Towards Efficient Constraint Handling in Neural Solvers for Routing Problems

2026-02-17

AI Summary

Existing neural solvers often struggle with path planning problems involving complex hard constraints due to inefficient or inapplicable constraint-handling mechanisms. This work proposes the Construct-and-Refine (CaR) framework, which for the first time enables shared representations and joint training between construction and refinement stages. By integrating a learned feasibility-refinement mechanism, CaR generates diverse, high-quality candidate solutions and efficiently satisfies hard constraints through an ultra-lightweight local search requiring only ten steps. The approach introduces a feasibility-mask replacement strategy and a shared encoder architecture, achieving substantial improvements over both classical and state-of-the-art neural solvers on canonical hard-constrained routing problems. Notably, CaR demonstrates significant gains in solution feasibility, quality, and computational efficiency.

Technology Category

• Constraint Satisfaction and Optimization: Solvers and Tools
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Search and Optimization: Learning to Search

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: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• constraint handling
• neural solvers
• routing problems
• hard constraints
• feasibility

Innovation

• constraint handling
• neural combinatorial optimization
• construction-refinement framework
• shared representation
• routing problems