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Benders decomposition for the hop-constrained survivable network design problem

Author

Listed:
  • 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)

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.

Suggested Citation

  • BOTTON, Quentin & FORTZ, Bernard & GOUVEIA, Luis & POSS, Michael, 2011. "Benders decomposition for the hop-constrained survivable network design problem," LIDAM Discussion Papers CORE 2011037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2011037
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2011.html
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    References listed on IDEAS

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    1. Gernot Grabher & Walter W. Powell (ed.), 2004. "Networks," Books, Edward Elgar Publishing, volume 0, number 2771.
    2. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, November.
    3. 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, December.
    4. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521715348.
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    6. Luis Gouveia, 1998. "Using Variable Redefinition for Computing Lower Bounds for Minimum Spanning and Steiner Trees with Hop Constraints," INFORMS Journal on Computing, INFORMS, vol. 10(2), pages 180-188, May.
    7. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521887427.
    8. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107069978.
    9. Gouveia, Luis, 1996. "Multicommodity flow models for spanning trees with hop constraints," European Journal of Operational Research, Elsevier, vol. 95(1), pages 178-190, November.
    10. 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.
    11. Luís Gouveia & Pedro Patrício & Amaro Sousa, 2008. "Hop-Constrained Node Survivable Network Design: An Application to MPLS over WDM," Networks and Spatial Economics, Springer, vol. 8(1), pages 3-21, March.
    12. 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.
    13. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Grigory Pastukhov & Alexander Veremyev & Vladimir Boginski & Eduardo L. Pasiliao, 2014. "Optimal design and augmentation of strongly attack-tolerant two-hop clusters in directed networks," Journal of Combinatorial Optimization, Springer, vol. 27(3), pages 462-486, April.
    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.
    3. 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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    More about this item

    Keywords

    network design; survivability; hop-constraints; benders decomposition; branch-and-cut algorithms;
    All these keywords.

    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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