An Efficient Algorithm for the Shortest Path Problem with Forbidden Paths

In this paper, we discuss the shortest path problem with forbidden paths (SPPFP), where the constraints come from a set of forbidden paths (arc sequences) that cannot be part of any feasible solution. SPPFP can be used to solve the problems with hard-to-modeled path constraints or to implement exact branching scheme. The method proposed by Villeneuve and Desaulmers first transfer the SPPFP problem to the k-shortest paths problem. We propose an algorithm which reduces execution time of solving the SPPFP problem via a nodes combination process. It improves the approach proposed by Villeneuve and Desaulniers. In addition, their algorithm for generating augmented paths could cause the inconsistency in particular situations. The proposed method also improves the weakness without increasing its time complexity.