Vehicle routing problems (VRPs) are a class of combinatorial problems with wide practical applications. While previous heuristic or learning-based works achieve decent solutions on small problem instances of up to 100 customers, their performance does not scale to large problems. This article presents a novel learning-augmented local search algorithm to solve large-scale VRP. The method iteratively improves the solution by identifying appropriate subproblems and $\textit{delegating}$ their improvement to a black box subsolver. At each step, we leverage spatial locality to consider only a linear number of subproblems, rather than exponential. We frame subproblem selection as a regression problem and train a Transformer on a generated training set of problem instances. We show that our method achieves state-of-the-art performance, with a speed-up of up to 15 times over strong baselines, on VRPs with sizes ranging from 500 to 3000.

翻译：车辆路由问题( VRPs) 是一系列具有广泛实际应用的组合问题。 虽然先前的超常或基于学习的工程在100个客户的小问题案例中取得了体面的解决方案, 但其性能并不至于大问题。 文章展示了一种新的学习强化本地搜索算法, 以解决大型VRP。 这种方法通过找出合适的子问题和$\ textit{offer} 来迭接改善解决方案, 将其改进为黑盒子溶解器。 每一步, 我们利用空间地点只考虑一个子问题的线性数量, 而不是指数化。 我们把子问题选择作为回归问题, 并训练一个变换器来训练一组生成的问题实例。 我们显示, 我们的方法在500至3000年的VRPs上取得了最先进的性能, 其速度超过强基线的15倍。