# OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models

arXiv: https://arxiv.org/abs/2402.10172 · HTML: https://mlsanity.com/paper/2402.10172/

## Key facts

- Cited by 109 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 15 Feb 2024.

## Builds on (most cited first, 8 of 8)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Improving language models by retrieving from trillions of tokens](https://mlsanity.com/paper/2112.04426/) (2021)
- [How Far Can Camels Go? Exploring the State of Instruction Tuning on Open Resources](https://mlsanity.com/paper/2306.04751/) (2023)
- [ART: Automatic multi-step reasoning and tool-use for large language models](https://mlsanity.com/paper/2303.09014/) (2023)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [Large Language Models for Supply Chain Optimization](https://mlsanity.com/paper/2307.03875/) (2023)
- [Augmenting Operations Research with Auto-Formulation of Optimization Models from Problem Descriptions](https://mlsanity.com/paper/2209.15565/) (2022)
- [Diagnosing Infeasible Optimization Problems Using Large Language Models](https://mlsanity.com/paper/2308.12923/) (2023)

## Built on by (most cited first, 30 of 109)

- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling](https://mlsanity.com/paper/2407.09887/) (2024)
- [Autoformulation of Mathematical Optimization Models Using LLMs](https://mlsanity.com/paper/2411.01679/) (2024)
- [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://mlsanity.com/paper/2505.11792/) (2025)
- [OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scale](https://mlsanity.com/paper/2407.19633/) (2024)
- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [A Survey of Optimization Modeling Meets LLMs: Progress and Future Directions](https://mlsanity.com/paper/2508.10047/) (2025)
- [CO-Bench: Benchmarking Language Model Agents in Algorithm Search for Combinatorial Optimization](https://mlsanity.com/paper/2504.04310/) (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)
- [OptimAI: Optimization from Natural Language Using LLM-Powered AI Agents](https://mlsanity.com/paper/2504.16918/) (2025)
- [HeuriGym: An Agentic Benchmark for LLM-Crafted Heuristics in Combinatorial Optimization](https://mlsanity.com/paper/2506.07972/) (2025)
- [Constructing Industrial-Scale Optimization Modeling Benchmark](https://mlsanity.com/paper/2602.10450/) (2026)
- [Improving Parallel Program Performance with LLM Optimizers via Agent-System Interfaces](https://mlsanity.com/paper/2410.15625/) (2024)
- [A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving](https://mlsanity.com/paper/2509.08269/) (2025)
- [Generalists vs. Specialists: Evaluating LLMs on Highly-Constrained Biophysical Sequence Optimization Tasks](https://mlsanity.com/paper/2410.22296/) (2024)
- [OptiMind: Teaching LLMs to Think Like Optimization Experts](https://mlsanity.com/paper/2509.22979/) (2025)
- [ORGEval: Graph-Theoretic Evaluation of LLMs in Optimization Modeling](https://mlsanity.com/paper/2510.27610/) (2025)
- [Decision Information Meets Large Language Models: The Future of Explainable Operations Research](https://mlsanity.com/paper/2502.09994/) (2025)
- [EquivaMap: Leveraging LLMs for Automatic Equivalence Checking of Optimization Formulations](https://mlsanity.com/paper/2502.14760/) (2025)
- [Generalizable Heuristic Generation Through LLMs with Meta-Optimization](https://mlsanity.com/paper/2505.20881/) (2025)
- [Large Language Models for Power Scheduling: A User-Centric Approach](https://mlsanity.com/paper/2407.00476/) (2024)
- [OptiChat: Bridging Optimization Models and Practitioners with Large Language Models](https://mlsanity.com/paper/2501.08406/) (2025)
- [EvoCut: Strengthening Integer Programs via Evolution-Guided Language Models](https://mlsanity.com/paper/2508.11850/) (2025)
- [SAC-Opt: Semantic Anchors for Iterative Correction in Optimization Modeling](https://mlsanity.com/paper/2510.05115/) (2025)
- [AI Agents for Inventory Control: Human-LLM-OR Complementarity](https://mlsanity.com/paper/2602.12631/) (2026)
- [ReLoop: Structured Modeling and Behavioral Verification for Reliable LLM-Based Optimization](https://mlsanity.com/paper/2602.15983/) (2026)
- [ConstraintBench: Benchmarking LLM Constraint Reasoning on Direct Optimization](https://mlsanity.com/paper/2602.22465/) (2026)
- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [FrontierOR: Benchmarking LLMs' Capacity for Efficient Algorithm Design in Large-Scale Optimization](https://mlsanity.com/paper/2605.25246/) (2026)

## Abstract (arXiv)

Optimization problems are pervasive in 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 because the expertise required to formulate and solve these problems limits the widespread adoption of optimization tools and techniques. This paper introduces OptiMUS, a Large Language Model (LLM)-based agent designed to formulate and solve (mixed integer) linear programming problems from their natural language descriptions. OptiMUS can develop mathematical models, write and debug solver code, evaluate the generated solutions, and improve its model and code based on these evaluations. OptiMUS utilizes a modular structure to process problems, allowing it to handle problems with long descriptions and complex data without long prompts. Experiments demonstrate that OptiMUS outperforms existing state-of-the-art methods on easy datasets by more than 20% and on hard datasets (including a new dataset, NLP4LP, released with this paper that features long and complex problems) by more than 30%.