# OptArgus: A Multi-Agent System to Detect Hallucinations in LLM-based Optimization Modeling

arXiv: https://arxiv.org/abs/2605.11738 · HTML: https://mlsanity.com/paper/2605.11738/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Medical and scientific domain agents, one of 16 directions in LLM agents and tool use.
- Builds on 6 of its 33 references that are in the map.
- First posted on arXiv 12 May 2026.

## Placed in

- LLM agents and tool use / [Medical and scientific domain agents](https://mlsanity.com/agents/medical-and-scientific-domain-agents/)

## Builds on (most cited first, 6 of 6)

- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Enhancing Mathematical Reasoning in Large Language Models with Self-Consistency-Based Hallucination Detection](https://mlsanity.com/paper/2504.09440/) (2025)
- [Constructing Industrial-Scale Optimization Modeling Benchmark](https://mlsanity.com/paper/2602.10450/) (2026)
- [ORGEval: Graph-Theoretic Evaluation of LLMs in Optimization Modeling](https://mlsanity.com/paper/2510.27610/) (2025)
- [Peering Inside the Black Box: Uncovering LLM Errors in Optimization Modelling through Component-Level Evaluation](https://mlsanity.com/paper/2510.16943/) (2025)
- [ProOPF: Benchmarking and Improving LLMs for Professional-Grade Power Systems Optimization Modeling](https://mlsanity.com/paper/2602.03070/) (2026)

## Built on by (most cited first, 3 of 3)

- [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)
- [Right Answers, Costly Models: The Efficiency Gap in LLM-based Optimization Modeling](https://mlsanity.com/paper/2609.38884/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used to translate natural-language optimization problems into mathematical formulations and solver code, but matching the reference objective value is not a reliable test of correctness: an artifact may agree numerically while still changing the underlying optimization semantics. We formulate this issue as optimization-modeling hallucination detection, namely structural consistency auditing over the problem description, symbolic model, and solver implementation. We develop, to our knowledge, the first fine-grained hallucination taxonomy specifically for optimization modeling, spanning objective, variable, constraint, and implementation failures. We use this taxonomy to design OptArgus, a multi-agent detector with conductor routing, specialist auditors, and evidence consolidation. To evaluate this setting, we introduce a three-part benchmark suite with 484 clean artifacts, 1266 controlled injected artifacts, and 6292 natural LLM-generated artifacts. Against a matched single-agent baseline, OptArgus produces fewer false alarms on clean artifacts, more accurate top-ranked localization on controlled single-error cases, and stronger detection on natural model outputs. Together, these contributions turn optimization-modeling hallucination detection into a concrete empirical problem and suggest that modular, taxonomy-grounded auditing is a practical route to more reliable optimization modeling.