A tabu search for the design of capacitated rooted survivable planar networks

Consider a rooted directed graph G with a subset of vertices called terminals, where each arc has a positive integer capacity and a non-negative cost. For a given positive integer k , we say that G is k -survivable if every of its subgraphs obtained by removing at most k arcs admits a feasible flow that routes one unit of flow from the root to every terminal. We aim at determining a k -survivable subgraph of G of minimum total cost. We focus on the case where the input graph G is planar and propose a tabu search algorithm whose main procedure takes advantage of planar graph duality properties. In particular, we prove that it is possible to test the k -survivability of a planar graph by solving a series of shortest path problems. Experiments indicate that the proposed tabu search algorithm produces optimal solutions in a very short computing time, when these are known.