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arXiv 2602.08253cs.AI
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G-LNS：基于生成式大邻域搜索的LLM自动启发式设计

G-LNS: Generative Large Neighborhood Search for LLM-Based Automatic Heuristic Design

Software College, Northeastern University（东北大学软件学院）；International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences（中国科学院大学国际理论物理亚太中心）；Taiji Laboratory for Gravitational Wave Universe, University of Chinese Academy of Sciences（中国科学院大学太极引力波宇宙实验室）；Tsinghua University（清华大学）

Baoyun Zhao, He Wang, Liang Zeng

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AI总结：

G-LNS通过生成式进化框架，结合LLM共同进化破坏与修复操作符，实现了大邻域搜索操作符的自动化设计，在复杂组合优化问题中表现出更强的性能和泛化能力。

摘要：

尽管大型语言模型（LLMs）近期在自动启发式设计（AHD）中展现出潜力，但现有方法通常围绕构造优先规则或参数化局部搜索指导来构建AHD，从而将搜索空间限制在固定的启发式形式中。此类设计在结构探索方面能力有限，难以在复杂的组合优化问题（COPs）中摆脱深局部最优。在本工作中，我们提出G-LNS，一种生成式进化框架，将基于LLM的AHD扩展到大邻域搜索（LNS）操作符的自动化设计。不同于先前方法将启发式独立进化，G-LNS利用LLMs共同进化紧密耦合的破坏和修复操作符对。一种合作评估机制明确捕捉它们的相互作用，使发现互补的操作符逻辑成为可能，这些逻辑共同执行有效的结构破坏和重建。在具有挑战性的COP基准测试中，如旅行商问题（TSP）和带容量车辆路径问题（CVRP），进行了广泛的实验，证明G-LNS显著优于基于LLM的AHD方法以及强大的经典求解器。发现的启发式不仅在减少计算预算的情况下实现了近最优解，还表现出在多样且未见过的实例分布中的鲁棒泛化能力。

英文摘要：

While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing approaches typically formulate AHD around constructive priority rules or parameterized local search guidance, thereby restricting the search space to fixed heuristic forms. Such designs offer limited capacity for structural exploration, making it difficult to escape deep local optima in complex Combinatorial Optimization Problems (COPs). In this work, we propose G-LNS, a generative evolutionary framework that extends LLM-based AHD to the automated design of Large Neighborhood Search (LNS) operators. Unlike prior methods that evolve heuristics in isolation, G-LNS leverages LLMs to co-evolve tightly coupled pairs of destroy and repair operators. A cooperative evaluation mechanism explicitly captures their interaction, enabling the discovery of complementary operator logic that jointly performs effective structural disruption and reconstruction. Extensive experiments on challenging COP benchmarks, such as Traveling Salesman Problems (TSP) and Capacitated Vehicle Routing Problems (CVRP), demonstrate that G-LNS significantly outperforms LLM-based AHD methods as well as strong classical solvers. The discovered heuristics not only achieve near-optimal solutions with reduced computational budgets but also exhibit robust generalization across diverse and unseen instance distributions.

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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