用大模型自动设计一组互补启发式算法，提升对多样化问题的适应能力。
EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design
- 基于大模型生成互补启发式集合，优化不同问题实例的适配性。
- 在三个任务上性能最高提升60%，显著优于现有方法。
- 适合需要多场景泛化能力的自动化求解系统开发者。
近年来，利用大语言模型（LLMs）进行自动化启发式设计（AHD）取得了显著进展。然而，现有方法仅设计单一启发式，难以在不同问题分布或设置间实现良好泛化。为此，本文提出自动化启发式集合设计（AHSD），旨在自动生成一个小型且互补的启发式集合，以覆盖多样化的实例，使每个实例至少可由集合中某一启发式优化。我们证明了AHSD的目标函数具有单调性和超模性。进而提出进化启发式集合（EoH-S）来实现该框架，引入互补种群管理和互补感知的遗传搜索两种新机制，有效生成高质量且互补的启发式集合。在涵盖多种规模与分布的三个AHD任务上的全面实验表明，EoH-S持续优于现有最先进的AHD方法，性能最高提升达60%。
原文摘要 · Abstract (English)
Automated Heuristic Design (AHD) using Large Language Models (LLMs) has achieved notable success in recent years. Despite the effectiveness of existing approaches, they only design a single heuristic to serve all problem instances, often inducing poor generalization across different distributions or settings. To address this issue, we propose Automated Heuristic Set Design (AHSD), a new formulation for LLM-driven AHD. The aim of AHSD is to automatically generate a small-sized complementary heuristic set to serve diverse problem instances, such that each problem instance could be optimized by at least one heuristic in this set. We show that the objective function of AHSD is monotone and supermodular. Then, we propose Evolution of Heuristic Set (EoH-S) to apply the AHSD formulation for LLM-driven AHD. With two novel mechanisms of complementary population management and complementary-aware memetic search, EoH-S could effectively generate a set of high-quality and complementary heuristics. Comprehensive experimental results on three AHD tasks with diverse instances spanning various sizes and distributions demonstrate that EoH-S consistently outperforms existing state-of-the-art AHD methods and achieves up to 60\% performance improvements.
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