RADAR: Learning to Route with Asymmetry-aware DistAnce Representations

2026-03-03

AI Summary

This work addresses the challenge that existing neural solvers struggle to effectively model asymmetric distances in vehicle routing problems (VRP), limiting their generalization capability. To overcome this, we propose the RADAR framework, which explicitly captures static asymmetry in inbound and outbound costs by initializing node embeddings via singular value decomposition (SVD). Furthermore, RADAR replaces the standard softmax with Sinkhorn normalization in the attention mechanism, endowing it with joint row-column distance awareness to better model dynamic asymmetries. Experimental results demonstrate that RADAR consistently outperforms strong baselines across multiple synthetic and real-world VRP benchmarks, achieving superior performance both in-distribution and out-of-distribution, thereby exhibiting remarkable generalization and solution quality.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• asymmetric vehicle routing problem
• distance representation
• relational features
• non-Euclidean distances
• real-world VRP

Innovation

• asymmetric vehicle routing
• Singular Value Decomposition
• Sinkhorn normalization
• distance-aware attention
• neural combinatorial optimization