Generating Robust Portfolios of Optimization Models using Large Language Models

2026-05-26

AI Summary

Optimization modeling typically relies on scarce domain-specific and optimization expertise, yet existing large language model (LLM) approaches generate only a single model, limiting reliability. This work proposes a novel framework that uniquely leverages LLMs simultaneously as stochastic generators and reasoning evaluators to construct a robust ensemble of multiple candidate models, enabling human–AI collaborative selection of high-quality solutions. The method provides a theoretical guarantee: as long as either the generator or the evaluator aligns with human preferences, the ensemble is assured to contain at least one high-quality model. Experimental results demonstrate that this approach significantly enhances the reliability and practical utility of generated optimization models across diverse modeling tasks.

Abstract

Mathematical optimization is a powerful tool for structured decision-making across domains such as resource allocation and planning. Formulating optimization models faithful to reality, though, remains a significant bottleneck as it typically demands both domain expertise and optimization knowledge that are often scarce. Recent advances in large language models (LLMs) promise to bridge this gap, enabling the generation of candidate optimization models from natural language descriptions. However, there is no guarantee that any single LLM-generated model is reliable, and existing approaches that output only one model are therefore risky. In this work, we propose a novel algorithm that generates a portfolio of optimization models, designed to be robust to the limitations of LLMs. Our method exploits the observation that a single LLM can play two distinct roles $\unicode{x2014}$ as a stochastic generator and as a reasoning evaluator $\unicode{x2014}$ and proposes a unified framework that leverages both capabilities in a complementary manner. We provide theoretical guarantees showing that, as long as either the generator or the evaluator is well-aligned with human preferences, the portfolio is guaranteed to contain high-quality candidates, enabling a principled human-in-the-loop process in which a decision-maker can review multiple candidates before committing to one. We further validate our approach empirically, demonstrating strong performance across a range of optimization modeling tasks.

Problem

• optimization models
• large language models
• model reliability
• portfolio generation
• robustness

Innovation

• large language models
• optimization modeling
• model portfolio
• human-in-the-loop
• robust generation