A local search metaheuristic algorithm for the vehicle routing problem with simultaneous pick-ups and deliveries

This article proposes a local search metaheuristic solution approach for the vehicle routing problem with simultaneous pick-ups and deliveries (VRPSPD), which models numerous practical transportation operations in the context of reverse logistics. The proposed algorithm is capable of exploring wide solution neighborhoods by statically encoding moves into special data structures. To avoid cycling and induce diversification, the overall search is coordinated by the use of the promises concept which is based on the aspiration criteria of tabu search. The proposed promises implementation is applied to basic solution features, namely solution arcs. In terms of the challenging capacity constraints imposed by the VRPSPD model, we present a constant-time feasibility checking procedure for the employed local search operators. The presented metaheuristic development was tested on eighteen large-scale VRPSPD benchmark instances derived from the literature. It proved to be both robust and effective, improving most of the previously best-known solutions of the examined test problems.