Solving Vehicle Routing Problem with Simultaneous Pickups and Deliveries Based on A Two-Layer Particle Swarm optimization

The vehicle routing problem with simultaneous pickups and deliveries (VRPSPD) considers the delivery and pickup demands problem in the vehicle routing problem (VRP), so the customers allocated to the vehicle should not exceed the vehicle carrying capacity during the visit. The VRPSPD is regarded as solving two sub-problems in the work, customer bases determination and best routes decision. Hence, this paper proposes a two-layer discrete particle swarm optimization (DPSO) for solving the VRPSPD. The outer layer DPSO is used to find the optimal allocation of vehicles of customers (customer bases) to meet the demands for delivery and pickup in the route of the visit. The inner DPSO is used to obtain the optimal routes of various vehicles. Meanwhile, the roulette wheel selection is applied as the mechanism for gaining the discrete particle positions. Finally, the VRPSPD of CMT1X type in OR Library is tested. The experimental results demonstrate that the method designed in this study is able to solve the vehicle routing problem with simultaneous pickups and deliveries effectively.