LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics

Large language models (LLMs), such as GPT-4 have demonstrated their ability to understand natural language and generate complex code snippets. This article introduces a novel LLM 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 closed box metaheuristic optimization algorithms for box-constrained, continuous optimization problems automatically. LLaMEA generates multiple algorithms that outperform state-of-the-art optimization algorithms (covariance matrix adaptation evolution strategy and differential evolution) on the 5-D closed box optimization benchmark (BBOB). The algorithms also show competitive performance on the 10- and 20-D instances of the test functions, although they have not seen such instances during the automated generation process. The results demonstrate the feasibility of the framework and identify future directions for automated generation and optimization of algorithms via LLMs.