RADAR: Learning to Route with Asymmetry-aware DistAnce Representations

TL;DR

RADAR introduces a scalable neural framework that effectively encodes asymmetric distance matrices in vehicle routing problems, improving generalization and performance on real-world asymmetric scenarios.

Contribution

It proposes a novel SVD-based initialization and Sinkhorn normalization to handle asymmetry, enhancing neural VRP solvers' scalability and accuracy.

Findings

RADAR outperforms baseline models on synthetic and real-world benchmarks.

It demonstrates strong generalization to out-of-distribution instances.

The approach effectively encodes static and dynamic asymmetry in VRPs.

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 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.