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 [Gouveia, L. 1998. Using variable redefinition for computing lower bounds for minimum spanning and Steiner trees with hop constraints. INFORMS J. Comput.
10(2) 180–188], we present a formulation for the problem valid for any K, L ≥ 1. We use a Benders decomposition method to efficiently handle the large number of variables and constraints. We show that our Benders cuts contain constraints used in previous studies to formulate the problem for L = 2, 3, 4, as well as new inequalities when L ≥ 5. Whereas 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.
