# Peering Inside the Black Box: Uncovering LLM Errors in Optimization Modelling through Component-Level Evaluation

arXiv: https://arxiv.org/abs/2510.16943 · HTML: https://mlsanity.com/paper/2510.16943/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2025.

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

- [The Path Ahead for Agentic AI: Challenges and Opportunities](https://mlsanity.com/paper/2601.02749/) (2026)
- [OptArgus: A Multi-Agent System to Detect Hallucinations in LLM-based Optimization Modeling](https://mlsanity.com/paper/2605.11738/) (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)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used to convert natural language descriptions into mathematical optimization formulations. Current evaluations often treat formulations as a whole, relying on coarse metrics like solution accuracy or runtime, which obscure structural or numerical errors. In this study, we present a comprehensive, component-level evaluation framework for LLM-generated formulations. Beyond the conventional optimality gap, our framework introduces metrics such as precision and recall for decision variables and constraints, constraint and objective root mean squared error (RMSE), and efficiency indicators based on token usage and latency. We evaluate GPT-5, LLaMA 3.1 Instruct, and DeepSeek Math across optimization problems of varying complexity under six prompting strategies. Results show that GPT-5 consistently outperforms other models, with chain-of-thought, self-consistency, and modular prompting proving most effective. Analysis indicates that solver performance depends primarily on high constraint recall and low constraint RMSE, which together ensure structural correctness and solution reliability. Constraint precision and decision variable metrics play secondary roles, while concise outputs enhance computational efficiency. These findings highlight three principles for NLP-to-optimization modeling: (i) Complete constraint coverage prevents violations, (ii) minimizing constraint RMSE ensures solver-level accuracy, and (iii) concise outputs improve computational efficiency. The proposed framework establishes a foundation for fine-grained, diagnostic evaluation of LLMs in optimization modeling.