mlsanityData to 14 Oct 2026

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

arXiv 2504.16918 ↗First posted 23 Apr 2025cs.CL cs.AIcited by 22

On the map: LLM agents and tool use → General LLM agent frameworks and benchmarks

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.

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.

Builds on

28 of 49 references.

Closest ancestors · 6

Same direction, newest first

  1. 2024A Survey on LLM-based Multi-Agent System: Recent Advances and New Frontiers in Application23 Dec
  2. 2024Scaling Large Language Model-based Multi-Agent Collaboration11 Jun
  3. 2024Language Agents as Optimizable Graphs26 Feb
  4. 2023A Dynamic LLM-Powered Agent Network for Task-Oriented Agent Collaboration3 Oct
  5. 2023SMART-LLM: Smart Multi-Agent Robot Task Planning using Large Language Models18 Sep
  6. 2023Building Cooperative Embodied Agents Modularly with Large Language Models5 Jul

Other references · 22

  1. 2023GPT-4 Technical Reportcited by 18,396
  2. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  3. 2021Convex optimizationcited by 2,515
  4. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,150
  5. 2019Introduction to Multi-Armed Banditscited by 481
  6. 2025rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinkingcited by 313
  7. 2024ResearchAgent: Iterative Research Idea Generation over Scientific Literature with Large Language Modelscited by 210
  8. 2024MapCoder: Multi-Agent Code Generation for Competitive Problem Solvingcited by 177
  9. 2023EconAgent: Large Language Model-Empowered Agents for Simulating Macroeconomic Activitiescited by 154
  10. 2025LIMR: Less is More for RL Scalingcited by 139
  11. 2023NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptionscited by 135
  12. 2024Simulating Classroom Education with LLM-Empowered Agentscited by 127
10 more
  1. 2024OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Modelscited by 109
  2. 2025MAPoRL: Multi-Agent Post-Co-Training for Collaborative Large Language Models with Reinforcement Learningcited by 86
  3. 2024o1-Coder: an o1 Replication for Codingcited by 78
  4. 2024Self-Evolving Multi-Agent Collaboration Networks for Software Developmentcited by 74
  5. 2024OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scalecited by 38
  6. 2024Simulating Financial Market via Large Language Model based Agentscited by 25
  7. 2024Self-Labeling the Job Shop Scheduling Problemcited by 23
  8. 2023COOPER: Coordinating Specialized Agents towards a Complex Dialogue Goalcited by 18
  9. 2025Leveraging Large Language Models for Effective and Explainable Multi-Agent Credit Assignmentcited by 18
  10. 2024Robust and Adaptive Optimization under a Large Language Model Lenscited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 8; 2026: 14.

22 papers.

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  1. 2025LLM-based Agentic Reasoning Frameworks: A Survey from Methods to Scenarioscited by 26
  2. 2025OR-R1: Automating Modeling and Solving of Operations Research Optimization Problem via Test-Time Reinforcement Learningcited by 17
  3. 2025AlphaOPT: Formulating Optimization Programs with Self-Improving LLM Experience Librarycited by 14
  4. 2026PerspectiveGap: A Benchmark for Multi-Agent Orchestration Promptingcited by 6
  5. 2025ORThought: Benchmarking and Automating Logistics Optimization Modelingcited by 5
  6. 2026NEMO: Execution-Aware Optimization Modeling via Autonomous Coding Agentscited by 5
  7. 2026NC2C: Automated Convexification of Generic Non-Convex Optimization Problemscited by 3
  8. 2026MIRROR: A Multi-Agent Framework with Iterative Adaptive Revision and Hierarchical Retrieval for Optimization Modeling in Operations Researchcited by 2
  9. 2026TriVAL: A Tri-Validation Framework for Faithful Automatic Optimization Modelingcited by 2
  10. 2025OptiHive: Ensemble Selection for LLM-Based Optimization via Statistical Modelingcited by 1
  11. 2025SOCRATES: Simulation Optimization with Correlated Replicas and Adaptive Trajectory Evaluationscited by 1
  12. 2025LinearizeLLM: An Agent-Based Framework for LLM-Driven Exact Linear Reformulation of Nonlinear Optimization Problemscited by 0
10 more
  1. 2025WISE: Weighted Iterative Society-of-Experts for Robust Multimodal Multi-Agent Debatecited by 0
  2. 2026EvoOpt-LLM: Evolving industrial optimization models with large language modelscited by 0
  3. 2026PARM: Pipeline-Adapted Reward Modelcited by 0
  4. 2026COOPA: A Modular LLM Agent Architecture for Operations Research Problemscited by 0
  5. 2026Adaptive Cluster-First Route-Second Decomposition for Industrial-Scale Vehicle Routingcited by 0
  6. 2026A2utoLPBench: An Auto-Generated, Agent-Friendly LP Benchmark via Inverse-KKT Constructioncited by 0
  7. 2026Robust Feasible Route Construction through Collaborative Partition Optimizationcited by 0
  8. 2026QuantumQUBO Agent: Automating Quadratic Unconstrained Binary Optimization (QUBO) Formulation Generation from Natural Languagecited by 0
  9. 2026SAILOR: Solver-Assisted Interactive LLM-based Optimization Recoverycited by 0
  10. 2026TACIT: Optimization Models that Learn from Their Mistakescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Let's Have a Conversation: Designing and Evaluating LLM Agents for Interactive Optimization
  2. 2025OPT-BENCH: Evaluating LLM Agent on Large-Scale Search Spaces Optimization Problems
  3. 2026Opti-Agent-Bench: Benchmarking End-to-End Optimization R&D Agents on Real-World Business Problems
  4. 2026OPT-Engine: Benchmarking the Limits of LLMs in Optimization Modeling via Complexity Scaling
  5. 2026From Soliloquy to Agora: Memory-Enhanced LLM Agents with Decentralized Debate for Optimization Modeling
  6. 2025OR-LLM-Agent: Automating Modeling and Solving of Operations Research Optimization Problems with Reasoning LLM
  7. 2025Toward a Trustworthy Optimization Modeling Agent via Verifiable Synthetic Data Generation
  8. 2026What Makes an LLM a Good Optimizer? A Trajectory Analysis of LLM-Guided Evolutionary Search