arXiv:2503.03137cs.AIcs.LG2025-03KDD被引 16

提出首个学习型动态搜索空间缩减框架,让神经路由求解器可高效处理千万级节点的复杂路径问题。

Learning to Reduce Search Space for Generalizable Neural Routing Solver

  • 基于问题特征自适应筛选节点,动态缩小搜索空间
  • 在1000万节点的VRP实例上保持高质量解,显著提升可扩展性
  • 适用于非均匀分布和强非空间约束的复杂场景,适合大规模物流优化

构造式神经组合优化(NCO)通过直接学习构建近似最优解,减少了对专家知识的依赖。然而,面对大规模实例时,高计算复杂度仍是挑战。现有动态搜索空间缩减(SSR)方法依赖几何距离剪枝,但在非均匀分布或强非空间约束的复杂实例上表现不佳。为此,我们提出学习型搜索空间缩减(L2R),首个基于学习的动态SSR框架。L2R从问题特征求取模式,自适应优先处理节点,在每一步实现搜索空间剪枝,从而实现高效且可扩展的解构造。大量实验表明,该框架在多种VRP变体上对不同规模和数据分布均具有鲁棒泛化能力。据我们所知,L2R是首个能有效扩展至含1000万节点的VRP实例并保持高质量解的神经求解器,显著推进了NCO在泛化与可扩展性上的边界。代码已公开于https://github.com/CIAM-Group/L2R。

原文摘要 · Abstract (English)

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.

神经优化路径规划可扩展性搜索剪枝

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