Time Dependent Vehicle Routing Problem with an Ant Colony System

IDSIA-02-03 Abstract The Time Dependent Vehicle Routing Problem, TDVRP, consists in optimally routing a fleet of vehicles of fixed capacity when the traveling times are dependent on time, that is, the time of the day when the trip on a leg was initiated. The delivery to a customer must also satisfy the customer’s delivery time window. The optimization consists in finding the solution that minimizes the number of tours (the number of vehicles used) and the total travel time. The speed distributions, from which the travel times can be calculated, are supposed to be known at the beginning of the optimization. This version of the VRP is motivated by the fact that in some circumstances, traffic conditions play an important role and can not be ignored in order to perform a realistic optimization. We present a new approach to this problem based on an Ant Colony System (ACS) using time dependent pheromones. Appropriate techniques for local search procedures in a time dependent context are also discussed. We discuss some aspects of this model, such as its tendency to favor travels on longer legs in times when speeds are higher, and how different factors can affect the optimization. From numerical experiments it is showed that best solutions known for the non time dependent case, in a time dependent context, might become unfeasible if time windows are considered, or suboptimal.