标题： 神经网络组合优化算法求解车辆路径问题：具有前景的全面综述 显示英文标题

标题： Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives

摘要： 尽管已经进行了几项针对专门解决车辆路径问题（VRPs）的神经组合优化（NCO）求解器的综述。 这些现有的综述并未涵盖最近出现的最先进（SOTA）NCO 求解器。 更重要的是，为了提供一个全面且最新覆盖的 NCO 求解器分类，基于我们对相关出版物和预印本的深入回顾，我们将所有 NCO 求解器分为四个不同的类别，即学习构造、学习改进、学习预测一次和学习预测多重性求解器。 随后，我们指出了 SOTA 求解器的不足之处，包括泛化能力差、无法解决大规模 VRP、无法同时处理大多数类型的 VRP 变体以及难以将这些 NCO 求解器与传统的运筹学算法进行比较。 同时，我们提出了有希望且可行的方向来克服这些不足。 此外，我们在小规模和大规模 VRP 上比较了来自强化学习、监督学习和无监督学习范式的代表性 NCO 求解器的性能。 最后，根据提出的分类，我们提供了一个配套的网页作为 NCO 求解器的实时存储库。 通过这次综述和实时存储库，我们希望使 VRP 的 NCO 求解器研究社区更加繁荣。 显示英文摘要

摘要： Although several surveys on Neural Combinatorial Optimization (NCO) solvers specifically designed to solve Vehicle Routing Problems (VRPs) have been conducted. These existing surveys did not cover the state-of-the-art (SOTA) NCO solvers emerged recently. More importantly, to provide a comprehensive taxonomy of NCO solvers with up-to-date coverage, based on our thorough review of relevant publications and preprints, we divide all NCO solvers into four distinct categories, namely Learning to Construct, Learning to Improve, Learning to Predict-Once, and Learning to Predict-Multiplicity solvers. Subsequently, we present the inadequacies of the SOTA solvers, including poor generalization, incapability to solve large-scale VRPs, inability to address most types of VRP variants simultaneously, and difficulty in comparing these NCO solvers with the conventional Operations Research algorithms. Simultaneously, we propose promising and viable directions to overcome these inadequacies. In addition, we compare the performance of representative NCO solvers from the Reinforcement, Supervised, and Unsupervised Learning paradigms across both small- and large-scale VRPs. Finally, following the proposed taxonomy, we provide an accompanying web page as a live repository for NCO solvers. Through this survey and the live repository, we hope to make the research community of NCO solvers for VRPs more thriving.