# From Understanding to Excelling: Template-Free Algorithm Design through Structural-Functional Co-Evolution

arXiv: https://arxiv.org/abs/2503.10721 · HTML: https://mlsanity.com/paper/2503.10721/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 38 references that are in the map.
- First posted on arXiv 13 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [AutoML-Zero: Evolving Machine Learning Algorithms From Scratch](https://mlsanity.com/paper/2003.03384/) (2020)
- [Automated Algorithm Selection: Survey and Perspectives](https://mlsanity.com/paper/1811.11597/) (2018)
- [A Systematic Survey on Large Language Models for Algorithm Design](https://mlsanity.com/paper/2410.14716/) (2024)
- [Multi-objective Evolution of Heuristic Using Large Language Model](https://mlsanity.com/paper/2409.16867/) (2024)
- [Towards Optimizing with Large Language Models](https://mlsanity.com/paper/2310.05204/) (2023)
- [In-the-loop Hyper-Parameter Optimization for LLM-Based Automated Design of Heuristics](https://mlsanity.com/paper/2410.16309/) (2024)
- [Large Language Model-Based Evolutionary Optimizer: Reasoning with elitism](https://mlsanity.com/paper/2403.02054/) (2024)
- [Automating the Practice of Science -- Opportunities, Challenges, and Implications](https://mlsanity.com/paper/2409.05890/) (2024)
- [Evolve Cost-aware Acquisition Functions Using Large Language Models](https://mlsanity.com/paper/2404.16906/) (2024)
- [Deep Insights into Automated Optimization with Large Language Models and Evolutionary Algorithms](https://mlsanity.com/paper/2410.20848/) (2024)
- [Methodology of Algorithm Engineering](https://mlsanity.com/paper/2310.18979/) (2023)
- [Incremental Quasi-Newton Methods with Faster Superlinear Convergence Rates](https://mlsanity.com/paper/2402.02359/) (2024)
- [AutoOptLib: Tailoring Metaheuristic Optimizers via Automated Algorithm Design](https://mlsanity.com/paper/2303.06536/) (2023)

## Built on by (most cited first, 2 of 2)

- [Meta Context Engineering via Agentic Skill Evolution](https://mlsanity.com/paper/2601.21557/) (2026)
- [LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regression](https://mlsanity.com/paper/2505.18602/) (2025)

## Abstract (arXiv)

Large language models (LLMs) have greatly accelerated the automation of algorithm generation and optimization. However, current methods such as EoH and FunSearch mainly rely on predefined templates and expert-specified functions that focus solely on the local evolution of key functionalities. Consequently, they fail to fully leverage the synergistic benefits of the overall architecture and the potential of global optimization. In this paper, we introduce an end-to-end algorithm generation and optimization framework based on LLMs. Our approach utilizes the deep semantic understanding of LLMs to convert natural language requirements or human-authored papers into code solutions, and employs a two-dimensional co-evolution strategy to optimize both functional and structural aspects. This closed-loop process spans problem analysis, code generation, and global optimization, automatically identifying key algorithm modules for multi-level joint optimization and continually enhancing performance and design innovation. Extensive experiments demonstrate that our method outperforms traditional local optimization approaches in both performance and innovation, while also exhibiting strong adaptability to unknown environments and breakthrough potential in structural design. By building on human research, our framework generates and optimizes novel algorithms that surpass those designed by human experts, broadening the applicability of LLMs for algorithm design and providing a novel solution pathway for automated algorithm development.