# CoEvo: Continual Evolution of Symbolic Solutions Using Large Language Models

arXiv: https://arxiv.org/abs/2412.18890 · HTML: https://mlsanity.com/paper/2412.18890/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2024.

## Built on by (most cited first, 7 of 7)

- [DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experience](https://mlsanity.com/paper/2506.04282/) (2025)
- [EvoEngineer: Mastering Automated CUDA Kernel Code Evolution with Large Language Models](https://mlsanity.com/paper/2510.03760/) (2025)
- [LLM-Based Scientific Equation Discovery via Physics-Informed Token-Regularized Policy Optimization](https://mlsanity.com/paper/2602.10576/) (2026)
- [Code Evolution for Control: Synthesizing Policies via LLM-Driven Evolutionary Search](https://mlsanity.com/paper/2601.06845/) (2026)
- [EvoVerilog: Large Langugage Model Assisted Evolution of Verilog Code](https://mlsanity.com/paper/2508.13156/) (2025)
- [From Hand-Crafted to LLM-Based Variation Operators in Metaheuristics: A Tutorial](https://mlsanity.com/paper/2609.31649/) (2026)
- [EvoMO-SR: Multiobjective LLM-based Evolution of Symbolic Expressions with substructure guidance](https://mlsanity.com/paper/2609.36187/) (2026)

## Abstract (arXiv)

The discovery of symbolic solutions -- mathematical expressions, logical rules, and algorithmic structures -- is fundamental to advancing scientific and engineering progress. However, traditional methods often struggle with search efficiency and fail to integrate knowledge effectively. While recent large language model-based (LLM-based) approaches have demonstrated improvements in search efficiency, they lack the ability to continually refine and expand upon discovered solutions and their underlying knowledge, limiting their potential for open-ended innovation. To address these limitations, we introduce CoEvo, a novel framework that leverages large language models within an evolutionary search methodology to continually generate and refine symbolic solutions. CoEvo integrates a dynamic knowledge library, enabling open-ended innovation of solutions through effective knowledge management. Additionally, CoEvo leverages multiple representations of solutions -- including natural language, mathematical expressions, and code -- to further enhance search efficiency. By combining the reasoning capabilities of LLMs with the exploratory power of evolutionary algorithms, CoEvo significantly improves the efficiency and scope of symbolic discovery. Our experimental results demonstrate that this method not only enhances the efficiency of searching for symbolic solutions but also supports the ongoing discovery process, akin to human scientific endeavors. This study represents a first effort in conceptualizing the search for symbolic solutions as a lifelong, iterative process, marking a significant step towards harnessing LLMs in the perpetual pursuit of scientific and engineering breakthroughs. Our code is available at https://github.com/pgg3/CoEvo.