A Variable Neighborhood Search for the Generalized Vehicle Routing Problem with Stochastic Demands

Abstract

In this work we consider the generalized vehicle routing problem with stochastic demands (GVRPSD) being a combination of the generalized vehicle routing problem, in which the nodes are partitioned into clusters, and the vehicle routing problem with stochastic demands, where the exact demands of the nodes are not known beforehand. It is an NP-hard problem for which we propose a variable neighborhood search (VNS) approach to minimize the expected tour length through all clusters. We use a permutation encoding for the cluster sequence and consider the preventive restocking strategy where the vehicle restocks before it potentially runs out of goods. The exact solution evaluation is based on dynamic programming and is very time-consuming. Therefore we propose a multi-level evaluation scheme to significantly reduce the time needed for solution evaluations. Two different algorithms for finding an initial solution and three well-known neighborhood structures for permutations are used within the VNS. Results show that the multi-level evaluation scheme is able to drastically reduce the overall run-time of the algorithm and that it is essential to be able to tackle larger instances. A comparison to an exact approach shows that the VNS is able to find an optimal or near-optimal solution in much shorter time.