An improved particle swarm optimization algorithm for the VRP with simultaneous pickup and delivery and time windows

In logistics, planners' main goal is to reduce operational cost as much as possible. Keeping this in mind, other aspects such as recycling arise as important issues for customers. As a consequence, planners often need to find a balance among all these aspects and operational costs. In this work, the vehicle routing problem with simultaneous pick-up and delivery and time windows is considered. Simultaneous pick-up and delivery (also called reverse logistics) allows us to address the problem of removing goods after they have been labelled as obsolete. To solve this complex combinatorial optimisation problem we use Particle Swarm Optimisation (PSO), a social-inspired algorithm. PSO aims to find a set of paths that minimises the total distance of the paths while serving, simultaneously, customers delivery and pick-up demands. Further, time windows constraints are also considered in this paper, which make the problem harder to solve. Including time windows makes also the problem more realistic, though. Results show that the PSO algorithm can find solutions that are quite competitive w.r.t. previously reported algorithms in the literature. Furthermore, the PSO algorithm solves the problem within an acceptable time.