Ant Colony Optimization and Its Application to the Vehicle Routing Problem with Pickups and Deliveries

Ant Colony Optimization (ACO) is a population-based metaheuristic that can be used to find approximate solutions to difficult optimization problems. It was first introduced for solving the Traveling Salesperson Problem. Since then many implementations of ACO have been proposed for a variety of combinatorial optimization problems. In this chapter, ACO is applied to the Vehicle Routing Problem with Pickups and Deliveries (VRPPD). VRPPD determines a set of vehicle routes originating and ending at a single depot and visiting all customers exactly once. The vehicles are not only required to deliver goods but also to pick up some goods from the customers. The objective is to minimize the total distance traversed. The chapter first provides an overview of the ACO approach. Next, VRPPD is described and the related literature is reviewed. Then, an ACO approach for VRPPD is presented. The approach proposes a new visibility function which attempts to capture the “delivery” and “pickup” nature of the problem. The performance of the approach is tested using well-known benchmark problems from the literature.