[2603.03388] RADAR: Learning to Route with Asymmetry-aware DistAnce Representations

Computer Science > Machine Learning arXiv:2603.03388 (cs) [Submitted on 3 Mar 2026] Title:RADAR: Learning to Route with Asymmetry-aware DistAnce Representations Authors:Hang Yi, Ziwei Huang, Yining Ma, Zhiguang Cao View a PDF of the paper titled RADAR: Learning to Route with Asymmetry-aware DistAnce Representations, by Hang Yi and 3 other authors View PDF HTML (experimental) Abstract: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 a...