A Combinatorial Branch And Bound For The Min-Max Regret Spanning Tree Problem

Uncertainty in optimization can be modeled with the concept of scenarios, each of which corresponds to possible values for each parameter of the problem. The min-max regret criterion aims at obtaining a solution minimizing the maximum deviation, over all possible scenarios, from the optimal value of each scenario. Well-known problems, such as the shortest path problem and the minimum spanning tree, become NP-hard under a min-max regret criterion. This work reports the development of a branch and bound approach to solve the Minimum Spanning Tree problem under a min-max regret criterion in the discrete scenario case. The approach is tested in a wide range of test instances and compared with a generic pseudo-polynomial algorithm.