A memetic algorithm for a vehicle routing problem with backhauls

This paper considers an extension of a vehicle routing problem with backhauls (VRPB). In this problem, a set of customers are divided in two subsets consisting of linehaul and backhaul customers. Each linehaul customer requires delivering its demands from the depot. In addition, a specified quantity of products should be picked up from the backhaul nodes to the depot. The VRPB is a well-known NP-hard problem in strong sense and a number of algorithms are proposed for approximate solutions of such a hard problem. In this paper, a memetic algorithm is proposed which uses different local search algorithms to solve the VRPB. Exploiting power of memetic algorithm, inter and intra-route node exchanges are used as a part of this evolutionary algorithm. Extensive computational tests on some instances taken from the literature reveal the effectiveness of the proposed algorithm.