A Hybrid Particle Swarm Optimization Algorithm for Multi-Objective Pickup and Delivery Problem with Time Windows

This paper studies the multi-objective pickup and delivery problem with time windows (PDPTW), in which a fleet of homogeneous vehicles with the same capacities located in a depot serve a collection of given transportation requests. Each request is composed of a pickup location, a delivery location and a given load. The PDPTW is to determine a vehicle scheduling strategy with the objectives of minimizing the number of vehicles utilized, the total travel distances and the total waiting times. A mixed integer programming model is built to formulate this multiobjective PDPTW. Then a novel hybrid particle swarm optimization (HPSO) is proposed to solve this problem. This algorithm adds particles neighbor information to diversify the particle swarm and use the variable neighborhood search (VNS) to enhance the convergence speed. Finally, some numerical experiments based on existing benchmark instances are given to show the effectiveness and feasibility of the algorithm.