The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in real-world VRP applications, Machine Learning (ML) methods have been used in combination with analytical approaches to enhance problem formulations and algorithmic performance across different problem solving scenarios. However, the relevant papers are scattered in several traditional research fields with very different, sometimes confusing, terminologies. This paper presents a first, comprehensive review of hybrid methods that combine analytical techniques with ML tools in addressing VRP problems. Specifically, we review the emerging research streams on ML-assisted VRP modelling and ML-assisted VRP optimisation. We conclude that ML can be beneficial in enhancing VRP modelling, and improving the performance of algorithms for both online and offline VRP optimisations. Finally, challenges and future opportunities of VRP research are discussed.

翻译：车辆运行问题(VRP)是经过最深入研究的组合优化问题之一,为此提出了许多模型和算法,为解决现实世界VRP应用中的复杂性、不确定性和动态问题,采用了机器学习(ML)方法,结合分析方法,在不同问题的解决设想中加强问题拟订和算法性能;然而,相关文件分散在几个传统研究领域,其术语非常不同,有时是混乱的。本文件首次对混合方法进行了全面审查,这些混合方法将分析技术和ML工具结合起来,以解决VRP问题。具体地说,我们审查了ML辅助VRP建模和ML辅助VRP优化的新兴研究流。我们的结论是,ML可以有利于加强VRP建模,改善在线和离线VRP优化的算法性。最后,讨论了VRP研究的挑战和未来机会。