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）是一种有前景的基于学习的方法，无需专家设计专用算法即可解决复杂的组合优化问题。然而，大多数构造型NCO方法无法解决大规模实例问题，这显著降低了其在现实应用中的实用性。本文提出了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下所有可用节点之间的关系，这有助于模型泛化至各种尺度的问题。此外，我们为所提出的LEHD模型开发了一种数据高效的训练方案和灵活的解决方案构建机制。通过在小型问题实例上训练，LEHD模型能够为旅行商问题（TSP）和容量限制车辆路径问题（CVRP）生成近优解，支持多达1000个节点，并且能很好地泛化解决现实世界的TSPLib和CVRPLib问题。这些结果证实了我们提出的LEHD模型能显著提升构造型NCO的最先进性能。代码可在https://github.com/CIAM-Group/NCO_code/tree/main/single_objective/LEHD获取。