Résumé (EN)

The hop-constrained survivable network design problem consists of finding a minimum cost subgraph containing K edge-disjoint paths with length at most H joining each pair of vertices in a given demand set. When all demands have a common vertex, the instance is said to be rooted. We propose a new extended formulation for the rooted case, called hop-level multicommodity flow (MCF), that can be significantly stronger than the previously known formulations, at the expense of having a larger number of variables and constraints, growing linearly with the number of edges and demands and quadratically with H. However, for the particular case where H = 2, it can be specialized into a very compact and efficient formulation. Even when H = 3, hop-level-MCF can still be quite efficient and it has solved several instances from the literature for the first time.