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方法在无需专家设计的情况下，解决复杂组合优化问题展现出良好性能。然而，现有方法在处理大规模问题时存在困难，限制了其实际应用性。为突破这一局限，本文提出一种新颖的自改进学习方法，以增强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改进机制，使模型能直接在大规模问题实例上进行训练，无需任何标注数据。借助创新的局部重构方法，该方法能迭代生成更优解作为伪标签，指导高效的模型训练。此外，我们设计了线性复杂度的注意力机制，使模型能以低计算开销高效处理大规模组合问题实例。在均匀分布和真实分布下、节点数高达10万的旅行商问题和容量受限车辆路径问题上的全面实验，证明了我们方法卓越的可扩展性。