Benders decomposition for the hop-constrained survivable network design problem
(2011) , 30 pages
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- Authors
- 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, 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 branchand- 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 signicantly faster than CPLEX 12 on the extended formulation.
- Affiliations
Louvain School of Management Operations and Information ULB GOM ULB GOM FCUL CIO
Citations
Botton, Q., Fortz, B., Poss, M., & Gouveia, L. (2011). Benders decomposition for the hop-constrained survivable network design problem (CORE Discussion Paper 2011/37). https://hdl.handle.net/2078.5/249884