The neural combinatorial optimization (NCO) approach has shown great potential for solving routing problems without the requirement of expert knowledge. However, existing constructive NCO methods cannot directly solve large-scale instances, which significantly limits their application prospects. To address these crucial shortcomings, this work proposes a novel Instance-Conditioned Adaptation Model (ICAM) for better large-scale generalization of neural combinatorial optimization. In particular, we design a powerful yet lightweight instance-conditioned adaptation module for the NCO model to generate better solutions for instances across different scales. In addition, we develop an efficient three-stage reinforcement learning-based training scheme that enables the model to learn cross-scale features without any labeled optimal solution. Experimental results show that our proposed method is capable of obtaining excellent results with a very fast inference time in solving Traveling Salesman Problems (TSPs) and Capacitated Vehicle Routing Problems (CVRPs) across different scales. To the best of our knowledge, our model achieves state-of-the-art performance among all RL-based constructive methods for TSP and CVRP with up to 1,000 nodes.

翻译：神经组合优化方法在无需专家知识的情况下解决路径规划问题展现出巨大潜力。然而，现有构造式神经组合优化方法无法直接求解大规模实例，这严重限制了其应用前景。为解决这一关键缺陷，本文提出了一种新颖的实例条件自适应模型（ICAM），以实现神经组合优化的更好大规模泛化能力。具体而言，我们为NCO模型设计了功能强大且轻量化的实例条件自适应模块，使其能够为不同规模实例生成更优解。此外，我们开发了一种高效的三阶段强化学习训练方案，使模型能够无需任何标注最优解学习跨尺度特征。实验结果表明，所提方法在解决不同规模的旅行商问题（TSP）和容量约束车辆路径问题（CVRP）时，能以极快推理时间获得卓越解。据我们所知，在基于强化学习的构造式方法中，我们的模型在解决节点数高达1000的TSP和CVRP问题时达到了最先进性能。