An ant colony system (ACS) for vehicle routing problem with simultaneous delivery and pickup

In this paper we use an ant colony system (ACS) algorithm to solve the vehicle routing problem with simultaneous delivery and pickup (VRPSDP) which is a combinatorial optimization problem. ACS is an algorithmic approach inspired by the foraging behavior of real ants. Artificial ants are used to construct a solution for the problem by using the pheromone information from previously generated solutions. The proposed ACS algorithm uses a construction rule as well as two multi-route local search schemes. The algorithm can also solve the vehicle routing problem with backhaul and mixed load (VRPBM). An extensive numerical experiment is performed on benchmark problem instances available in literature. It is found that ACS gives good results compared to the existing algorithms. (C) 2009 Elsevier Ltd. All rights reserved.