A MILP-based VND for the min-max regret Shortest Path Tree Problem with interval costs

The min-max regret Shortest Path Tree problem (RSPT) is a NP-Hard Robust Optimization counterpart of the Shortest Path Tree problem, where arcs costs are modeled as intervals of possible values. This problem arises from the uncertainty in link quality the routing protocols for IPv6 Low Wireless Personal Area Networks have to handle. In this paper, we propose a Variable Neighborhood Descent (VND) heuristic based on a Mixed Integer Linear Programming formulation. An exact algorithm based on the same formulation is used to assess the quality of this heuristic. Computational experiments show that VND has an average optimality gap of 0.91%, being smaller that with the best heuristic in literature for RSPT.