A Modified Max-Min Ant System for Vehicle Routing Problems

The vehicle routing problem (VRP) is an important problem occurring in many distribution systems, which is also defined as a family of different versions such as the capacitated vehicle routing problem (CVRP) and the vehicle routing problem with time windows (VRPTW). The ant colony optimization (ACO) is a metaheuristic for combinatorial optimization problems, and the max-min ant system (MMAS) is a variation of ACO. This paper surveys on the research on the modified MMAS algorithm for solving the CVRP and VRPTW. First, this paper introduces the CVRP and VRPTW, and the basic principles of the ACO. Then, the modified MMAS algorithm and its application to the solution of the VRP and of its variations are presented in this paper. Results of empirical simulation using the well-known benchmark CVRP and VRPTW problems have shown that the method proposed in this paper performs highly competitive in terms of solution quality.