MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows

MACS-VRPTW, an Ant Colony Optimization based approach useful to solve vehicle routing problems with time windows is presented. MACS-VRPTW is organized with a hierarchy of artificial ant colonies designed to successively optimize a multiple objective function: the first colony minimizes the number of vehicles while the second colony minimizes the traveled distances. Cooperation between colonies is performed by exchanging information through pheromone updating. We show that MACS-VRPTW is competitive with the best known existing methods both in terms of solution quality and computation time. Moreover, MACS-VRPTW improves some of the best solutions known for a number of problem instances in the literature.