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Benders decomposition for the hop-constrained survivable network design problem


  • 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)


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.

Suggested Citation

  • BOTTON, Quentin & FORTZ, Bernard & GOUVEIA, Luis & POSS, Michael, 2011. "Benders decomposition for the hop-constrained survivable network design problem," CORE Discussion Papers 2011037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2011037

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    References listed on IDEAS

    1. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521715348.
    2. Gernot Grabher & Walter W. Powell (ed.), 2004. "Networks," Books, Edward Elgar Publishing, volume 0, number 2771.
    3. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, November.
    4. 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.
    5. 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.
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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.
    2. Alexander Veremyev & Vladimir Boginski & Eduardo Pasiliao, 2015. "Analytical characterizations of some classes of optimal strongly attack-tolerant networks and their Laplacian spectra," Journal of Global Optimization, Springer, vol. 61(1), pages 109-138, January.

    More about this item


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

    JEL classification:

    • M10 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - General
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General


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