An Ant Colony Optimization Approach for the Mixed Vehicle Routing Problem with Backhauls

The Vehicle Routing Problem with Backhauls (VRPB) 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. In the mixed VRPB (MVRPB) each customer has either a delivery or a pick-up 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 pick-up 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. A maximum route length restriction may also be imposed on the vehicles. From a practical point of view MVRPB models situations such as distribution of bottled drinks, chemicals, LPG tanks, etc. In the case of the bottled drinks for instance, full bottles are delivered to customers and empty ones are brought back either for re-use or for recycling. In the chemicals case, some hazardous materials may need to be returned for safe disposal. Regulations or environmental issues may also force companies to take responsibility for their products throughout their lifetime. For this problem, we propose an Ant Colony Optimization (ACO) approach utilizing a new visibility function which attempts to capture the “delivery and pick-up” nature of the problem. We perform an extensive experimental study to compare the performance of the proposed approach with those of the well-known benchmark problems from the literature. Our numerical tests show that the proposed approach provides encouraging results.