Novel Ant Colony Optimization Methods for Simplifying Solution Construction in Vehicle Routing Problems

As a novel evolutionary searching technique, ant colony optimization (ACO) has gained wide research attention and can be used as a tool for optimizing an array of mathematical functions. In transportation systems, when ACO is applied to solve the vehicle routing problem (VRP), the path of each ant is only “part” of a feasible solution. In other words, multiple ants' paths may constitute one feasible solution. Previous works mainly focus on the algorithm itself, such as revising the pheromone updating scheme and combining ACO with other optimization methods. However, this body of literature ignores the important procedure of constructing feasible solutions with those “parts”. To overcome this problem, this paper presents a novel ACO algorithm (called AMR) to solve the VRP. The proposed algorithm allows ants to go in and out the depots more than once until they have visited all customers, which simplifies the procedure of constructing feasible solutions. To further enhance AMR, we propose two extensions (AMR-SA and AMR-SA-II) by integrating AMR with other saving algorithms. The computational results for standard benchmark problems are reported and compared with those from other ACO methods. Experimental results indicate that the proposed algorithms outperform the existing ACO algorithms.