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

arXiv: https://arxiv.org/abs/2405.20132 · HTML: https://mlsanity.com/paper/2405.20132/

## Key facts

- Cited by 97 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 63 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 25 of 25)

- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [EvoPrompt: Connecting LLMs with Evolutionary Algorithms Yields Powerful Prompt Optimizers](https://mlsanity.com/paper/2309.08532/) (2023)
- [Instruction Induction: From Few Examples to Natural Language Task Descriptions](https://mlsanity.com/paper/2205.10782/) (2022)
- [Self-Taught Optimizer (STOP): Recursively Self-Improving Code Generation](https://mlsanity.com/paper/2310.02304/) (2023)
- [Is Temperature the Creativity Parameter of Large Language Models?](https://mlsanity.com/paper/2405.00492/) (2024)
- [In-context Learning with Retrieved Demonstrations for Language Models: A Survey](https://mlsanity.com/paper/2401.11624/) (2024)
- [Large Language Models As Evolution Strategies](https://mlsanity.com/paper/2402.18381/) (2024)
- [Algorithm Evolution Using Large Language Model](https://mlsanity.com/paper/2311.15249/) (2023)
- [IOHprofiler: A Benchmarking and Profiling Tool for Iterative Optimization Heuristics](https://mlsanity.com/paper/1810.05281/) (2018)
- [IOHexperimenter: Benchmarking Platform for Iterative Optimization Heuristics](https://mlsanity.com/paper/2111.04077/) (2021)
- [IOHanalyzer: Detailed Performance Analyses for Iterative Optimization Heuristics](https://mlsanity.com/paper/2007.03953/) (2020)
- [Tuning as a Means of Assessing the Benefits of New Ideas in Interplay with Existing Algorithmic Modules](https://mlsanity.com/paper/2102.12905/) (2021)
- [Benchmarking Discrete Optimization Heuristics with IOHprofiler](https://mlsanity.com/paper/1912.09237/) (2019)
- [Evolving the Structure of Evolution Strategies](https://mlsanity.com/paper/1610.05231/) (2016)
- [Modular Differential Evolution](https://mlsanity.com/paper/2304.09524/) (2023)
- [Explainable Benchmarking for Iterative Optimization Heuristics](https://mlsanity.com/paper/2401.17842/) (2024)
- [Large-scale Benchmarking of Metaphor-based Optimization Heuristics](https://mlsanity.com/paper/2402.09800/) (2024)
- [Large Language and Text-to-3D Models for Engineering Design Optimization](https://mlsanity.com/paper/2307.01230/) (2023)
- [Using the Empirical Attainment Function for Analyzing Single-objective Black-box Optimization Algorithms](https://mlsanity.com/paper/2404.02031/) (2024)
- [Performance assessment and exhaustive listing of 500+ nature inspired metaheuristic algorithms](https://mlsanity.com/paper/2212.09479/) (2022)
- [Analysis of modular CMA-ES on strict box-constrained problems in the SBOX-COST benchmarking suite](https://mlsanity.com/paper/2305.15102/) (2023)
- [Benchmarking Algorithms for Submodular Optimization Problems Using IOHProfiler](https://mlsanity.com/paper/2302.01464/) (2023)

## Built on by (most cited first, 30 of 97)

- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [Agentic Large Language Models, a survey](https://mlsanity.com/paper/2503.23037/) (2025)
- [A Systematic Survey on Large Language Models for Algorithm Design](https://mlsanity.com/paper/2410.14716/) (2024)
- [CodeEvolve: an open source evolutionary coding agent for algorithmic discovery and optimization](https://mlsanity.com/paper/2510.14150/) (2025)
- [EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design](https://mlsanity.com/paper/2508.03082/) (2025)
- [Toward Automated Algorithm Design: A Survey and Practical Guide to Meta-Black-Box-Optimization](https://mlsanity.com/paper/2411.00625/) (2024)
- [HiFo-Prompt: Prompting with Hindsight and Foresight for LLM-based Automatic Heuristic Design](https://mlsanity.com/paper/2508.13333/) (2025)
- [Nature-Inspired Population-Based Evolution of Large Language Models](https://mlsanity.com/paper/2503.01155/) (2025)
- [Deep Insights into Automated Optimization with Large Language Models and Evolutionary Algorithms](https://mlsanity.com/paper/2410.20848/) (2024)
- [A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving](https://mlsanity.com/paper/2509.08269/) (2025)
- [LLaMEA-BO: A Large Language Model Evolutionary Algorithm for Automatically Generating Bayesian Optimization Algorithms](https://mlsanity.com/paper/2505.21034/) (2025)
- [Fitness Landscape of Large Language Model-Assisted Automated Algorithm Search](https://mlsanity.com/paper/2504.19636/) (2025)
- [BLADE: Benchmark suite for LLM-driven Automated Design and Evolution of iterative optimisation heuristics](https://mlsanity.com/paper/2504.20183/) (2025)
- [MetaBox-v2: A Unified Benchmark Platform for Meta-Black-Box Optimization](https://mlsanity.com/paper/2505.17745/) (2025)
- [Combinatorial Optimization for All: Using LLMs to Aid Non-Experts in Improving Optimization Algorithms](https://mlsanity.com/paper/2503.10968/) (2025)
- [Large Language Models and Evolutionary Computation: A Critical Review of Bidirectional Interaction, Automated Algorithm Design, and Co-Adaptive Systems](https://mlsanity.com/paper/2505.15741/) (2025)
- [LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regression](https://mlsanity.com/paper/2505.18602/) (2025)
- [Fine-tuning Large Language Model for Automated Algorithm Design](https://mlsanity.com/paper/2507.10614/) (2025)
- [Instance Generation for Meta-Black-Box Optimization through Latent Space Reverse Engineering](https://mlsanity.com/paper/2509.15810/) (2025)
- [EvoCAD: Evolutionary CAD Code Generation with Vision Language Models](https://mlsanity.com/paper/2510.11631/) (2025)
- [MadEvolve: Evolutionary Optimization of Cosmological Algorithms with Large Language Models](https://mlsanity.com/paper/2602.15951/) (2026)
- [From Code to Play: Benchmarking Program Search for Games Using Large Language Models](https://mlsanity.com/paper/2412.04057/) (2024)
- [BBOPlace-Bench: Benchmarking Black-Box Optimization for Chip Placement](https://mlsanity.com/paper/2510.23472/) (2025)
- [Improving Existing Optimization Algorithms with LLMs](https://mlsanity.com/paper/2502.08298/) (2025)
- [Reasoning Capabilities of Large Language Models on Dynamic Tasks](https://mlsanity.com/paper/2505.10543/) (2025)
- [Behaviour Space Analysis of LLM-driven Meta-heuristic Discovery](https://mlsanity.com/paper/2507.03605/) (2025)
- [Pareto-Grid-Guided Large Language Models for Fast and High-Quality Heuristics Design in Multi-Objective Combinatorial Optimization](https://mlsanity.com/paper/2507.20923/) (2025)
- [Evolving Excellence: Automated Optimization of LLM-based Agents](https://mlsanity.com/paper/2512.09108/) (2025)
- [GEAR: Genetic AutoResearch for Agentic Code Evolution](https://mlsanity.com/paper/2605.13874/) (2026)
- [Mutation Without Variation: Convergence Dynamics in LLM-Driven Program Evolution](https://mlsanity.com/paper/2606.05408/) (2026)

## Abstract (arXiv)

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 algorithms also show competitive performance on the 10- and 20-dimensional 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.