Neural combinatorial optimization (NCO) is a promising learning-based approach for solving challenging combinatorial optimization problems without specialized algorithm design by experts. However, most constructive NCO methods cannot solve problems with large-scale instance sizes, which significantly diminishes their usefulness for real-world applications. In this work, we propose a novel Light Encoder and Heavy Decoder (LEHD) model with a strong generalization ability to address this critical issue. The LEHD model can learn to dynamically capture the relationships between all available nodes of varying sizes, which is beneficial for model generalization to problems of various scales. Moreover, we develop a data-efficient training scheme and a flexible solution construction mechanism for the proposed LEHD model. By training on small-scale problem instances, the LEHD model can generate nearly optimal solutions for the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) with up to 1000 nodes, and also generalizes well to solve real-world TSPLib and CVRPLib problems. These results confirm our proposed LEHD model can significantly improve the state-of-the-art performance for constructive NCO. The code is available at https://github.com/CIAM-Group/NCO_code/tree/main/single_objective/LEHD.

翻译：神经组合优化（NCO）是一种无需专家专门设计算法、基于学习的解决复杂组合优化问题的有前景方法。然而，大多数构造型NCO方法无法解决大规模实例问题，这显著削弱了其在实际应用中的实用性。本研究提出一种具有强泛化能力的新型轻量编码器与重型解码器（LEHD）模型，以解决这一关键问题。LEHD模型能够学习动态捕捉不同规模所有可用节点间的关系，这有利于模型泛化至各类规模问题。此外，我们为该模型开发了数据高效训练方案与灵活解构造机制。通过在小规模实例上训练，LEHD模型可为旅行商问题（TSP）和容量受限车辆路径问题（CVRP）生成多达1000个节点的近最优解，并能良好泛化至求解实际TSPLib和CVRPLib问题。这些结果证实，我们提出的LEHD模型可显著提升构造型NCO的当前最优性能。代码已开源：https://github.com/CIAM-Group/NCO_code/tree/main/single_objective/LEHD