Large Language Models (LLMs) such as GPT-4 have demonstrated their ability to understand natural language and generate complex code snippets. This paper introduces a novel Large Language Model Evolutionary Algorithm (LLaMEA) framework, leveraging GPT models for the automated generation and refinement of algorithms. Given a set of criteria and a task definition (the search space), LLaMEA iteratively generates, mutates and selects algorithms based on performance metrics and feedback from runtime evaluations. This framework offers a unique approach to generating optimized algorithms without requiring extensive prior expertise. We show how this framework can be used to generate novel black-box metaheuristic optimization algorithms automatically. LLaMEA generates multiple algorithms that outperform state-of-the-art optimization algorithms (Covariance Matrix Adaptation Evolution Strategy and Differential Evolution) on the five dimensional black box optimization benchmark (BBOB). The results demonstrate the feasibility of the framework and identify future directions for automated generation and optimization of algorithms via LLMs.

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