A Hybrid Genetic Algorithm for the Location-Routing Problem with Simultaneous Pickup and Delivery

In this paper, we consider the Location-Routing Problem with simultaneous pickup and delivery (LRPSPD) which is a general case of the location-routing problem. The LRPSPD is defined as finding locations of the depots and designing vehicle routes in such a way that pickup and delivery demands of each customer must be performed with same vehicle and the overall cost is minimized. Since the LRPSPD is an NP-hard problem, we propose a hybrid heuristic approach based on genetic algorithms (GA) and simulated annealing (SA) to solve the problem. To evaluate the performance of the proposed approach, we conduct an experimental study and compare its results with those obtained by a branch-and-cut algorithm on a set of instances derived from the literature. Computational results indicate that the proposed hybrid algorithm is able to find optimal or very good quality solutions in a reasonable computation time.