Automatic Heuristic Design (AHD) is an active research area due to its utility in solving complex search and NP-hard combinatorial optimization problems in the real world. The recent advancements in Large Language Models (LLMs) introduce new possibilities by coupling LLMs with evolutionary computation to automatically generate heuristics, known as LLM-based Evolutionary Program Search (LLM-EPS). While previous LLM-EPS studies obtained great performance on various tasks, there is still a gap in understanding the properties of heuristic search spaces and achieving a balance between exploration and exploitation, which is a critical factor in large heuristic search spaces. In this study, we address this gap by proposing two diversity measurement metrics and perform an analysis on previous LLM-EPS approaches, including FunSearch, EoH, and ReEvo. Results on black-box AHD problems reveal that while EoH demonstrates higher diversity than FunSearch and ReEvo, its objective score is unstable. Conversely, ReEvo's reflection mechanism yields good objective scores but fails to optimize diversity effectively. With this finding in mind, we introduce HSEvo, an adaptive LLM-EPS framework that maintains a balance between diversity and convergence with a harmony search algorithm. Through experimentation, we find that HSEvo achieved high diversity indices and good objective scores while remaining cost-effective. These results underscore the importance of balancing exploration and exploitation and understanding heuristic search spaces in designing frameworks in LLM-EPS.

翻译：自动启发式设计（AHD）因其在解决现实世界中复杂搜索和NP难组合优化问题中的实用性，已成为一个活跃的研究领域。大型语言模型（LLM）的最新进展通过与进化计算结合来自动生成启发式方法（称为基于LLM的进化程序搜索，LLM-EPS），为此领域引入了新的可能性。尽管以往的LLM-EPS研究在各种任务中取得了优异性能，但在理解启发式搜索空间特性以及实现探索与利用之间的平衡方面仍存在不足，而这在大规模启发式搜索空间中是一个关键因素。本研究通过提出两种多样性度量指标，并对包括FunSearch、EoH和ReEvo在内的现有LLM-EPS方法进行分析，以弥补这一不足。在黑盒AHD问题上的实验结果表明，虽然EoH展现出比FunSearch和ReEvo更高的多样性，但其目标得分不稳定。相反，ReEvo的反思机制能获得良好的目标得分，却未能有效优化多样性。基于这一发现，我们提出了HSEvo——一种自适应LLM-EPS框架，该框架通过和声搜索算法在多样性与收敛性之间保持平衡。实验表明，HSEvo在保持成本效益的同时，实现了较高的多样性指数和良好的目标得分。这些结果强调了在LLM-EPS框架设计中平衡探索与利用、以及理解启发式搜索空间的重要性。