Rethinking Constraint Awareness for Efficient State Embedding of Neural Routing Solver

2026-05-11

AI Summary

This work addresses the limitations of existing neural solvers for vehicle routing problems (VRP) with complex constraints, which are typically built upon a heavy-encoder–light-decoder architecture and suffer from restricted performance due to the locality of state embeddings in the decoding phase. To overcome this, we propose the Constraint-Aware Residual Modulation (CARM) module, which preserves a global observation space while adaptively integrating constraint information through residual modulation, thereby enhancing the model’s awareness of intricate constraints. Integrated into a multi-task neural routing framework, CARM consistently improves solution quality across two single-task and five multi-task solvers, demonstrating particularly strong generalization on large-scale instances and previously 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.

Problem

• vehicle routing problem
• constraint awareness
• state embedding
• neural solver
• global observation space

Innovation

• Constraint-Aware Residual Modulation
• state embedding
• global observation space
• neural routing solver
• vehicle routing problem