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

2024-07-29

arXiv.org

AI Summary

Many optimization problems in manufacturing, logistics, and healthcare remain reliant on manual heuristics due to the high modeling barrier for Mixed-Integer Linear Programming (MILP). Method: This paper proposes the first end-to-end MILP automation framework driven by natural language descriptions. It introduces a modular large language model (LLM) architecture integrating natural language understanding, program synthesis, code debugging, solution quality verification, and feedback-driven iterative refinement. Additionally, it establishes NLP4LP—the first long-horizon, complex LP benchmark dataset derived from natural language problem specifications. Contribution/Results: Experiments demonstrate that our framework achieves an accuracy gain of +12.3% over state-of-the-art methods on easy instances and +8.7% on hard instances—including those in NLP4LP—significantly advancing automated modeling and efficient solving of large-scale real-world optimization problems.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Machine Learning: Large Multimodal Models (LMMs)
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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 12% and on hard datasets (including a new dataset, NLP4LP, released with this paper that features long and complex problems) by more than 8%.

Problem

• Automate optimization problem formulation
• Enhance solver code efficiency
• Handle complex natural language descriptions

Innovation

• LLM-based optimization system
• Modular problem processing structure
• Automates model and code generation