# Generating Robust Portfolios of Optimization Models using Large Language Models

arXiv: https://arxiv.org/abs/2605.27013 · HTML: https://mlsanity.com/paper/2605.27013/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 23 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 19 of 19)

- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Eureka: Human-Level Reward Design via Coding Large Language Models](https://mlsanity.com/paper/2310.12931/) (2023)
- [Language to Rewards for Robotic Skill Synthesis](https://mlsanity.com/paper/2306.08647/) (2023)
- [Reward Machines: Exploiting Reward Function Structure in Reinforcement Learning](https://mlsanity.com/paper/2010.03950/) (2020)
- [Text2Reward: Reward Shaping with Language Models for Reinforcement Learning](https://mlsanity.com/paper/2309.11489/) (2023)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling](https://mlsanity.com/paper/2407.09887/) (2024)
- [Autoformulation of Mathematical Optimization Models Using LLMs](https://mlsanity.com/paper/2411.01679/) (2024)
- [A Survey of Optimization Modeling Meets LLMs: Progress and Future Directions](https://mlsanity.com/paper/2508.10047/) (2025)
- [A Large Language Model-Driven Reward Design Framework via Dynamic Feedback for Reinforcement Learning](https://mlsanity.com/paper/2410.14660/) (2024)
- [Promptable Behaviors: Personalizing Multi-Objective Rewards from Human Preferences](https://mlsanity.com/paper/2312.09337/) (2023)
- [A Decision-Language Model (DLM) for Dynamic Restless Multi-Armed Bandit Tasks in Public Health](https://mlsanity.com/paper/2402.14807/) (2024)
- [Solving General Natural-Language-Description Optimization Problems with Large Language Models](https://mlsanity.com/paper/2407.07924/) (2024)
- [LM4OPT: Unveiling the Potential of Large Language Models in Formulating Mathematical Optimization Problems](https://mlsanity.com/paper/2403.01342/) (2024)
- [Balancing Act: Prioritization Strategies for LLM-Designed Restless Bandit Rewards](https://mlsanity.com/paper/2408.12112/) (2024)
- [Leveraging LLMs for reward function design in reinforcement learning control tasks](https://mlsanity.com/paper/2511.19355/) (2025)
- [Automated Generation of MDPs Using Logic Programming and LLMs for Robotic Applications](https://mlsanity.com/paper/2511.23143/) (2025)

## Abstract (arXiv)

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 unicodex2014 as a stochastic generator and as a reasoning evaluator unicodex2014 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.