arXiv:2601.19395cs.LG2026-01

提出新型Transformer,高效解决复杂现实车辆路径问题

SEAFormer: A Spatial Proximity and Edge-Aware Transformer for Real-World Vehicle Routing Problems

  • 通过聚类邻近注意力降低计算复杂度至O(n)
  • 引入轻量边感知模块,有效利用边级信息
  • 首个可高效求解1000+节点真实路径问题的神经方法

现实世界车辆路径问题(RWVRPs)需在大规模下处理复杂、序列依赖的挑战,如配送时间窗、补货或充电停靠点、非对称行程成本等。尽管近期神经方法在经典VRP基准上表现优异,但因忽略序列依赖性和低效利用边级信息,难以应对RWVRPs。本文提出SEAFormer,一种结合节点与边级信息的新型Transformer。首先,聚类邻近注意力(CPA)通过局部感知聚类将注意力复杂度从O(n²)降至O(n),同时保持全局视角,支持大规模实例高效训练。其次,轻量边感知模块通过残差融合捕获成对特征,有效整合边级信息并加速收敛。在四种不同规模的RWVRP变体上进行的大量实验表明,SEAFormer显著优于现有最先进方法。特别地,它是首个能有效求解1000+节点RWVRPs的神经方法,同时在经典VRP上也表现更优,适用于研究基准与真实场景。

原文摘要 · Abstract (English)

Real-world Vehicle Routing Problems (RWVRPs) require solving complex, sequence-dependent challenges at scale with constraints such as delivery time window, replenishment or recharging stops, asymmetric travel cost, etc. While recent neural methods achieve strong results on large-scale classical VRP benchmarks, they struggle to address RWVRPs because their strategies overlook sequence dependencies and underutilize edge-level information, which are precisely the characteristics that define the complexity of RWVRPs. We present SEAFormer, a novel transformer that incorporates both node-level and edge-level information in decision-making through two key innovations. First, our Clustered Proximity Attention (CPA) exploits locality-aware clustering to reduce the complexity of attention from $O(n^2)$ to $O(n)$ while preserving global perspective, allowing SEAFormer to efficiently train on large instances. Second, our lightweight edge-aware module captures pairwise features through residual fusion, enabling effective incorporation of edge-based information and faster convergence. Extensive experiments across four RWVRP variants with various scales demonstrate that SEAFormer achieves superior results over state-of-the-art methods. Notably, SEAFormer is the first neural method to solve 1,000+ node RWVRPs effectively, while also achieving superior performance on classic VRPs, making it a versatile solution for both research benchmarks and real-world applications.

路径规划Transformer车辆调度边缘感知

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