Recently, neural networks (NN) have made great strides in combinatorial optimization. However, they face challenges when solving the capacitated arc routing problem (CARP) which is to find the minimum-cost tour covering all required edges on a graph, while within capacity constraints. In tackling CARP, NN-based approaches tend to lag behind advanced metaheuristics, since they lack directed arc modeling and efficient learning methods tailored for complex CARP. In this paper, we introduce an NN-based solver to significantly narrow the gap with advanced metaheuristics while exhibiting superior efficiency. First, we propose the direction-aware attention model (DaAM) to incorporate directionality into the embedding process, facilitating more effective one-stage decision-making. Second, we design a supervised reinforcement learning scheme that involves supervised pre-training to establish a robust initial policy for subsequent reinforcement fine-tuning. It proves particularly valuable for solving CARP that has a higher complexity than the node routing problems (NRPs). Finally, a path optimization method is proposed to adjust the depot return positions within the path generated by DaAM. Experiments illustrate that our approach surpasses heuristics and achieves decision quality comparable to state-of-the-art metaheuristics for the first time while maintaining superior efficiency.

本文介绍了一种基于神经网络的求解程序，它能够显著缩小与先进元启发式方法之间的差距，并展现出卓越的效率。该求解程序利用方向感知的注意力模型（DaAM）和监督强化学习方案，同时提出了路径优化方法，成功解决了容量限制的弧路由问题，在保持出色效率的同时获得了与最先进的元启发式方法相媲美的决策质量。

一种高效的基于学习的求解器，可与元启发式算法相媲美，用于容量约束弧路线问题