GPGLS: Genetic Programming Guided Local Search for Large-Scale Vehicle Routing Problems

Saining Liu, João Guilherme Cavalcanti Costa, Yi Mei, Mengjie Zhang

Abstract: The Vehicle Routing Problem (VRP) is a classical combinatorial optimization problem. In this paper, we focus on Large-Scale VRP (LSVRP), which contains more than 200 customers. In particular, the Knowledge Guided Local Search (KGLS) has shown highly competitive performance for LSVRP, due to the strength of GLS for jumping out of local optima and improved utility functions of GLS. The newly discovered good or effective utility function used by KGLS suggests that the default utility function used in the traditional GLS is by no means the optimal. However, manually designing better utility function for GLS is very time-consuming and can involve much trial-and-error. To address this issue, we proposed to use Genetic Programming (GP) to automatically design utility functions for GLS. We developed a GP training framework in which an individual stands for a possible utility function for GLS. To evaluate a GP individual, GLS runs on the training instances, where the GP individual is used as the utility function to identify the edges to penalize. We also designed a set of terminals to capture a wide range of possible factors for the utility function. The results on the commonly used X dataset demonstrates that GP successfully evolved significantly better GLS algorithms than the competitive KGLS on a majority of the large-scale X instances. The further analysis also shows the effectiveness of the newly learned GLS utility functions that take into account new factors which are not been considered by GLS and KGLS.