Towards Efficient Constraint Handling in Neural Solvers for Routing Problems

ICLR 2026 Conference Submission5102 Authors

Keywords: Routing Problems; Deep Reinforcement Learning; Constraint Handling; Combinatorial Optimization

TL;DR: We advance neural VRP solvers’ constraint handling capability with Construct-and-Refine (CaR), a simple and generic framework featuring shared representation and joint training.

Abstract: Neural solvers have achieved impressive progress in addressing simple routing problems, particularly excelling in computational efficiency. However, their advantages under complex constraints remain nascent, for which current constraint-handling schemes via feasibility masking or implicit feasibility awareness can be inefficient or inapplicable for hard constraints. In this paper, we present Construct-and-Refine (CaR), the first general and efficient constraint-handling framework for neural routing solvers based on explicit learning-based feasibility refinement. Unlike prior construction-search hybrids that target reducing optimality gaps through heavy improvements yet still struggle with hard constraints, CaR achieves efficient constraint handling by designing a joint training framework that guides the construction module to generate diverse and high-quality solutions well-suited for a lightweight improvement process, e.g., 10 steps versus 5k steps in prior work. Moreover, CaR presents the first use of construction-improvement-shared representation, enabling potential knowledge sharing across paradigms by unifying the encoder, especially in more complex constrained scenarios. We evaluate CaR on typical hard routing constraints to showcase its broader applicability. Results demonstrate that CaR achieves superior feasibility, solution quality, and efficiency compared to both classical and neural state-of-the-art solvers.

Primary Area: other topics in machine learning (i.e., none of the above)

Submission Number: 5102