The vehicle routing problem with two-dimensional loading constraints (2L-CVRP) and the last-in-first-out (LIFO) rule presents significant practical and algorithmic challenges. While numerous heuristic approaches have been proposed to address its complexity, stemming from two NP-hard problems: the vehicle routing problem (VRP) and the two-dimensional bin packing problem (2D-BPP), less attention has been paid to developing exact algorithms. Bridging this gap, this article presents an exact algorithm that integrates advanced machine learning techniques, specifically a novel combination of attention and recurrence mechanisms. This integration accelerates the state-of-the-art exact algorithm by a median of 29.79% across various problem instances. Moreover, the proposed algorithm successfully resolves an open instance in the standard test-bed, demonstrating significant improvements brought about by the incorporation of machine learning models. Code is available at https://github.com/xyfffff/NCG-for-2L-CVRP.

本研究论文通过整合注意力和循环机制的先进机器学习技术，提出了一种精确算法来解决具有二维装载约束和后进先出规则的车辆路径问题。该算法在各个问题实例中平均加速了29.79%，并成功解决了标准测试环境中的一个开放问题，表明了机器学习模型的结合带来的显著改进。

一种基于神经列生成理论的二维装箱车辆路径问题的求解方法