Hybrid metaheuristic for the single vehicle routing problem with deliveries and selective pickups

This paper presents a hybrid metaheuristic for the single vehicle routing problem with deliveries and selective pickups (SVRPDSP). A vehicle departs loaded from the depot, visit every customer delivering a certain amount of goods according to their demand, and optionally pickup items from those customers, receiving a profit for each pickup realized. The vehicle has a limited capacity, which may turn impossible to attend all pickups, or make this unprofitable if it has to come back later in the customer after unloaded enough to fit the pickup demand. The objective is to find a minimal cost feasible route, the cost being the total travel costs minus the total revenue earned with pickups. Despite the many real applications, the literature is scarce. We propose an evolutionary algorithm whose crossover and mutation operators use data mining strategies to capture good characteristics from the parents and the population. Solutions are improved by a VNS algorithm during the process, and new solutions are introduced regularly to avoid premature convergence, using good constructive algorithms. The algorithm was tested with a benchmark of 68 instances, and the results compared to other publications. The results show the robustness of the method and 7 new solutions were found, including 2 new optimal solutions.