In-depth analysis of granular local search for capacitated vehicle routing

Local search (LS) belongs to the core components of most state-of-the-art metaheuristics for vehicle routing problems (VRPs). Over the last decades, many variants of LS using different neighborhood operators, exploration strategies, and speedup techniques have been developed. These design choices can critically influence the performance of an LS in terms of both solution quality and computational effort. Despite the importance of LS in metaheuristics for VRPs, systematic investigations on the impact and importance of different design decisions in LS are nonexistent even for basic VRP variants, and clear recommendations on meaningful combinations of these decisions are not available. In this paper, we systematically study the impact of design decisions in a granular LS for the capacitated VRP (CVRP). To this end, we compare the performance of a large number of algorithmic variants of the granular LS on two CVRP benchmark sets. We use a Wilcoxon signed-rank test to determine non-dominated algorithmic variants, and we use performance profiles to visualize the results with regard to solution quality and runtime. In this way, we are able to identify good combinations of decisions and give final design recommendations on granular LS. Several of these recommendations disagree with popular choices in the literature and are therefore valuable for researchers and practitioners working on VRPs.