Hybrid dynamic programming with bounding algorithm for the multi-profit orienteering problem

Abstract

The multi-profit orienteering problem (MPOP), a variant of the orienteering problem, was introduced in 2020. In MPOP, each vertex has multiple profits, and a profit is determined by the time of visit. Therefore, the vertices to visit as well as the visit sequence and visit times must be optimally selected. The purpose of MPOP is to maximize the total profits collected from the vertices while satisfying the travel time limit constraint. To date, no exact algorithm has been developed for MPOP. This paper proposes a dynamic programming (DP)-based exact algorithm for MPOP for the first time. The proposed algorithm combines DP, ng-route relaxed DP, incumbent solution generation algorithms, and bounding rules. The proposed algorithm can obtain the optimal solutions for 33 previously unsolved benchmark instances and update the best solutions in 23 benchmark instances for MPOP. © 2022 Elsevier B.V.