Neural Networks for Local Search and Crossover in Vehicle Routing: A Possible Overkill?

Extensive research has been conducted, over recent years, on various ways of enhancing heuristic search for combinatorial optimization problems with machine learning algorithms. In this study, we investigate the use predictions from graph neural networks (GNNs) in form heatmaps to improve Hybrid Genetic Search (HGS), a state-of-the-art algorithm Capacitated Vehicle Routing Problem (CVRP). The crossover and local-search components HGS are instrumental finding improved solutions, yet these essentially rely simple greedy or random choices. It seems intuitive attempt incorporate additional knowledge at levels. Throughout vast experimental campaign more than 10,000 problem instances, show that exploiting sophisticated strategies using measures node relatedness (heatmaps, simply distance) within algorithmic can significantly enhance performance. However, contrary initial expectations, also observed did not present significant advantages simpler distance purposes. Therefore, faced common —though rarely documented— situation overkill: GNNs indeed performance an important task, but ablation analysis demonstrated alternatives perform equally well.