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Design of survivable networks with vulnerability constraints

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  • Gouveia, Luis
  • Leitner, Markus

Abstract

We consider the Network Design Problem with Vulnerability Constraints (NDPVC) which simultaneously addresses resilience against failures (network survivability) and bounds on the lengths of each communication path (hop constraints). Solutions to the NDPVC are subgraphs containing a path of length at most Hst for each commodity {s, t} and a path of length at most Hst′ between s and t after at most k−1 edge failures. We first show that a related and well known problem from the literature, the Hop-Constrained Survivable Network Design Problem (kHSNDP), that addresses the same two measures produces solutions that are too conservative in the sense that they might be too expensive in practice or may even fail to provide feasible solutions. We also explain that the reason for this difference is that Mengerian-like theorems not hold in general when considering hop-constraints. Three graph theoretical characterizations of feasible solutions to the NDPVC are derived and used to propose integer linear programming formulations. In a computational study we compare these alternatives with respect to the lower bounds obtained from the corresponding linear programming relaxations and their capability of solving instances to proven optimality. In addition, we show that in many cases, the solutions produced by solving the NDPVC are cheaper than those obtained by the related kHSNDP.

Suggested Citation

  • Gouveia, Luis & Leitner, Markus, 2017. "Design of survivable networks with vulnerability constraints," European Journal of Operational Research, Elsevier, vol. 258(1), pages 89-103.
    • Handle: RePEc:eee:ejores:v:258:y:2017:i:1:p:89-103
    DOI: 10.1016/j.ejor.2016.09.003
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    References listed on IDEAS

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    1. Anantaram Balakrishnan & Thomas L. Magnanti & Prakash Mirchandani, 1994. "Modeling and Heuristic Worst-Case Performance Analysis of the Two-Level Network Design Problem," Management Science, INFORMS, vol. 40(7), pages 846-867, July.
    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.
    3. 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.
    4. Luis Gouveia & Pedro Patrício & Amaro Sousa, 2016. "Lexicographical minimization of routing hops in hop-constrained node survivable networks," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 62(2), pages 417-434, June.
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    Cited by:

    1. Gouveia, Luis & Leitner, Markus & Ruthmair, Mario, 2017. "Extended formulations and branch-and-cut algorithms for the Black-and-White Traveling Salesman Problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 908-928.
    2. Yajun Lu & Hosseinali Salemi & Balabhaskar Balasundaram & Austin Buchanan, 2022. "On Fault-Tolerant Low-Diameter Clusters in Graphs," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3181-3199, November.

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