A hybrid algorithm for the vehicle routing problem

Ant Colony Optimization (ACO) is a metaheuristic method that inspired by the behavior of real ant colonies. In this paper, we propose a hybrid ACO algorithm for solving vehicle routing problem (VRP) heuristically in combination with an exact algorithm to improve both the performance of the algorithm and the quality of solutions. In the basic VRP, geographically scattered customers of known demand are supplied from a single depot by a fleet of identically capacitated vehicles which are subject to architecture weight limit and, in some cases, to a limit on the distance traveled. Only one vehicle is allowed to supply each customer. The objective is to design least cost routes for the vehicles to service the customers. The intuition of the proposed algorithm is that nodes which are near to each other will probably belong to the same branch of the minimum spanning tree of the problem graph and thus will probably belong to the same route in VRP. In the proposed algorithm, in each iteration, we first apply a modified implementation of Prim's algorithm to the graph of the problem to obtain a feasible minimum spanning tree (MST) solution. Given a clustering of client nodes, the solution is to find a route in these clusters by using ACO with a modified version of transition rule of the ants. At the end of each iteration, ACO tries to improve the quality of solutions by using a local search algorithm, and update the associated weights of the graph arcs.