A Multi-Stage Metaheuristic Algorithm for Shortest Simple Path Problem With Must-Pass Nodes

The shortest simple path problem with must-pass nodes (SSPP-MPN) aims to find a minimum-cost simple path in a directed graph, where some specified nodes must be visited. We call these specified nodes as must-pass nodes. The SSPP-MPN has been proven to be NP-hard when the number of specified nodes is more than one, and it is at least as difficult as the traveling salesmen problem (TSP), a well-known NP-hard problem. In this paper, we propose a multi-stage metaheuristic algorithm based on multiple strategies such as k-opt move, candidate path search, conflicting nodes promotion, and connectivity relaxation for solving the SSPP-MPN. The main idea of the proposed algorithm is to transform the problem into classical TSP by relaxing the simple path constraint and try to repair the obtained solutions in order to meet the demands of the original problem. The computational results tested on three sets of totally 863 instances and comparisons with reference algorithms show the efficacy of the proposed algorithm in terms of both solution quality and computational efficiency.