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A Flexible, Natural Formulation for the Network Design Problem with Vulnerability Constraints

Author

Listed:
  • Okan Arslan

    (HEC Montréal, Montreal, Quebec H3T 2A7, Canada)

  • Ola Jabali

    (Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milan, Italy)

  • Gilbert Laporte

    (HEC Montréal, Montreal, Quebec H3T 2A7, Canada)

Abstract

Given a graph, a set of origin-destination (OD) pairs with communication requirements, and an integer k ≥ 2, the network design problem with vulnerability constraints (NDPVC) is to identify a subgraph with the minimum total edge costs such that, between each OD pair, there exist a hop-constrained primary path and a hop-constrained backup path after any k − 1 edges of the graph fail. Formulations exist for single-edge failures (i.e., k = 2). To solve the NDPVC for an arbitrary number of edge failures, we develop two natural formulations based on the notion of length-bounded cuts. We compare their strengths and flexibilities in solving the problem for k ≥ 3. We study different methods to separate infeasible solutions by computing length-bounded cuts of a given size. Experimental results show that, for single-edge failures, our formulation increases the number of solved benchmark instances from 61% (obtained within a two-hour limit by the best published algorithm) to more than 95%, thus increasing the number of solved instances by 1,065. Our formulation also accelerates the solution process for larger hop limits and efficiently solves the NDPVC for general k . We test our best algorithm for two to five simultaneous edge failures and investigate the impact of multiple failures on the network design.

Suggested Citation

  • Okan Arslan & Ola Jabali & Gilbert Laporte, 2020. "A Flexible, Natural Formulation for the Network Design Problem with Vulnerability Constraints," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 120-134, January.
    • Handle: RePEc:inm:orijoc:v:32:y:2020:i:1:p:120-134
    DOI: 10.1287/ijoc.2018.0869
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    References listed on IDEAS

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    1. 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.
    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. M. W. P. Savelsbergh, 1994. "Preprocessing and Probing Techniques for Mixed Integer Programming Problems," INFORMS Journal on Computing, INFORMS, vol. 6(4), pages 445-454, November.
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