Selective Vehicle Routing Problem: A Hybrid Genetic Algorithm Approach

Abstract

In this paper we deal with a selective vehicle routing problem (SVRP), which was proposed in Posada et al. [20]. In the SVRP each node belongs to one or several clusters. Contrary to classical vehicle routing problems, here it is not necessary to visit all nodes, but to visit appropriate nodes in such a way that all clusters are visited exactly once. A genetic algorithm (GA) based on random key representation is proposed to solve this VRP variant. The proposed algorithm is a hybrid metaheuristic which integrates randomized constructive solutions, a variable neighborhood search procedure, an order-first cluster-second operator, and a mixed-integer linear model to repair unfeasible solutions. The metaheuristic is tested by using instances with up to 63 nodes adapted from the generalized vehicle routing problem (GVRP). The GVRP is a special case of this SVRP where each node belongs to exactly one cluster. The results allow to evaluate the impact of different clusters configuration on the instance complexity, the impact of each algorithm’s component on the metaheuristic performance, and the efficiency of the method by a comparison with a mixed-integer linear program.