Solving the robust shortest path problem with interval data using a probabilistic metaheuristic approach

This paper addresses the robust shortest path problem with interval data, i.e. the case of classical shortest path problem with given source and sink when arc weights are not fixed but take their values from some intervals associated with arcs. The problem consists in finding a shortest path that minimizes so called robust deviation, i.e. deviation from an optimal solution under the worst case realization of interval weights. As it was proven in [9], the problem is NP-hard, therefore it is of great interest to tackle it with some metaheuristic approach, namely simulated annealing, in order to calculate an approximate solution for the large scale instances efficiently. We describe theoretical aspects and present the results of computational experiments. To the best of our knowledge, this is the first attempt to develop metaheuristic approach for solving the robust shortest path problem.