RADAR: 基于不对称距离表示的学习路由
RADAR: Learning to Route with Asymmetry-aware DistAnce Representations
AI总结：
RADAR通过引入不对称距离表示，提升神经求解器在解决不对称车辆路径问题中的性能和泛化能力。
摘要：
最近的神经求解器在车辆路径问题（VRPs）上取得了强劲的性能，但它们主要假设对称的欧几里得距离，限制了在现实世界场景中的应用。核心挑战是编码VRPs中不对称距离矩阵中的关系特征。早期尝试直接编码这些矩阵，但往往无法生成紧凑的嵌入，并且在大规模情况下泛化能力差。在本文中，我们提出RADAR，一个可扩展的神经框架，它通过增强现有的神经VRP求解器，使其能够处理不对称输入。RADAR从静态和动态两个视角处理不对称性。它利用奇异值分解（SVD）对不对称距离矩阵进行初始化，生成紧凑且可泛化的嵌入，这些嵌入本质上编码了每个节点的入站和出站成本中的静态不对称性。为进一步在嵌入交互过程中建模动态不对称性，它用Sinkhorn归一化替代标准softmax，使注意力权重具有行和列距离意识。在合成和现实世界基准上的广泛实验表明，RADAR在分布内和分布外实例上均优于强大的基线，证明了其强大的泛化能力和在解决不对称VRPs中的优越性能。
英文摘要：
Recent neural solvers have achieved strong performance on vehicle routing problems (VRPs), yet they mainly assume symmetric Euclidean distances, restricting applicability to real-world scenarios. A core challenge is encoding the relational features in asymmetric distance matrices of VRPs. Early attempts directly encoded these matrices but often failed to produce compact embeddings and generalized poorly at scale. In this paper, we propose RADAR, a scalable neural framework that augments existing neural VRP solvers with the ability to handle asymmetric inputs. RADAR addresses asymmetry from both static and dynamic perspectives. It leverages Singular Value Decomposition (SVD) on the asymmetric distance matrix to initialize compact and generalizable embeddings that inherently encode the static asymmetry in the inbound and outbound costs of each node. To further model dynamic asymmetry in embedding interactions during encoding, it replaces the standard softmax with Sinkhorn normalization that imposes joint row and column distance awareness in attention weights. Extensive experiments on synthetic and real-world benchmarks across various VRPs show that RADAR outperforms strong baselines on both in-distribution and out-of-distribution instances, demonstrating robust generalization and superior performance in solving asymmetric VRPs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
