# A Survey of Optimization Modeling Meets LLMs: Progress and Future Directions

arXiv: https://arxiv.org/abs/2508.10047 · HTML: https://mlsanity.com/paper/2508.10047/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 40 references that are in the map.
- First posted on arXiv 12 Aug 2025.

## Builds on (most cited first, 23 of 23)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Scaling Large Language Model-based Multi-Agent Collaboration](https://mlsanity.com/paper/2406.07155/) (2024)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [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)
- [Large Language Models for Supply Chain Optimization](https://mlsanity.com/paper/2307.03875/) (2023)
- [Autoformulation of Mathematical Optimization Models Using LLMs](https://mlsanity.com/paper/2411.01679/) (2024)
- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [Diagnosing Infeasible Optimization Problems Using Large Language Models](https://mlsanity.com/paper/2308.12923/) (2023)
- [Solving General Natural-Language-Description Optimization Problems with Large Language Models](https://mlsanity.com/paper/2407.07924/) (2024)
- [To the Globe (TTG): Towards Language-Driven Guaranteed Travel Planning](https://mlsanity.com/paper/2410.16456/) (2024)
- [Leveraging Large Language Models for Solving Rare MIP Challenges](https://mlsanity.com/paper/2409.04464/) (2024)
- [Decision Information Meets Large Language Models: The Future of Explainable Operations Research](https://mlsanity.com/paper/2502.09994/) (2025)
- [Chain-of-Knowledge: Integrating Knowledge Reasoning into Large Language Models by Learning from Knowledge Graphs](https://mlsanity.com/paper/2407.00653/) (2024)
- [City-LEO: Toward Transparent City Management Using LLM with End-to-End Optimization](https://mlsanity.com/paper/2406.10958/) (2024)
- [Operational Research Literature as a Use Case for the Open Research Knowledge Graph](https://mlsanity.com/paper/2006.13733/) (2020)
- [LLM-based Frameworks for Power Engineering from Routine to Novel Tasks](https://mlsanity.com/paper/2305.11202/) (2023)

## Built on by (most cited first, 30 of 31)

- [StepORLM: A Self-Evolving Framework With Generative Process Supervision For Operations Research Language Models](https://mlsanity.com/paper/2509.22558/) (2025)
- [Constructing Industrial-Scale Optimization Modeling Benchmark](https://mlsanity.com/paper/2602.10450/) (2026)
- [OptiMind: Teaching LLMs to Think Like Optimization Experts](https://mlsanity.com/paper/2509.22979/) (2025)
- [SAC-Opt: Semantic Anchors for Iterative Correction in Optimization Modeling](https://mlsanity.com/paper/2510.05115/) (2025)
- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [Opt-Verifier: Unleashing the Power of LLMs for Optimization Modeling via Dual-Side Verification](https://mlsanity.com/paper/2605.29556/) (2026)
- [Strategy-Aware Optimization Modeling with Reasoning LLMs](https://mlsanity.com/paper/2605.02545/) (2026)
- [From Soliloquy to Agora: Memory-Enhanced LLM Agents with Decentralized Debate for Optimization Modeling](https://mlsanity.com/paper/2604.25847/) (2026)
- [REG: A Regularization Optimizer for Robust Training Dynamics](https://mlsanity.com/paper/2510.03691/) (2025)
- [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)
- [Execution-Verified Reinforcement Learning for Optimization Modeling](https://mlsanity.com/paper/2604.00442/) (2026)
- [Democratizing Large-Scale Re-Optimization with LLM-Guided Model Patches](https://mlsanity.com/paper/2605.18692/) (2026)
- [TriVAL: A Tri-Validation Framework for Faithful Automatic Optimization Modeling](https://mlsanity.com/paper/2605.23966/) (2026)
- [Grammar-Aware Literate Generative Mathematical Programming with Compiler-in-the-Loop](https://mlsanity.com/paper/2601.17670/) (2026)
- [AutoOR: Scalably Post-training LLMs to Autoformulate Operations Research Problems](https://mlsanity.com/paper/2604.16804/) (2026)
- [Automated Reformulation of Robust Optimization via Memory-Augmented Large Language Models](https://mlsanity.com/paper/2605.11813/) (2026)
- [Models Can Model, But Can't Bind: Structured Grounding in Text-to-Optimization](https://mlsanity.com/paper/2605.21751/) (2026)
- [MiniOpt: Reasoning to Model and Solve General Optimization Problems with Limited Resources](https://mlsanity.com/paper/2606.25832/) (2026)
- [WildSplat: Feedforward Gaussian Splatting from Unposed In-the-Wild Images](https://mlsanity.com/paper/2607.05347/) (2026)
- [PEARL: Solver-in-the-Loop Interactive Optimization Modeling from Natural Language](https://mlsanity.com/paper/2607.18256/) (2026)
- [Co-evolving Agent Architectures and Interpretable Reasoning for Automated Optimization](https://mlsanity.com/paper/2604.17708/) (2026)
- [Generating Robust Portfolios of Optimization Models using Large Language Models](https://mlsanity.com/paper/2605.27013/) (2026)
- [Large Language Models as Optimizers: A Survey of Direct vs. Tool-Augmented Approaches and Their Performance Frontiers](https://mlsanity.com/paper/2606.15577/) (2026)
- [EvoOptiGraph: Weakness-Driven Coevolution via Graph-Based Structural Generation for Optimization Modeling](https://mlsanity.com/paper/2606.26578/) (2026)
- [IR2Solve: Structured Intermediate Representations for Cost-Efficient Optimization Autoformulation](https://mlsanity.com/paper/2608.02641/) (2026)
- [Admission Without Answers: Label-Free Certification and Experience Learning for LLM-Based Optimization Modeling](https://mlsanity.com/paper/2608.15565/) (2026)
- [SAILOR: Solver-Assisted Interactive LLM-based Optimization Recovery](https://mlsanity.com/paper/2609.13945/) (2026)
- [Relative Generalization Invariance of LLM Pretraining](https://mlsanity.com/paper/2609.33016/) (2026)
- [Learning to Optimize through Solver-Grounded Self-Play](https://mlsanity.com/paper/2609.34205/) (2026)
- [TACIT: Optimization Models that Learn from Their Mistakes](https://mlsanity.com/paper/2609.38434/) (2026)

## Abstract (arXiv)

By virtue of its great utility in solving real-world problems, optimization modeling has been widely employed for optimal decision-making across various sectors, but it requires substantial expertise from operations research professionals. With the advent of large language models (LLMs), new opportunities have emerged to automate the procedure of mathematical modeling. This survey presents a comprehensive and timely review of recent advancements that cover the entire technical stack, including data synthesis and fine-tuning for the base model, inference frameworks, benchmark datasets, and performance evaluation. In addition, we conducted an in-depth analysis on the quality of benchmark datasets, which was found to have a surprisingly high error rate. We cleaned the datasets and constructed a new leaderboard with fair performance evaluation in terms of base LLM model and datasets. We also build an online portal that integrates resources of cleaned datasets, code and paper repository to benefit the community. Finally, we identify limitations in current methodologies and outline future research opportunities.