# OptiMUS: Optimization Modeling Using MIP Solvers and large language models

arXiv: https://arxiv.org/abs/2310.06116 · HTML: https://mlsanity.com/paper/2310.06116/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 46 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Mathematical Capabilities of ChatGPT](https://mlsanity.com/paper/2301.13867/) (2023)
- [Reinforcement Learning for Combinatorial Optimization: A Survey](https://mlsanity.com/paper/2003.03600/) (2020)
- [ART: Automatic multi-step reasoning and tool-use for large language models](https://mlsanity.com/paper/2303.09014/) (2023)
- [How well do Large Language Models perform in Arithmetic tasks?](https://mlsanity.com/paper/2304.02015/) (2023)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [Diagnosing Infeasible Optimization Problems Using Large Language Models](https://mlsanity.com/paper/2308.12923/) (2023)

## Built on by (most cited first, 30 of 39)

- [Evolutionary Computation in the Era of Large Language Model: Survey and Roadmap](https://mlsanity.com/paper/2401.10034/) (2024)
- [Large Language Model (LLM) for Telecommunications: A Comprehensive Survey on Principles, Key Techniques, and Opportunities](https://mlsanity.com/paper/2405.10825/) (2024)
- [LLaMoCo: Instruction Tuning of Large Language Models for Optimization Code Generation](https://mlsanity.com/paper/2403.01131/) (2024)
- [Large Language Model-Based Evolutionary Optimizer: Reasoning with elitism](https://mlsanity.com/paper/2403.02054/) (2024)
- [AlphaOPT: Formulating Optimization Programs with Self-Improving LLM Experience Library](https://mlsanity.com/paper/2510.18428/) (2025)
- [Automated Optimization Modeling via a Localizable Error-Driven Perspective](https://mlsanity.com/paper/2602.11164/) (2026)
- [Deep Insights into Automated Optimization with Large Language Models and Evolutionary Algorithms](https://mlsanity.com/paper/2410.20848/) (2024)
- [From Large Language Models and Optimization to Decision Optimization CoPilot: A Research Manifesto](https://mlsanity.com/paper/2402.16269/) (2024)
- [Leveraging Large Language Models for Solving Rare MIP Challenges](https://mlsanity.com/paper/2409.04464/) (2024)
- [SolverLLM: Leveraging Test-Time Scaling for Optimization Problem via LLM-Guided Search](https://mlsanity.com/paper/2510.16916/) (2025)
- [OptiChat: Bridging Optimization Models and Practitioners with Large Language Models](https://mlsanity.com/paper/2501.08406/) (2025)
- [LLM-OptiRA: LLM-Driven Optimization of Resource Allocation for Non-Convex Problems in Wireless Communications](https://mlsanity.com/paper/2505.02091/) (2025)
- [MoE2: Optimizing Collaborative Inference for Edge Large Language Models](https://mlsanity.com/paper/2501.09410/) (2025)
- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [City-LEO: Toward Transparent City Management Using LLM with End-to-End Optimization](https://mlsanity.com/paper/2406.10958/) (2024)
- [Ask, Clarify, Optimize: Human-LLM Agent Collaboration for Smarter Inventory Control](https://mlsanity.com/paper/2601.00121/) (2025)
- [CHORUS: Zero-shot Hierarchical Retrieval and Orchestration for Generating Linear Programming Code](https://mlsanity.com/paper/2505.01485/) (2025)
- [Let's Have a Conversation: Designing and Evaluating LLM Agents for Interactive Optimization](https://mlsanity.com/paper/2604.02666/) (2026)
- [Gala: Global LLM Agents for Text-to-Model Translation](https://mlsanity.com/paper/2509.08970/) (2025)
- [Empowering Real-World: A Survey on the Technology, Practice, and Evaluation of LLM-driven Industry Agents](https://mlsanity.com/paper/2510.17491/) (2025)
- [LISTEN to Your Preferences: An LLM Framework for Multi-Objective Selection](https://mlsanity.com/paper/2510.25799/) (2025)
- [ORPilot: A Production-Oriented Agentic LLM-for-OR Tool for Optimization Modeling](https://mlsanity.com/paper/2605.02728/) (2026)
- [Automated Conversion of Static to Dynamic Scheduler via Natural Language](https://mlsanity.com/paper/2405.06697/) (2024)
- [AutoRNet: Automatically Optimizing Heuristics for Robust Network Design via Large Language Models](https://mlsanity.com/paper/2410.17656/) (2024)
- [REMoH: A Reflective Evolution of Multi-objective Heuristics approach via Large Language Models](https://mlsanity.com/paper/2506.07759/) (2025)
- [ModelLens: Finding the Best for Your Task from Myriads of Models](https://mlsanity.com/paper/2605.07075/) (2026)
- [Agentic MIP Research: Accelerated Constraint Handler Generation](https://mlsanity.com/paper/2605.09186/) (2026)
- [Leveraging LLM Agents for Automated Optimization Modeling for SASP Problems: A Graph-RAG based Approach](https://mlsanity.com/paper/2501.18320/) (2025)
- [Optimization Problem Solving Can Transition to Evolutionary Agentic Workflows](https://mlsanity.com/paper/2505.04354/) (2025)
- [LM4Opt-RA: A Multi-Candidate LLM Framework with Structured Ranking for Automating Network Resource Allocation](https://mlsanity.com/paper/2512.00039/) (2025)

## Abstract (arXiv)

Optimization problems are pervasive across various sectors, from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers, as the expertise required to formulate and solve these problems limits the widespread adoption of optimization tools and techniques. We introduce OptiMUS, a Large Language Model (LLM)-based agent designed to formulate and solve MILP problems from their natural language descriptions. OptiMUS is capable of developing mathematical models, writing and debugging solver code, developing tests, and checking the validity of generated solutions. To benchmark our agent, we present NLP4LP, a novel dataset of linear programming (LP) and mixed integer linear programming (MILP) problems. Our experiments demonstrate that OptiMUS solves nearly twice as many problems as a basic LLM prompting strategy. OptiMUS code and NLP4LP dataset are available at hrefhttps://github.com/teshnizi/OptiMUShttps://github.com/teshnizi/OptiMUS