Too Big, so Fail? -- Enabling Neural Construction Methods to Solve Large-Scale Routing Problems (2309.17089v1)

Abstract: In recent years new deep learning approaches to solve combinatorial optimization problems, in particular NP-hard Vehicle Routing Problems (VRP), have been proposed. The most impactful of these methods are sequential neural construction approaches which are usually trained via reinforcement learning. Due to the high training costs of these models, they usually are trained on limited instance sizes (e.g. serving 100 customers) and later applied to vastly larger instance size (e.g. 2000 customers). By means of a systematic scale-up study we show that even state-of-the-art neural construction methods are outperformed by simple heuristics, failing to generalize to larger problem instances. We propose to use the ruin recreate principle that alternates between completely destroying a localized part of the solution and then recreating an improved variant. In this way, neural construction methods like POMO are never applied to the global problem but just in the reconstruction step, which only involves partial problems much closer in size to their original training instances. In thorough experiments on four datasets of varying distributions and modalities we show that our neural ruin recreate approach outperforms alternative forms of improving construction methods such as sampling and beam search and in several experiments also advanced local search approaches.