An ant colony algorithm for the mixed vehicle routing problem with backhauls

The Vehicle Routing Problem with Pickup and Delivery (VRPPD) is a variant of the Vehicle Routing Problem where the vehicles are not only required to deliver goods but also to pick up some goods from the customers. The Mixed Vehicle Routing Problem with Backhauls (MVRPB) is a special case of VRPPD where each customer has either a delivery or a pickup demand to be satisfied and the customers can be visited in any order along the route. Given a fleet of vehicles and a set of customers with known pickup or delivery demands MVRPB determines a set of vehicle routes originating and ending at a single depot and visiting all customers exactly once. The objective is to minimize the total distance traversed with the least number of vehicles. For this problem, we propose an Ant Colony Optimization algorithm with a new visibility function which attempts to capture the “delivery” and “pickup” nature of the problem. Our numerical tests to compare the performance of the proposed approach with those of the well-known benchmark problems reveal that the proposed approach provides encouraging results.