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arXiv 2602.16012cs.AIcs.LGmath.OC
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向神经求解器在路由问题中高效处理约束的方向

Towards Efficient Constraint Handling in Neural Solvers for Routing Problems

Nanyang Technological University（南洋理工大学）；Singapore Management University（新加坡管理学院）；Shandong University（山东大学）；Eindhoven University of Technology（埃因霍温理工大学）；MIT（麻省理工学院）

Jieyi Bi, Zhiguang Cao, Jianan Zhou, Wen Song, Yaoxin Wu, Jie Zhang, Yining Ma, Cathy Wu

备注：
Accepted by ICLR 2026
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AI总结：

本文提出了一种新的神经求解器约束处理框架CaR，通过显式学习的可行性细化方法，提升了在复杂约束下的求解效率和质量。

摘要：

神经求解器在解决简单路由问题上取得了显著进展，特别是在计算效率方面表现突出。然而，它们在复杂约束下的优势仍处于初级阶段，目前的约束处理方案通过可行性遮蔽或隐式可行性意识来处理约束，但对硬约束来说可能效率低下或不适用。在本文中，我们提出了构造与细化（CaR），这是第一个基于显式学习的可行性细化的通用且高效的神经路由求解器约束处理框架。与以往的构造-搜索混合方法不同，后者通过大量改进来减少最优性差距，但仍难以处理硬约束，而CaR通过设计一个联合训练框架，引导构造模块生成多样且高质量的解决方案，适合轻量级改进过程，例如10步与5k步相比。此外，CaR首次引入了构造-改进-共享表示，通过统一编码器，使潜在的知识在更复杂的约束场景中得以共享。我们评估了CaR在典型硬约束路由问题上的表现，以展示其更广泛的应用性。结果表明，与经典和神经状态的最先进求解器相比，CaR在可行性、解决方案质量和效率方面均表现优异。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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