# Opt-Verifier: Unleashing the Power of LLMs for Optimization Modeling via Dual-Side Verification

arXiv: https://arxiv.org/abs/2605.29556 · HTML: https://mlsanity.com/paper/2605.29556/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 52 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 21 of 21)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Dual Learning for Machine Translation](https://mlsanity.com/paper/1611.00179/) (2016)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [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)
- [LLaMoCo: Instruction Tuning of Large Language Models for Optimization Code Generation](https://mlsanity.com/paper/2403.01131/) (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)
- [Stronger-MAS: Multi-Agent Reinforcement Learning for Collaborative LLMs](https://mlsanity.com/paper/2510.11062/) (2025)
- [OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling](https://mlsanity.com/paper/2510.22192/) (2025)
- [Automated Optimization Modeling via a Localizable Error-Driven Perspective](https://mlsanity.com/paper/2602.11164/) (2026)
- [CoCo-MILP: Inter-Variable Contrastive and Intra-Constraint Competitive MILP Solution Prediction](https://mlsanity.com/paper/2511.09209/) (2025)
- [Joint Optimization of Multi-agent Memory System](https://mlsanity.com/paper/2603.12631/) (2026)

## Built on by (most cited first, 5 of 5)

- [Falsification-Based Verification of LLM-Generated Optimization Models: Sound Test Batteries and Their Detection Limits](https://mlsanity.com/paper/2607.16646/) (2026)
- [Admission Without Answers: Label-Free Certification and Experience Learning for LLM-Based Optimization Modeling](https://mlsanity.com/paper/2608.15565/) (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)
- [OR for AI That Does OR: Routing LLMs up the Escalator inside the OSCAR Framework](https://mlsanity.com/paper/2610.00912/) (2026)

## Abstract (arXiv)

Building mathematical optimization models is critical in operations research (OR), while it requires substantial human expertise. Recent advancements have utilized large language models (LLMs) to automate this modeling process. However, existing works often struggle to verify the correctness of the generated optimization models, without checking the rationality of the constraints and variables or the validity of solutions to the generated models. This hampers the subsequent verification and correction steps, and thus it severely hurts the modeling accuracy. To address this challenge, we propose a novel LLM-based framework with Dual-side Verification (Opt-Verifier) from both structure and solution perspectives, thereby improving the modeling accuracy. The structure-side verification ensures that the modeling structure of the generated optimization models aligns with the original problem description, accurately capturing the problem's constraints and requirements. Meanwhile, the solution-side verification interprets and evaluates the solutions' validity, confirming that the optimization models are logically and mathematically sound. Experiments on popular benchmarks demonstrate that our approach achieves over 20% improvement in accuracy.