Particle Swarm Optimization to solve the Vehicle Routing Problem with Heterogeneous fleet, Mixed Backhauls, and time windows

Many distribution companies must deliver and pick up goods to satisfy customers. This problem is called the Vehicle Routing Problem with Mixed linehauls and Backhauls (VRPMB) which considers that some goods must be delivered from a depot to linehaul customers, while others must be picked up at backhaul customers to be brought to the depot. This paper studies an enriched version called Heterogeneous fleet VRPMB with Time Windows or HVRPMBTW which has not much been studied in the literature. A Particle Swarm Optimization heuristic (PSO) is proposed to solve this problem. This approach uses and models the social behavior of bird flocking, fish schooling. The adaptation and implementation of PSO search strategy to HVRPMBTW is explained, then the results are compared to previous works (Ant Colony Optimization) and compared also to the high quality solutions obtained by an exact method (solver CPLEX). Good promising results are reported and have shown the effectiveness of the method.