A formulation for a hop constrained survivable network design problem

This article presents an integer linear model for the hop constrained node survivable network design problem. The formulation is focused on networks represented by undirected graphs with not rooted demands, considering costs in arcs and in optional (Steiner) nodes, too. The proposed model allows setting different values of parameters for constraints between each pair of terminal nodes, including hop length and number of node disjoint paths constraints. This work includes calculating lower and upper bounds to the optimal solution. Since this kind of problems are NPhard, it is useful to combine the presented formulation with heuristic methods in order to solve effectively large problem instances. The model was tested over the graphs with up to 85 nodes and 148 arcs, in order to validate it in cases with known solution.