Publication Type

Conference Proceeding Article

Version

publishedVersion

Publication Date

4-2026

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.

Keywords

Neural Combinatorial Optimization, Vehicle Routing Problem

Discipline

Artificial Intelligence and Robotics | Operations Research, Systems Engineering and Industrial Engineering

Research Areas

Intelligent Systems and Optimization

Areas of Excellence

Sustainability

Publication

Proceedings of the Fourteenth International Conference on Learning Representations (ICLR 2026), Rio de Janeiro, Brazil, April 23-27

First Page

1

Last Page

24

Publisher

ICLR

City or Country

Rio de Janeiro, Brazil

Additional URL

https://openreview.net/forum?id=lWdxX5s9T1

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