OptArgus: A Multi-Agent System to Detect Hallucinations in LLM-based Optimization Modeling
Authors: Zhong Li, Zihan Guo, Xiaohan Lu, Juntao Wang, Jie Song, Chao Shen, Jiageng Wu, Mingyang Sun
Organizations: ♣Great Bay University · ▲Peking University · ♡Jilin University · ♠Shenzhen Loop Area Institute · ⋆Zhejiang University · (B1) · (B2)
Abstract
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 \emph{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.
Large language models now translate natural-language descriptions of decision problems into solver-ready optimization models, but they fail silently. A generated model often runs and still formulates the wrong problem. This paper develops a theory of falsification-based verification for this setting. Every numeric quantity in the description is a typed slot, and a candidate model is tested only through solver calls on slot-transformed instances; no reference model or label is consulted. From duality, comparative statics, and polyhedral limit arguments we derive a battery of test classes covering directions, curvature, crush probes, prohibitive limits, annihilation, and exchange. Every test is sound, so a violation certifies unfaithfulness and the false-positive rate is zero by design. We characterize what such verification can never see, give conditions under which the canonical error classes are detected with certainty, and prove that no fixed-threshold perturbation tester is simultaneously sound and nontrivial. Experiments on 326 ground-truth models from NL4OPT and four benchmark families confirm the theory. The battery attains a 0.0% false-positive rate against 54.9% for a threshold tester, detects 70.0% of certified conditional-class mutants, convicts 40.4% of the mutants invisible to execution-accuracy scoring, and reproduces the predicted detectability pattern including its zeros.
LLM-based agents are increasingly deployed to solve optimization problems, yet existing benchmarks evaluate them on pre-structured mathematical formulations that bypass the most critical challenge: translating complex business requirements into correct models and solve efficiently. We introduce Opti-Agent-Bench, an end-to-end benchmark that evaluates Large Language Models (LLMs) across the complete optimization R&D pipeline, from understanding business-language descriptions through mathematical modeling, algorithm selection, and code implementation, to solution report generation. Our design rests on three pillars: (1) businesssemantic authenticity with anti-template traps that defeat pattern matching; (2) modular evaluation with cross-module consistency checking across Problem Understanding, Formal Modeling, Implementation, and Reporting; and (3) the ORAC bi-level validity framework that simultaneously ensures task quality and scoring integrity. Across several industrialscale tasks spanning integer programming, robust optimization, stochastic programming, and non-convex optimization, we expose critical failure modes of current models, including constraint omission, model-code inconsistency, and report-implementation divergence, that remain invisible under conventional single-metric evaluation.
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.