A Survey of Optimization Modeling Meets LLMs: Progress and Future Directions

TL;DR

This survey reviews recent progress in integrating optimization modeling with large language models, highlighting advancements, dataset quality issues, and future research directions in automating mathematical modeling.

Contribution

It provides a comprehensive overview of technical developments, dataset cleaning, and community resources, along with analysis of dataset errors and future research opportunities.

Findings

High error rate in benchmark datasets identified

Cleaned datasets and established a new leaderboard

Developed an online portal with resources for the community

Abstract

By virtue of its great utility in solving real-world problems, optimization modeling has been widely employed for optimal decision-making across various sectors, but it requires substantial expertise from operations research professionals. With the advent of large language models (LLMs), new opportunities have emerged to automate the procedure of mathematical modeling. This survey presents a comprehensive and timely review of recent advancements that cover the entire technical stack, including data synthesis and fine-tuning for the base model, inference frameworks, benchmark datasets, and performance evaluation. In addition, we conducted an in-depth analysis on the quality of benchmark datasets, which was found to have a surprisingly high error rate. We cleaned the datasets and constructed a new leaderboard with fair performance evaluation in terms of base LLM model and datasets. We also build an online portal that integrates resources of cleaned datasets, code and paper repository to benefit the community. Finally, we identify limitations in current methodologies and outline future research opportunities.