RADAR: Learning to Route with Asymmetry-aware DistAnce Representations
arXiv:2603.03388v1 Announce Type: new 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 t
arXiv:2603.03388v1 Announce Type: new 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.
Executive Summary
The RADAR framework addresses the challenge of asymmetric distance matrices in vehicle routing problems by leveraging Singular Value Decomposition and Sinkhorn normalization to encode static and dynamic asymmetry. This approach enables existing neural solvers to handle asymmetric inputs, demonstrating robust generalization and superior performance on both in-distribution and out-of-distribution instances. RADAR's ability to model asymmetry from both static and dynamic perspectives makes it a significant contribution to the field of vehicle routing problems.
Key Points
- ▸ RADAR proposes a scalable neural framework to handle asymmetric inputs in vehicle routing problems
- ▸ It leverages Singular Value Decomposition to initialize compact and generalizable embeddings
- ▸ Sinkhorn normalization is used to model dynamic asymmetry in embedding interactions
Merits
Improved Generalization
RADAR's ability to handle asymmetric inputs enables it to generalize well to out-of-distribution instances, making it a robust solution for real-world scenarios
Demerits
Computational Complexity
The use of Singular Value Decomposition and Sinkhorn normalization may increase the computational complexity of the framework, potentially limiting its scalability
Expert Commentary
The RADAR framework represents a significant advancement in the field of vehicle routing problems, particularly in its ability to handle asymmetric inputs. By leveraging Singular Value Decomposition and Sinkhorn normalization, RADAR is able to model both static and dynamic asymmetry, enabling it to generalize well to out-of-distribution instances. However, further research is needed to fully explore the potential of RADAR and its applications in real-world scenarios. The framework's ability to handle asymmetric inputs makes it a valuable tool for logistics and transportation systems, where asymmetric distance matrices are common.
Recommendations
- ✓ Further research is needed to explore the potential of RADAR in real-world scenarios
- ✓ The development of more efficient algorithms for computing Singular Value Decomposition and Sinkhorn normalization could improve the scalability of the framework