A hybrid genetic search based approach for the generalized vehicle routing problem

This paper introduces a novel meta-heuristic for addressing a variant of the classical Capacitated Vehicle Routing Problem (CVRP) known as the Generalized Vehicle Routing Problem (GVRP). In the GVRP, nodes are organized into clusters, with the constraint that only one node from each cluster must be visited. The proposed meta-heuristic is a Hybrid Genetic Search (HGS) that leverages recent advancements in CVRP methodologies, adapting successful strategies and techniques from CVRP to the GVRP context. To evaluate the performance of the HGS meta-heuristic, we perform an extensive computational analysis on numerous benchmark instances ranging from small to large sizes. To thoroughly analyze the algorithm’s average behavior, convergence profiles over time are reported for the considered instances. Results show that the proposed algorithm achieves 174 new best solutions out of the 498 instances considered. In only six instances out of 498, the algorithm is unable to reach or improve upon the best-known solution in the literature. These results suggest that the proposed meta-heuristic has significant potential in addressing real-world generalized vehicle routing challenges. Code available at: https://github.com/vlatorre847/HGSGVRP.