# OptiMind: Teaching LLMs to Think Like Optimization Experts

arXiv: https://arxiv.org/abs/2509.22979 · HTML: https://mlsanity.com/paper/2509.22979/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 9 of 9)

- [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)
- [OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling](https://mlsanity.com/paper/2502.11102/) (2025)
- [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)
- [A Survey of Optimization Modeling Meets LLMs: Progress and Future Directions](https://mlsanity.com/paper/2508.10047/) (2025)
- [ORThought: Benchmarking and Automating Logistics Optimization Modeling](https://mlsanity.com/paper/2508.14410/) (2025)

## Built on by (most cited first, 10 of 10)

- [ConstraintBench: Benchmarking LLM Constraint Reasoning on Direct Optimization](https://mlsanity.com/paper/2602.22465/) (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)
- [Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems](https://mlsanity.com/paper/2606.04816/) (2026)
- [Text2Model: Modeling Copilots for Text-to-Model Translation](https://mlsanity.com/paper/2604.12955/) (2026)
- [Budget-Efficient Automatic Algorithm Design via Code Graph](https://mlsanity.com/paper/2605.10598/) (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)
- [Learning to Optimize through Solver-Grounded Self-Play](https://mlsanity.com/paper/2609.34205/) (2026)
- [LLMs as Adaptive Meta-Solvers: Strategy-Diverse RL for Industrial-Scale Optimization](https://mlsanity.com/paper/2609.34427/) (2026)
- [Right Answers, Costly Models: The Efficiency Gap in LLM-based Optimization Modeling](https://mlsanity.com/paper/2609.38884/) (2026)

## Abstract (arXiv)

Mathematical programming -- the task of expressing operations and decision-making problems in precise mathematical language -- is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise. Recent advances in large language models for complex reasoning have spurred interest in automating this task, translating natural language into executable optimization models. Current approaches, however, achieve limited accuracy, hindered by scarce and noisy training data without leveraging domain knowledge. In this work, we systematically integrate optimization expertise to improve formulation accuracy for mixed-integer linear programming, a key family of mathematical programs. Our OptiMind framework leverages semi-automated, class-based error analysis to guide both training and inference, explicitly preventing common mistakes within each optimization class. Our resulting fine-tuned LLM significantly improves formulation accuracy by 20.7% across multiple optimization benchmarks, with consistent gains under test-time scaling methods such as self-consistency and multi-turn feedback, enabling further progress toward robust LLM-assisted optimization formulation.