A novel two-level optimization approach for clustered vehicle routing problem

In this paper, we are addressing the clustered vehicle routing problem (CluVRP) which is a variant of the classical capacitated vehicle routing problem (CVRP). The following are the main characteristics of this problem: the vertices of the graph are partitioned into a given number of clusters and we are looking for a minimum-cost collection of routes starting and ending at the depot, visiting all the vertices exactly once, except the depot, and with the additional constraint that once a vehicle enters a cluster it visits all the vertices within the cluster before leaving it. We describe a novel two-level optimization approach for CluVRP obtained by decomposing the problem into two logical and natural smaller subproblems: an upper-level (global) subproblem and a lower-level (local) subproblem, and solving them separately. The goal of the first subproblem is to determine the (global) routes visiting the clusters using a genetic algorithm, while the goal of the second subproblem is, to determine for the above mentioned routes, the visiting order within the clusters. The second subproblem is solved by transforming each global route into a traveling salesman problem (TSP) which then is optimally computed using the Concorde TSP solver. Extensive computational results are reported and discussed for an often used set of benchmark instances. The obtained results show an improvement of the quality of the achieved solutions and prove the efficiency of our approach as compared to the existing methods from the literature.