The integration of Large Language Models (LLMs) with evolutionary computation (EC) has introduced a promising paradigm for automating the design of metaheuristic algorithms. However, existing frameworks, such as the Large Language Model Evolutionary Algorithm (LLaMEA), often lack precise control over mutation mechanisms, leading to inefficiencies in solution space exploration and potentially suboptimal convergence. This paper introduces a novel approach to mutation control within LLM-driven evolutionary frameworks, inspired by theory of genetic algorithms. Specifically, we propose dynamic mutation prompts that adaptively regulate mutation rates, leveraging a heavy-tailed power-law distribution to balance exploration and exploitation. Experiments using GPT-3.5-turbo and GPT-4o models demonstrate that GPT-3.5-turbo fails to adhere to the specific mutation instructions, while GPT-4o is able to adapt its mutation based on the prompt engineered dynamic prompts. Further experiments show that the introduction of these dynamic rates can improve the convergence speed and adaptability of LLaMEA, when using GPT-4o. This work sets the starting point for better controlled LLM-based mutations in code optimization tasks, paving the way for further advancements in automated metaheuristic design.

翻译：将大语言模型（LLMs）与进化计算（EC）相结合，为自动化设计元启发式算法引入了一种前景广阔的范式。然而，现有框架，如大语言模型进化算法（LLaMEA），通常缺乏对变异机制的精确控制，导致解空间探索效率低下，并可能产生次优收敛。本文受遗传算法理论启发，提出了一种在LLM驱动的进化框架内进行变异控制的新方法。具体而言，我们提出了动态变异提示，其利用重尾幂律分布自适应地调节变异率，以平衡探索与利用。使用GPT-3.5-turbo和GPT-4o模型进行的实验表明，GPT-3.5-turbo无法遵循特定的变异指令，而GPT-4o能够根据经过设计的动态提示调整其变异行为。进一步的实验表明，在使用GPT-4o时，引入这些动态变异率可以提高LLaMEA的收敛速度和适应性。这项工作为在代码优化任务中实现更好控制的、基于LLM的变异奠定了基础，为自动化元启发式设计的进一步发展铺平了道路。