Rethinking Constraint Awareness for Efficient State Embedding of Neural Routing Solver

TL;DR

This paper introduces the CARM module to enhance constraint awareness in neural routing solvers, significantly improving their scalability and generalization across complex vehicle routing problem variants.

Contribution

It proposes a novel Constraint-Aware Residual Modulation (CARM) module that adaptively incorporates constraint information into state embeddings, addressing a key bottleneck in existing neural solvers.

Findings

CARM boosts baseline solver performance across multiple VRP variants.

Solvers with CARM scale better to large instances.

CARM improves generalization to unseen VRP variants.

Abstract

Heavy-Encoder-Light-Decoder (HELD) neural routing solvers have emerged as a promising paradigm due to their broad applicability across multiple vehicle routing problems (VRPs). However, they typically struggle with VRP variants with complex constraints. To address this limitation, this paper systematically revisits existing neural solvers from the perspective of the generation mechanism for state embeddings (i.e., query vector prior to compatibility calculation) during decoding. We identify that current mechanisms restrict the observation space during attention computation, introducing a key bottleneck to achieving high-quality solutions. Through detailed empirical analysis, we demonstrate the necessity of preserving a global observation space. To overcome the constraint-agnostic drawback inherent to global observation spaces, we propose a simple yet powerful Constraint-Aware Residual Modulation (CARM) module. By adaptively modulating the context embedding with constraint-relevant variables, CARM effectively enhances constraint awareness, enabling the neural solver to fully leverage the global observation space and generate an efficient state embedding. Extensive experimental results across two single-task and five multi-task neural routing solvers confirm that the CARM module consistently boosts baseline performance. Notably, solvers equipped with our CARM achieve substantial improvements in scaling to large-scale instances and in generalizing to unseen VRP variants. These findings provide valuable insights for the architectural design of neural routing solvers.