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    1. Duranton, Gilles & Martin, Philippe & Mayer, Thierry & Mayneris, Florian, 2010. "The Economics of Clusters: Lessons from the French Experience," OUP Catalogue, Oxford University Press, number 9780199592203.
    2. Pirkul, Hasan & Soni, Samit, 2003. "New formulations and solution procedures for the hop constrained network design problem," European Journal of Operational Research, Elsevier, vol. 148(1), pages 126-140, July.
    3. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, November.
    4. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521887427, November.
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    Cited by:
    1. Souza, Fernanda S.H. & Gendreau, Michel & Mateus, Geraldo R., 2014. "Branch-and-price algorithm for the Resilient Multi-level Hop-constrained Network Design," European Journal of Operational Research, Elsevier, vol. 233(1), pages 84-93.

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