# Deep Insights into Automated Optimization with Large Language Models and Evolutionary Algorithms

arXiv: https://arxiv.org/abs/2410.20848 · HTML: https://mlsanity.com/paper/2410.20848/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 96 references that are in the map.
- First posted on arXiv 28 Oct 2024.

## Builds on (most cited first, 30 of 54)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [Black-Box Tuning for Language-Model-as-a-Service](https://mlsanity.com/paper/2201.03514/) (2022)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [Explainable Artificial Intelligence: Understanding, Visualizing and Interpreting Deep Learning Models](https://mlsanity.com/paper/1708.08296/) (2017)
- [EvoPrompt: Connecting LLMs with Evolutionary Algorithms Yields Powerful Prompt Optimizers](https://mlsanity.com/paper/2309.08532/) (2023)
- [Evolution through Large Models](https://mlsanity.com/paper/2206.08896/) (2022)
- [EvoPrompting: Language Models for Code-Level Neural Architecture Search](https://mlsanity.com/paper/2302.14838/) (2023)
- [Large Language Models as Evolutionary Optimizers](https://mlsanity.com/paper/2310.19046/) (2023)
- [Language Model Crossover: Variation through Few-Shot Prompting](https://mlsanity.com/paper/2302.12170/) (2023)
- [Black-Box Prompt Optimization: Aligning Large Language Models without Model Training](https://mlsanity.com/paper/2311.04155/) (2023)
- [LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics](https://mlsanity.com/paper/2405.20132/) (2024)
- [Evolutionary Computation in the Era of Large Language Model: Survey and Roadmap](https://mlsanity.com/paper/2401.10034/) (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)
- [Evolving Code with A Large Language Model](https://mlsanity.com/paper/2401.07102/) (2024)
- [OptiMUS: Optimization Modeling Using MIP Solvers and large language models](https://mlsanity.com/paper/2310.06116/) (2023)
- [Language Models as Black-Box Optimizers for Vision-Language Models](https://mlsanity.com/paper/2309.05950/) (2023)

## Built on by (most cited first, 12 of 12)

- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [HiFo-Prompt: Prompting with Hindsight and Foresight for LLM-based Automatic Heuristic Design](https://mlsanity.com/paper/2508.13333/) (2025)
- [A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving](https://mlsanity.com/paper/2509.08269/) (2025)
- [EquivaMap: Leveraging LLMs for Automatic Equivalence Checking of Optimization Formulations](https://mlsanity.com/paper/2502.14760/) (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)
- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [Can Large Language Models Be Trusted as Evolutionary Optimizers for Network-Structured Combinatorial Problems?](https://mlsanity.com/paper/2501.15081/) (2025)
- [TIDE: Tuning-Integrated Dynamic Evolution for LLM-Based Automated Heuristic Design](https://mlsanity.com/paper/2601.21239/) (2026)
- [From Understanding to Excelling: Template-Free Algorithm Design through Structural-Functional Co-Evolution](https://mlsanity.com/paper/2503.10721/) (2025)
- [Teaching LLMs to Think Mathematically: A Critical Study of Decision-Making via Optimization](https://mlsanity.com/paper/2508.18091/) (2025)
- [Hierarchical Optimization via LLM-Guided Objective Evolution for Mobility-on-Demand Systems](https://mlsanity.com/paper/2510.10644/) (2025)
- [Structure-Aware Cooperative Ensemble Evolutionary Optimization on Combinatorial Problems with Multimodal Large Language Models](https://mlsanity.com/paper/2510.21906/) (2025)

## Abstract (arXiv)

Designing optimization approaches, whether heuristic or meta-heuristic, usually demands extensive manual intervention and has difficulty generalizing across diverse problem domains. The combination of Large Language Models (LLMs) and Evolutionary Algorithms (EAs) offers a promising new approach to overcome these limitations and make optimization more automated. In this setup, LLMs act as dynamic agents that can generate, refine, and interpret optimization strategies, while EAs efficiently explore complex solution spaces through evolutionary operators. Since this synergy enables a more efficient and creative search process, we first conduct an extensive review of recent research on the application of LLMs in optimization. We focus on LLMs' dual functionality as solution generators and algorithm designers. Then, we summarize the common and valuable designs in existing work and propose a novel LLM-EA paradigm for automated optimization. Furthermore, centered on this paradigm, we conduct an in-depth analysis of innovative methods for three key components: individual representation, variation operators, and fitness evaluation. We address challenges related to heuristic generation and solution exploration, especially from the LLM prompts' perspective. Our systematic review and thorough analysis of the paradigm can assist researchers in better understanding the current research and promoting the development of combining LLMs with EAs for automated optimization.