# OptimAI: Optimization from Natural Language Using LLM-Powered AI Agents

arXiv: https://arxiv.org/abs/2504.16918 · HTML: https://mlsanity.com/paper/2504.16918/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 23 Apr 2025.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 28 of 28)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [A Dynamic LLM-Powered Agent Network for Task-Oriented Agent Collaboration](https://mlsanity.com/paper/2310.02170/) (2023)
- [Scaling Large Language Model-based Multi-Agent Collaboration](https://mlsanity.com/paper/2406.07155/) (2024)
- [Building Cooperative Embodied Agents Modularly with Large Language Models](https://mlsanity.com/paper/2307.02485/) (2023)
- [ResearchAgent: Iterative Research Idea Generation over Scientific Literature with Large Language Models](https://mlsanity.com/paper/2404.07738/) (2024)
- [MapCoder: Multi-Agent Code Generation for Competitive Problem Solving](https://mlsanity.com/paper/2405.11403/) (2024)
- [EconAgent: Large Language Model-Empowered Agents for Simulating Macroeconomic Activities](https://mlsanity.com/paper/2310.10436/) (2023)
- [SMART-LLM: Smart Multi-Agent Robot Task Planning using Large Language Models](https://mlsanity.com/paper/2309.10062/) (2023)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [Simulating Classroom Education with LLM-Empowered Agents](https://mlsanity.com/paper/2406.19226/) (2024)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [Language Agents as Optimizable Graphs](https://mlsanity.com/paper/2402.16823/) (2024)
- [MAPoRL: Multi-Agent Post-Co-Training for Collaborative Large Language Models with Reinforcement Learning](https://mlsanity.com/paper/2502.18439/) (2025)
- [o1-Coder: an o1 Replication for Coding](https://mlsanity.com/paper/2412.00154/) (2024)
- [Self-Evolving Multi-Agent Collaboration Networks for Software Development](https://mlsanity.com/paper/2410.16946/) (2024)
- [A Survey on LLM-based Multi-Agent System: Recent Advances and New Frontiers in Application](https://mlsanity.com/paper/2412.17481/) (2024)
- [OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scale](https://mlsanity.com/paper/2407.19633/) (2024)
- [Simulating Financial Market via Large Language Model based Agents](https://mlsanity.com/paper/2406.19966/) (2024)
- [Self-Labeling the Job Shop Scheduling Problem](https://mlsanity.com/paper/2401.11849/) (2024)
- [COOPER: Coordinating Specialized Agents towards a Complex Dialogue Goal](https://mlsanity.com/paper/2312.11792/) (2023)
- [Leveraging Large Language Models for Effective and Explainable Multi-Agent Credit Assignment](https://mlsanity.com/paper/2502.16863/) (2025)
- [Robust and Adaptive Optimization under a Large Language Model Lens](https://mlsanity.com/paper/2501.00568/) (2024)

## Built on by (most cited first, 22 of 22)

- [LLM-based Agentic Reasoning Frameworks: A Survey from Methods to Scenarios](https://mlsanity.com/paper/2508.17692/) (2025)
- [OR-R1: Automating Modeling and Solving of Operations Research Optimization Problem via Test-Time Reinforcement Learning](https://mlsanity.com/paper/2511.09092/) (2025)
- [AlphaOPT: Formulating Optimization Programs with Self-Improving LLM Experience Library](https://mlsanity.com/paper/2510.18428/) (2025)
- [PerspectiveGap: A Benchmark for Multi-Agent Orchestration Prompting](https://mlsanity.com/paper/2606.08878/) (2026)
- [ORThought: Benchmarking and Automating Logistics Optimization Modeling](https://mlsanity.com/paper/2508.14410/) (2025)
- [NEMO: Execution-Aware Optimization Modeling via Autonomous Coding Agents](https://mlsanity.com/paper/2601.21372/) (2026)
- [NC2C: Automated Convexification of Generic Non-Convex Optimization Problems](https://mlsanity.com/paper/2601.04789/) (2026)
- [MIRROR: A Multi-Agent Framework with Iterative Adaptive Revision and Hierarchical Retrieval for Optimization Modeling in Operations Research](https://mlsanity.com/paper/2602.03318/) (2026)
- [TriVAL: A Tri-Validation Framework for Faithful Automatic Optimization Modeling](https://mlsanity.com/paper/2605.23966/) (2026)
- [OptiHive: Ensemble Selection for LLM-Based Optimization via Statistical Modeling](https://mlsanity.com/paper/2508.02503/) (2025)
- [SOCRATES: Simulation Optimization with Correlated Replicas and Adaptive Trajectory Evaluations](https://mlsanity.com/paper/2511.00685/) (2025)
- [LinearizeLLM: An Agent-Based Framework for LLM-Driven Exact Linear Reformulation of Nonlinear Optimization Problems](https://mlsanity.com/paper/2510.15969/) (2025)
- [WISE: Weighted Iterative Society-of-Experts for Robust Multimodal Multi-Agent Debate](https://mlsanity.com/paper/2512.02405/) (2025)
- [EvoOpt-LLM: Evolving industrial optimization models with large language models](https://mlsanity.com/paper/2602.01082/) (2026)
- [PARM: Pipeline-Adapted Reward Model](https://mlsanity.com/paper/2604.18327/) (2026)
- [COOPA: A Modular LLM Agent Architecture for Operations Research Problems](https://mlsanity.com/paper/2606.27611/) (2026)
- [Adaptive Cluster-First Route-Second Decomposition for Industrial-Scale Vehicle Routing](https://mlsanity.com/paper/2606.31820/) (2026)
- [A2utoLPBench: An Auto-Generated, Agent-Friendly LP Benchmark via Inverse-KKT Construction](https://mlsanity.com/paper/2607.02141/) (2026)
- [Robust Feasible Route Construction through Collaborative Partition Optimization](https://mlsanity.com/paper/2607.03694/) (2026)
- [QuantumQUBO Agent: Automating Quadratic Unconstrained Binary Optimization (QUBO) Formulation Generation from Natural Language](https://mlsanity.com/paper/2609.10629/) (2026)
- [SAILOR: Solver-Assisted Interactive LLM-based Optimization Recovery](https://mlsanity.com/paper/2609.13945/) (2026)
- [TACIT: Optimization Models that Learn from Their Mistakes](https://mlsanity.com/paper/2609.38434/) (2026)

## Abstract (arXiv)

Optimization plays a vital role in scientific research and practical applications. However, formulating a concrete optimization problem described in natural language into a mathematical form and selecting a suitable solver to solve the problem requires substantial domain expertise. We introduce OptimAI, a framework for solving Optimization problems described in natural language by leveraging LLM-powered AI agents, and achieve superior performance over current state-of-the-art methods. Our framework is built upon the following key roles: (1) a formulator that translates natural language problem descriptions into precise mathematical formulations; (2) a planner that constructs a high-level solution strategy prior to execution; and (3) a coder and a code critic capable of interacting with the environment and reflecting on outcomes to refine future actions. Ablation studies confirm that all roles are essential; removing the planner or code critic results in 5.8× and 3.1× drops in productivity, respectively. Furthermore, we introduce UCB-based debug scheduling to dynamically switch between alternative plans, yielding an additional 3.3× productivity gain. Our design emphasizes multi-agent collaboration, and our experiments confirm that combining diverse models leads to performance gains. Our approach attains 88.1% accuracy on the NLP4LP dataset and 82.3% on the Optibench dataset, reducing error rates by 58% and 52%, respectively, over prior best results.