Dynamic programming approaches to solve the shortest path problem with forbidden paths

In this paper, the shortest path problem with forbidden paths is addressed. The problem under consideration is formulated as a particular instance of the resource-constrained shortest path problem. Different versions of a dynamic programming-based solution approach are defined and implemented. The proposed algorithms can be viewed as an extension of the node selection approach proposed by Desrochers in 1988. An extensive computational test is carried out on a meaningful number of random instances with the purpose of assessing the behaviour of the developed solution approaches. A comparison with the state-of-the-art method proposed to address the problem under study is also made. The computational results are very encouraging and highlight that the proposed algorithms are very efficient.