OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scale

TL;DR

OptiMUS-0.3 leverages large language models to automatically formulate, solve, and improve optimization problems from natural language descriptions, significantly outperforming existing methods on diverse datasets.

Contribution

The paper introduces OptiMUS-0.3, a novel LLM-based system that automates the modeling and solving of optimization problems from natural language, enhancing accessibility and efficiency.

Findings

Outperforms state-of-the-art methods by over 22% on easy datasets.

Achieves more than 24% improvement on complex datasets, including a new challenging dataset.

Demonstrates robustness in handling long and complex problem descriptions.

Abstract

Optimization problems are pervasive in sectors from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers because the expertise required to formulate and solve these problems limits the widespread adoption of optimization tools and techniques. We introduce a Large Language Model (LLM)-based system designed to formulate and solve (mixed integer) linear programming problems from their natural language descriptions. Our system is capable of developing mathematical models, writing and debugging solver code, evaluating the generated solutions, and improving efficiency and correctness of its model and code based on these evaluations. OptiMUS-0.3 utilizes a modular structure to process problems, allowing it to handle problems with long descriptions and complex data without long prompts. Experiments demonstrate that OptiMUS-0.3 outperforms existing state-of-the-art methods on easy datasets by more than 22% and on hard datasets (including a new dataset, NLP4LP, released with this paper that features long and complex problems) by more than 24%.