# Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model

arXiv: https://arxiv.org/abs/2401.02051 · HTML: https://mlsanity.com/paper/2401.02051/

## Key facts

- Cited by 268 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 92 references that are in the map.
- First posted on arXiv 4 Jan 2024.

## Builds on (most cited first, 30 of 45)

- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Eureka: Human-Level Reward Design via Coding Large Language Models](https://mlsanity.com/paper/2310.12931/) (2023)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [AutoML: A Survey of the State-of-the-Art](https://mlsanity.com/paper/1908.00709/) (2019)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [Large Language Models as Commonsense Knowledge for Large-Scale Task Planning](https://mlsanity.com/paper/2305.14078/) (2023)
- [Large Language Model Guided Tree-of-Thought](https://mlsanity.com/paper/2305.08291/) (2023)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [EvoPrompt: Connecting LLMs with Evolutionary Algorithms Yields Powerful Prompt Optimizers](https://mlsanity.com/paper/2309.08532/) (2023)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances](https://mlsanity.com/paper/2012.10658/) (2020)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (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)
- [DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems](https://mlsanity.com/paper/2210.04123/) (2022)

## Built on by (most cited first, 30 of 268)

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Automated Design of Agentic Systems](https://mlsanity.com/paper/2408.08435/) (2024)
- [Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agents](https://mlsanity.com/paper/2505.22954/) (2025)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [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)
- [CUDA-L1: Improving CUDA Optimization via Contrastive Reinforcement Learning](https://mlsanity.com/paper/2507.14111/) (2025)
- [RouteFinder: Towards Foundation Models for Vehicle Routing Problems](https://mlsanity.com/paper/2406.15007/) (2024)
- [Meta Context Engineering via Agentic Skill Evolution](https://mlsanity.com/paper/2601.21557/) (2026)
- [LLaMoCo: Instruction Tuning of Large Language Models for Optimization Code Generation](https://mlsanity.com/paper/2403.01131/) (2024)
- [CodeEvolve: an open source evolutionary coding agent for algorithmic discovery and optimization](https://mlsanity.com/paper/2510.14150/) (2025)
- [Discovering Preference Optimization Algorithms with and for Large Language Models](https://mlsanity.com/paper/2406.08414/) (2024)
- [ALE-Bench: A Benchmark for Long-Horizon Objective-Driven Algorithm Engineering](https://mlsanity.com/paper/2506.09050/) (2025)
- [Self-Improving Language Models for Evolutionary Program Synthesis: A Case Study on ARC-AGI](https://mlsanity.com/paper/2507.14172/) (2025)
- [Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops](https://mlsanity.com/paper/2607.07663/) (2026)
- [LLM4AD: A Platform for Algorithm Design with Large Language Model](https://mlsanity.com/paper/2412.17287/) (2024)
- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [Inference-Time Computations for LLM Reasoning and Planning: A Benchmark and Insights](https://mlsanity.com/paper/2502.12521/) (2025)
- [Learning to Handle Complex Constraints for Vehicle Routing Problems](https://mlsanity.com/paper/2410.21066/) (2024)
- [CO-Bench: Benchmarking Language Model Agents in Algorithm Search for Combinatorial Optimization](https://mlsanity.com/paper/2504.04310/) (2025)
- [Large Language Models as End-to-end Combinatorial Optimization Solvers](https://mlsanity.com/paper/2509.16865/) (2025)
- [StepORLM: A Self-Evolving Framework With Generative Process Supervision For Operations Research Language Models](https://mlsanity.com/paper/2509.22558/) (2025)
- [Toward Automated Algorithm Design: A Survey and Practical Guide to Meta-Black-Box-Optimization](https://mlsanity.com/paper/2411.00625/) (2024)
- [Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives](https://mlsanity.com/paper/2406.00415/) (2024)
- [FunBO: Discovering Acquisition Functions for Bayesian Optimization with FunSearch](https://mlsanity.com/paper/2406.04824/) (2024)
- [Self-Guiding Exploration for Combinatorial Problems](https://mlsanity.com/paper/2405.17950/) (2024)
- [HeuriGym: An Agentic Benchmark for LLM-Crafted Heuristics in Combinatorial Optimization](https://mlsanity.com/paper/2506.07972/) (2025)
- [HeurAgenix: Leveraging LLMs for Solving Complex Combinatorial Optimization Challenges](https://mlsanity.com/paper/2506.15196/) (2025)
- [The FM Agent](https://mlsanity.com/paper/2510.26144/) (2025)

## Abstract (arXiv)

Heuristics are widely used for dealing with complex search and optimization problems. However, manual design of heuristics can be often very labour extensive and requires rich working experience and knowledge. This paper proposes Evolution of Heuristic (EoH), a novel evolutionary paradigm that leverages both Large Language Models (LLMs) and Evolutionary Computation (EC) methods for Automatic Heuristic Design (AHD). EoH represents the ideas of heuristics in natural language, termed thoughts. They are then translated into executable codes by LLMs. The evolution of both thoughts and codes in an evolutionary search framework makes it very effective and efficient for generating high-performance heuristics. Experiments on three widely studied combinatorial optimization benchmark problems demonstrate that EoH outperforms commonly used handcrafted heuristics and other recent AHD methods including FunSearch. Particularly, the heuristic produced by EoH with a low computational budget (in terms of the number of queries to LLMs) significantly outperforms widely-used human hand-crafted baseline algorithms for the online bin packing problem.