Vehicle routing problem with simultaneous delivery and pickup and intermediary delivery

We address a variant of the Vehicle Routing Problem with Backhauls where delivery of the goods picked up from one node to another is allowed along the same vehicle route. The remaining goods in the vehicle are transported back to the depot. Two objectives exist: the primary one is to minimize the total distance traveled; the secondary is to maximize intra-route deliveries. To achieve these goals, we propose a hybrid metaheuristic which consists of an Ant Colony Optimization algorithm for the route construction and a Tabu Search algorithm for the route improvement. To test the performance of our approach, we generate benchmark data based on the well-known problem instances in the literature. Since the variant presented in this paper has not been addressed previously in the literature, only benchmark results with respect to the first objective are available. For this dual objective problem, we attempt to generate a Pareto curve for different levels of the first objective to investigate the trade-off between the two objective functions