A Revised Ant Colony System Approach to Vehicle Routing Problems

Vehicle routing problems have various extensions such as time windows, multiple vehicles, backhauls, simultaneous delivery and pick-up, etc. The objectives of all these problems are to design optimal routes minimizing total distance traveled, minimizing number of vehicles, etc that satisfy corresponding constraints. In this study, an ant colony optimization based heuristic that can be used to solve various vehicle routing problems is proposed. The objective function considered to minimize the total distance traveled by all vehicles. The heuristic is applied to vehicle routing problem with time windows and vehicle routing with simultaneous delivery and pick-up. Vehicles are identical and capacities of the vehicles are finite. The time window constraints in the first problem are assumed to be strict. The proposed heuristic consists of four steps. First, a candidate list is formed for each customer in order to reduce computational time. Second, a feasible solution is found, and initial pheromone trails on each arc is calculated using it. Then, routes are constructed based on Dorigo et al. (1997). While visibility is calculated during route construction process, the distance between two customers, customers’ distance to the depot and the time window associated with the customer to whom the ant is considered to move are considered. Pheromone trails are modified by both local and global pheromone update. Finally, constructed routes are improved using 2-opt algorithm. The algorithm have been tested on the benchmark problem instances of Solomon (1987) for vehicle routing problem with time windows, and benchmark problem instances of Min (1989) and Dethloff (2001) for vehicle routing with simultaneous delivery and pick-up. The algorithm is proven to give good results when compared to the best known results in the literature.