# A Systematic Survey on Large Language Models for Algorithm Design

arXiv: https://arxiv.org/abs/2410.14716 · HTML: https://mlsanity.com/paper/2410.14716/

## Key facts

- Cited by 69 papers in the map (data through 14 Oct 2026).
- Builds on 84 of its 169 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Builds on (most cited first, 30 of 84)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [Automatic Prompt Optimization with "Gradient Descent" and Beam Search](https://mlsanity.com/paper/2305.03495/) (2023)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [PlanBench: An Extensible Benchmark for Evaluating Large Language Models on Planning and Reasoning about Change](https://mlsanity.com/paper/2206.10498/) (2022)
- [Can LLMs Generate Novel Research Ideas? A Large-Scale Human Study with 100+ NLP Researchers](https://mlsanity.com/paper/2409.04109/) (2024)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Physics of Language Models: Part 3.1, Knowledge Storage and Extraction](https://mlsanity.com/paper/2309.14316/) (2023)
- [PromptAgent: Strategic Planning with Language Models Enables Expert-level Prompt Optimization](https://mlsanity.com/paper/2310.16427/) (2023)
- [Instruction Induction: From Few Examples to Natural Language Task Descriptions](https://mlsanity.com/paper/2205.10782/) (2022)
- [LIFT: Language-Interfaced Fine-Tuning for Non-Language Machine Learning Tasks](https://mlsanity.com/paper/2206.06565/) (2022)
- [Direct Preference Optimization of Video Large Multimodal Models from Language Model Reward](https://mlsanity.com/paper/2404.01258/) (2024)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [Large Language Models to Enhance Bayesian Optimization](https://mlsanity.com/paper/2402.03921/) (2024)
- [Large Language Models as Evolutionary Optimizers](https://mlsanity.com/paper/2310.19046/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [HPOBench: A Collection of Reproducible Multi-Fidelity Benchmark Problems for HPO](https://mlsanity.com/paper/2109.06716/) (2021)
- [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)
- [Navigation with Large Language Models: Semantic Guesswork as a Heuristic for Planning](https://mlsanity.com/paper/2310.10103/) (2023)
- [LLMatic: Neural Architecture Search via Large Language Models and Quality Diversity Optimization](https://mlsanity.com/paper/2306.01102/) (2023)
- [LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery](https://mlsanity.com/paper/2405.09783/) (2024)
- [Self-Organized Agents: A LLM Multi-Agent Framework toward Ultra Large-Scale Code Generation and Optimization](https://mlsanity.com/paper/2404.02183/) (2024)
- [Bayesian optimization for materials design](https://mlsanity.com/paper/1506.01349/) (2015)

## Built on by (most cited first, 30 of 69)

- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design](https://mlsanity.com/paper/2508.03082/) (2025)
- [LLM4AD: A Platform for Algorithm Design with Large Language Model](https://mlsanity.com/paper/2412.17287/) (2024)
- [HiFo-Prompt: Prompting with Hindsight and Foresight for LLM-based Automatic Heuristic Design](https://mlsanity.com/paper/2508.13333/) (2025)
- [The Evolution of Tool Use in LLM Agents: From Single-Tool Call to Multi-Tool Orchestration](https://mlsanity.com/paper/2603.22862/) (2026)
- [ARS: Automatic Routing Solver with Large Language Models](https://mlsanity.com/paper/2502.15359/) (2025)
- [CipherBank: Exploring the Boundary of LLM Reasoning Capabilities through Cryptography Challenges](https://mlsanity.com/paper/2504.19093/) (2025)
- [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)
- [Generalizable Heuristic Generation Through LLMs with Meta-Optimization](https://mlsanity.com/paper/2505.20881/) (2025)
- [EvoCut: Strengthening Integer Programs via Evolution-Guided Language Models](https://mlsanity.com/paper/2508.11850/) (2025)
- [Towards Universal Offline Black-Box Optimization via Learning Language Model Embeddings](https://mlsanity.com/paper/2506.07109/) (2025)
- [G-LNS: Generative Large Neighborhood Search for LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2602.08253/) (2026)
- [Leveraging Large Language Models to Develop Heuristics for Emerging Optimization Problems](https://mlsanity.com/paper/2503.03350/) (2025)
- [Evolution of Optimization Algorithms for Global Placement via Large Language Models](https://mlsanity.com/paper/2504.17801/) (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)
- [Fine-tuning Large Language Model for Automated Algorithm Design](https://mlsanity.com/paper/2507.10614/) (2025)
- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [TrajEvo: Designing Trajectory Prediction Heuristics via LLM-driven Evolution](https://mlsanity.com/paper/2505.04480/) (2025)
- [BBOPlace-Bench: Benchmarking Black-Box Optimization for Chip Placement](https://mlsanity.com/paper/2510.23472/) (2025)
- [RedAHD: Reduction-Based End-to-End Automatic Heuristic Design with Large Language Models](https://mlsanity.com/paper/2505.20242/) (2025)
- [Behaviour Space Analysis of LLM-driven Meta-heuristic Discovery](https://mlsanity.com/paper/2507.03605/) (2025)
- [Discovering heuristics in a complex SAT solver with large language models](https://mlsanity.com/paper/2507.22876/) (2025)
- [Experience-Guided Reflective Co-Evolution of Prompts and Heuristics for Automatic Algorithm Design](https://mlsanity.com/paper/2509.24509/) (2025)
- [Code Evolution for Control: Synthesizing Policies via LLM-Driven Evolutionary Search](https://mlsanity.com/paper/2601.06845/) (2026)
- [STRCMP: Integrating Graph Structural Priors with Language Models for Combinatorial Optimization](https://mlsanity.com/paper/2506.11057/) (2025)
- [TIDE: Tuning-Integrated Dynamic Evolution for LLM-Based Automated Heuristic Design](https://mlsanity.com/paper/2601.21239/) (2026)
- [RankEvolve: Automating the Discovery of Retrieval Algorithms via LLM-Driven Evolution](https://mlsanity.com/paper/2602.16932/) (2026)

## Abstract (arXiv)

Algorithm design is crucial for effective problem-solving across various domains. The advent of Large Language Models (LLMs) has notably enhanced the automation and innovation within this field, offering new perspectives and promising solutions. In just a few years, this integration has yielded remarkable progress in areas ranging from combinatorial optimization to scientific discovery. Despite this rapid expansion, a holistic understanding of the field is hindered by the lack of a systematic review, as existing surveys either remain limited to narrow sub-fields or with different objectives. This paper seeks to provide a systematic review of algorithm design with LLMs. We introduce a taxonomy that categorises the roles of LLMs as optimizers, predictors, extractors and designers, analyzing the progress, advantages, and limitations within each category. We further synthesize literature across the three phases of the algorithm design pipeline and across diverse algorithmic applications that define the current landscape. Finally, we outline key open challenges and opportunities to guide future research. To support future research and collaboration, we provide an accompanying repository at: https://github.com/FeiLiu36/LLM4AlgorithmDesign.