A algorithm for the Vehicle Problem

In this paper, we propose a hybrid ACO algorithm for solving vehicle routing problem (VRP) heuristically in combination with an exact In the basic VRP, geographically scattered customers of known demand are supplied from a single depot by a fleet of identically capacitated vehicles. 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. 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 searchalgorithm, and update the associated weights of the graph arcs