This paper explores the potential of large language models (LLMs) to implement evolutionary optimization algorithms, specifically Evolution Strategies (ES). The authors introduce a novel prompting strategy that transforms LLMs into recombination operators, allowing them to perform black-box optimization (BBO) tasks. The method involves discretizing the search space, sorting solutions by performance, and querying the LLM to propose improvements. Empirical results show that the proposed EvoLLM approach outperforms traditional baselines on synthetic BBOB functions and small neuroevolution tasks. The paper also investigates the impact of prompt design, discretization resolution, and context length, finding that smaller LLM models generally perform better. Additionally, the authors demonstrate that fine-tuning the LLM using teacher algorithm trajectories can further enhance its performance. The study highlights the versatility and potential of LLMs in optimization tasks, suggesting that they can act as 'plug-in' recombination operators in evolutionary algorithms.This paper explores the potential of large language models (LLMs) to implement evolutionary optimization algorithms, specifically Evolution Strategies (ES). The authors introduce a novel prompting strategy that transforms LLMs into recombination operators, allowing them to perform black-box optimization (BBO) tasks. The method involves discretizing the search space, sorting solutions by performance, and querying the LLM to propose improvements. Empirical results show that the proposed EvoLLM approach outperforms traditional baselines on synthetic BBOB functions and small neuroevolution tasks. The paper also investigates the impact of prompt design, discretization resolution, and context length, finding that smaller LLM models generally perform better. Additionally, the authors demonstrate that fine-tuning the LLM using teacher algorithm trajectories can further enhance its performance. The study highlights the versatility and potential of LLMs in optimization tasks, suggesting that they can act as 'plug-in' recombination operators in evolutionary algorithms.