mlsanityData to 7 Oct 2026

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

arXiv 2402.10172 ↗First posted 15 Feb 2024cs.AI cs.MAcited by 105

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Cited by 24 in LLM agents and tool use, but placed by its own abstract, which didn’t fit.

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%.

Key facts. Cited by 105 papers in the map (data through 7 Oct 2026). Builds on 8 of its 27 references that are in the map. First posted on arXiv 15 Feb 2024.

Builds on

8 of 27 references.

References · 8

  1. 2023LLaMA: Open and Efficient Foundation Language Modelscited by 13,958
  2. 2021Improving language models by retrieving from trillions of tokenscited by 1,278
  3. 2023How Far Can Camels Go? Exploring the State of Instruction Tuning on Open Resourcescited by 405
  4. 2023ART: Automatic multi-step reasoning and tool-use for large language modelscited by 193
  5. 2023NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptionscited by 133
  6. 2023Large Language Models for Supply Chain Optimizationcited by 61
  7. 2022Augmenting Operations Research with Auto-Formulation of Optimization Models from Problem Descriptionscited by 54
  8. 2023Diagnosing Infeasible Optimization Problems Using Large Language Modelscited by 27

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 10; 2025: 38; 2026: 57.

105 papers.

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  1. 2024LLMOPT: Learning to Define and Solve General Optimization Problems from Scratchcited by 102
  2. 2024OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modelingcited by 66
  3. 2024Autoformulation of Mathematical Optimization Models Using LLMscited by 48
  4. 2025Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modelingcited by 44
  5. 2024OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scalecited by 37
  6. 2024Towards Foundation Models for Mixed Integer Linear Programmingcited by 30
  7. 2025A Survey of Optimization Modeling Meets LLMs: Progress and Future Directionscited by 30
  8. 2025CO-Bench: Benchmarking Language Model Agents in Algorithm Search for Combinatorial Optimizationcited by 28
  9. 2025StepORLM: A Self-Evolving Framework With Generative Process Supervision For Operations Research Language Modelscited by 26
  10. 2024Toward Automated Algorithm Design: A Survey and Practical Guide to Meta-Black-Box-Optimizationcited by 23
  11. 2025OptimAI: Optimization from Natural Language Using LLM-Powered AI Agentscited by 22
  12. 2025HeuriGym: An Agentic Benchmark for LLM-Crafted Heuristics in Combinatorial Optimizationcited by 19
38 more
  1. 2024Improving Parallel Program Performance with LLM Optimizers via Agent-System Interfacescited by 11
  2. 2026Constructing Industrial-Scale Optimization Modeling Benchmarkcited by 10
  3. 2025Decision Information Meets Large Language Models: The Future of Explainable Operations Researchcited by 9
  4. 2025EquivaMap: Leveraging LLMs for Automatic Equivalence Checking of Optimization Formulationscited by 9
  5. 2025A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solvingcited by 9
  6. 2025OptiMind: Teaching LLMs to Think Like Optimization Expertscited by 9
  7. 2024Large Language Models for Power Scheduling: A User-Centric Approachcited by 8
  8. 2024Generalists vs. Specialists: Evaluating LLMs on Highly-Constrained Biophysical Sequence Optimization Taskscited by 8
  9. 2025OptiChat: Bridging Optimization Models and Practitioners with Large Language Modelscited by 8
  10. 2025EvoCut: Strengthening Integer Programs via Evolution-Guided Language Modelscited by 8
  11. 2025SAC-Opt: Semantic Anchors for Iterative Correction in Optimization Modelingcited by 8
  12. 2026ReLoop: Structured Modeling and Behavioral Verification for Reliable LLM-Based Optimizationcited by 8
  13. 2025Generalizable Heuristic Generation Through LLMs with Meta-Optimizationcited by 7
  14. 2025ORGEval: Graph-Theoretic Evaluation of LLMs in Optimization Modelingcited by 7
  15. 2026AI Agents for Inventory Control: Human-LLM-OR Complementaritycited by 6
  16. 2026ConstraintBench: Benchmarking LLM Constraint Reasoning on Direct Optimizationcited by 6
  17. 2025R-ConstraintBench: Evaluating LLMs on NP-Complete Schedulingcited by 5
  18. 2026OPT-Engine: Benchmarking the Limits of LLMs in Optimization Modeling via Complexity Scalingcited by 5
  19. 2026NEMO: Execution-Aware Optimization Modeling via Autonomous Coding Agentscited by 5
  20. 2026Opt-Verifier: Unleashing the Power of LLMs for Optimization Modeling via Dual-Side Verificationcited by 5
  21. 2024Abstract Operations Research Modeling Using Natural Language Inputscited by 4
  22. 2025Satellite Edge Artificial Intelligence with Large Models: Architectures and Technologiescited by 4
  23. 2025Large Language Models in Operations Research: Methods, Applications, and Challengescited by 4
  24. 2026OptiRepair: Closed-Loop Diagnosis and Repair of Supply Chain Optimization Models with LLM Agentscited by 4
  25. 2026Strategy-Aware Optimization Modeling with Reasoning LLMscited by 4
  26. 2026FrontierOR: Benchmarking LLMs' Capacity for Efficient Algorithm Design in Large-Scale Optimizationcited by 4
  27. 2025What can large language models do for sustainable food?cited by 3
  28. 2025Automatic MILP Model Construction for Multi-Robot Task Allocation and Scheduling Based on Large Language Modelscited by 3
  29. 2025Performance of LLMs on Stochastic Modeling Operations Research Problems: From Theory to Practicecited by 3
  30. 2025CALM Before the STORM: Unlocking Native Reasoning for Optimization Modelingcited by 3
  31. 2025An Agent-Based Framework for the Automatic Validation of Mathematical Optimization Modelscited by 3
  32. 2026From Soliloquy to Agora: Memory-Enhanced LLM Agents with Decentralized Debate for Optimization Modelingcited by 3
  33. 2025Large Language Model-Driven Surrogate-Assisted Evolutionary Algorithm for Expensive Optimizationcited by 2
  34. 2025LISTEN to Your Preferences: An LLM Framework for Multi-Objective Selectioncited by 2
  35. 2026MIRROR: A Multi-Agent Framework with Iterative Adaptive Revision and Hierarchical Retrieval for Optimization Modeling in Operations Researchcited by 2
  36. 2026Execution-Verified Reinforcement Learning for Optimization Modelingcited by 2
  37. 2026ORPilot: A Production-Oriented Agentic LLM-for-OR Tool for Optimization Modelingcited by 2
  38. 2026Formalize, Don't Optimize: The Heuristic Trap in LLM-Generated Combinatorial Solverscited by 2

50 most cited of 105 All 105 (JSON)