标题： 神经组合优化算法在解决车辆路径问题中的应用：一个综合概述与展望 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）求解器的调查，但它们并未涵盖最近出现的最先进的（SOTA）NCO求解器。 更重要的是，为了建立一个全面且最新的NCO求解器分类，我们系统地回顾了相关出版物和预印本，将它们分为四种不同的类型，即学习构建、学习改进、学习预测一次和学习预测多次的求解器。 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，我们讨论了正在进行的努力，识别了开放的不足之处，并提出了有前景且可行的方向来克服这些不足。 值得注意的是，现有的努力只关注这些不足之一或两个，没有尝试同时解决所有问题。 此外，我们在不同规模的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求解器的实时仓库。 通过这项调查和实时仓库，我们的目标是促进NCO领域的进一步发展。 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, they did not cover the state-of-the-art (SOTA) NCO solvers emerged recently. More importantly, to establish a comprehensive and up-to-date taxonomy of NCO solvers, we systematically review relevant publications and preprints, categorizing them into four distinct types, 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 discuss on-going efforts, identify open inadequacies, as well as propose promising and viable directions to overcome these inadequacies. Notably, existing efforts focus on only one or two of these inadequacies, with none attempting to address all of them concurrently. In addition, we compare the performance of representative NCO solvers from the Reinforcement, Supervised, and Unsupervised Learning paradigms across VRPs of varying scales. 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 aim to foster further advancements in the NCO community.