The end-to-end neural combinatorial optimization (NCO) method shows promising performance in solving complex combinatorial optimization problems without the need for expert design. However, existing methods struggle with large-scale problems, hindering their practical applicability. To overcome this limitation, this work proposes a novel Self-Improved Learning (SIL) method for better scalability of neural combinatorial optimization. Specifically, we develop an efficient self-improved mechanism that enables direct model training on large-scale problem instances without any labeled data. Powered by an innovative local reconstruction approach, this method can iteratively generate better solutions by itself as pseudo-labels to guide efficient model training. In addition, we design a linear complexity attention mechanism for the model to efficiently handle large-scale combinatorial problem instances with low computation overhead. Comprehensive experiments on the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) with up to 100K nodes in both uniform and real-world distributions demonstrate the superior scalability of our method.

翻译：端到端神经组合优化（NCO）方法在解决复杂组合优化问题时无需专家设计，展现出良好性能。然而，现有方法难以应对大规模问题，限制了其实用性。为突破这一局限，本文提出一种新颖的自提升学习（SIL）方法，旨在提升神经组合优化的可扩展性。具体而言，我们开发了一种高效的自提升机制，可直接在大规模问题实例上训练模型，且无需任何标注数据。该方法借助创新的局部重构方法，能自主迭代生成更优解作为伪标签，以指导高效的模型训练。此外，我们为模型设计了线性复杂度的注意力机制，使其能够以较低的计算开销高效处理大规模组合问题实例。在均匀分布和真实数据分布下、节点规模高达10万的旅行商问题（TSP）与容量受限车辆路径问题（CVRP）上的综合实验表明，我们的方法具有卓越的可扩展性。