The minmax regret robust shortest path problem in a finite multi-scenario model

The robust shortest path problem is a network optimization problem that can be defined to deal with uncertainty of costs associated with the arcs of a network. Two models have been considered for the robust shortest path problem: interval data and discrete data sets. This work addresses the robust shortest path problem with a minmax regret objective function on a finite multi-scenario model. This problem consists in finding an optimal path in the sense that it has the minimum maximum deviation from the shortest one over all scenarios. With this goal some properties of the problem and of its optimal solutions are derived. These results allow to introduce three approaches, a labeling algorithm, an algorithm based on ranking loopless paths, and a hybrid algorithm which ranks loopless paths in a suitable way to apply the early elimination of useless solutions. The algorithms are tested on random networks and compared with a previous method for the same problem. The obtained computational results are reported and discussed. They show that the labeling and the hybrid approaches outperform the others.