LM4OPT: Unveiling the Potential of Large Language Models in Formulating Mathematical Optimization Problems

In the rapidly evolving field of natural language processing, the translation of linguistic descriptions into mathematical formulation of optimization problems presents a formidable challenge, demanding intricate understanding and processing capabilities from LLMs. This study compares prominent LLMs, including GPT-3.5, GPT-4, and Llama-2-7b, in zero-shot and one-shot settings for this task. Our findings show GPT-4's superior performance, particularly in the one-shot scenario. A central part of this research is the introduction of `LM4OPT,' a progressive fine-tuning framework for Llama-2-7b that utilizes noisy embeddings and specialized datasets. However, this research highlights a notable gap in the contextual understanding capabilities of smaller models such as Llama-2-7b compared to larger counterparts, especially in processing lengthy and complex input contexts. Our empirical investigation, utilizing the NL4Opt dataset, unveils that GPT-4 surpasses the baseline performance established by previous research, achieving an F1-score of 0.63, solely based on the problem description in natural language, and without relying on any additional named entity information. GPT-3.5 follows closely, both outperforming the fine-tuned Llama-2-7b. These findings not only benchmark the current capabilities of LLMs in a novel application area but also lay the groundwork for future improvements in mathematical formulation of optimization problems from natural language input.