Constructive neural combinatorial optimization (NCO) offers a promising paradigm for solving vehicle routing problems (VRPs) by directly learning to construct approximate optimal solutions, thereby reducing reliance on expert knowledge for algorithm design. However, scaling these methods to handle large-scale instances remains challenging due to high computational complexity. While recent dynamic search space reduction (SSR) methods can improve inference efficiency through geometric distance-based pruning, they often struggle on complex instances with non-uniform distributions or when optimal solutions rely heavily on non-spatial constraints. To address this critical issue, we propose Learning to Reduce (L2R), which is the first learning-based dynamic SSR framework. L2R learns to adaptively prioritize nodes by extracting patterns from problem-specific features to prune the search space at each step, enabling efficient and scalable solution construction. Extensive experiments show that our L2R framework generalizes robustly to different problem scales and data distributions on various VRP variants. To the best of our knowledge, L2R is the first neural solver to effectively scale to VRP instances with $10$ million nodes while maintaining high solution quality, which significantly pushes the frontier of NCO in terms of generalization and scalability. Our code is available at https://github.com/CIAM-Group/L2R.

翻译：构造性神经组合优化通过直接学习构造近似最优解来求解车辆路径问题，为减少算法设计中对专家知识的依赖提供了一种有前景的范式。然而，由于高计算复杂度，将这些方法扩展到大规模实例仍具挑战性。尽管最近基于几何距离剪枝的动态搜索空间缩减方法能提升推理效率，但面对非均匀分布的复杂实例或当最优解高度依赖非空间约束时，这些方法往往表现不佳。为解决这一关键问题，我们提出首个基于学习的动态搜索空间缩减框架——L2R。该框架通过提取问题特定特征中的模式学习自适应优先选择节点，逐步剪枝搜索空间，从而实现高效且可扩展的解构造。大量实验表明，L2R框架在各类VRP变体上能稳健泛化至不同问题规模和数据分布。据我们所知，L2R是首个有效扩展至包含1000万个节点的VRP实例且保持高求解质量的神经求解器，显著推动了NCO在泛化性与可扩展性方面的前沿。我们的代码已开源至https://github.com/CIAM-Group/L2R。