LM4OPT: Unveiling the potential of Large Language Models in formulating mathematical optimization problems

Abstract

In the fast-paced domain of natural language processing, converting linguistic descriptions into mathematical optimization problems is a complex task, requiring profound comprehension and processing skills from Large Language Models (LLMs). In this study, various LLMs were evaluated, including GPT-3.5, GPT-4, and smaller variants with seven billion parameters: Llama-2, Falcon, Mistral, and Zephyr. This research investigated their performance in both zero-shot and one-shot settings for this task, revealing that GPT-4 outperformed others, particularly in the one-shot scenario. A core contribution of this study is the development of LM4OPT, a progressive fine-tuning framework specifically designed for smaller LLMs. This framework leverages noisy embeddings and specialized datasets to enhance the performance of the models. Regardless of the inherent limitations of smaller models in processing complex and lengthy input contexts, our experimental results indicate a significant reduction in the performance disparity between smaller and larger models when the former are fine-tuned using LM4OPT. Our empirical study, utilizing the NL4Opt dataset, unveils that GPT-4 surpasses the baseline performance established by previous research, achieving an accuracy of 63.30 % , 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 progressively fine-tuned smaller models.