Peering Inside the Black Box: Uncovering LLM Errors in Optimization Modelling through Component-Level Evaluation
This work addresses the need for fine-grained evaluation in NLP-to-optimization modeling, offering diagnostic tools for researchers and practitioners, though it is incremental in improving existing evaluation methods.
The study tackled the problem of evaluating LLMs in converting natural language to optimization formulations by introducing a component-level framework with metrics like precision and recall for constraints, and found that GPT-5 outperformed other models with specific prompting strategies, emphasizing constraint recall and RMSE as key for solver performance.
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.