A Hybrid PSO Algorithm for Vehicle Routing Problem with Simultaneous Delivery and Pickup

In this paper a hybrid algorithm named IPSO-VND is proposed and applied to solving the vehicle routing problem with simultaneous pickup and delivery (VRPSPD). The IPSO-VND algorithm combines two meta-heuristics: Improved Particle Swarm Optimization (IPSO) is used to find a group of excellent solutions, and then the Variable Neighborhood Descent (VND) is implemented to deeply search to achieve the optimal solution around these solutions. During the IPSO procedure, in order to make up for the change of a particle’s position, a velocity component is added to the movement of any particle which has been optimized or made feasible. During the VND procedure, three different neighborhood structures: insertion, swap and cross are successively used. Computational results on the benchmark problems show that our IPSO-VND algorithm is effective.