Dynamic preprocessing for the minmax regret robust shortest path problem with finite multi-scenarios

The minmax regret robust shortest path problem aims at finding a path that minimizes the maximum deviation from the shortest paths over all scenarios. It is assumed that different arc costs are associated with different scenarios. This paper introduces a technique to reduce the network, before a minmax regret robust shortest path algorithm is applied. The preprocessing method enhances others explored in previous research. The introduced method acts dynamically and allows to update the conditions to be checked as new network nodes that can be discarded are identified. Computational results on random and Karasan networks are reported, which compare the dynamic preprocessing algorithm and its former static version. Two robust shortest path algorithms as well as the resolution of a mixed integer linear formulation by a solver are tested with and without these preprocessing rules.