# Solver-Independent Automated Problem Formulation via LLMs for High-Cost Simulation-Driven Design

arXiv: https://arxiv.org/abs/2512.18682 · HTML: https://mlsanity.com/paper/2512.18682/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 58 references that are in the map.
- First posted on arXiv 21 Dec 2025.

## Builds on (most cited first, 16 of 16)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing](https://mlsanity.com/paper/2406.08464/) (2024)
- [On LLMs-Driven Synthetic Data Generation, Curation, and Evaluation: A Survey](https://mlsanity.com/paper/2406.15126/) (2024)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [CLoSD: Closing the Loop between Simulation and Diffusion for multi-task character control](https://mlsanity.com/paper/2410.03441/) (2024)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [Augmenting Operations Research with Auto-Formulation of Optimization Models from Problem Descriptions](https://mlsanity.com/paper/2209.15565/) (2022)
- [OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling](https://mlsanity.com/paper/2502.11102/) (2025)
- [LLaMoCo: Instruction Tuning of Large Language Models for Optimization Code Generation](https://mlsanity.com/paper/2403.01131/) (2024)
- [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://mlsanity.com/paper/2505.11792/) (2025)
- [Scalable and Effective Arithmetic Tree Generation for Adder and Multiplier Designs](https://mlsanity.com/paper/2405.06758/) (2024)
- [ParetoHqD: Fast Offline Multiobjective Alignment of Large Language Models using Pareto High-quality Data](https://mlsanity.com/paper/2504.16628/) (2025)

## Built on by (most cited first, 1 of 1)

- [BBOWP-Bench: Evaluating LLMs on Black-Box Optimization Word Problems](https://mlsanity.com/paper/2608.02612/) (2026)

## Abstract (arXiv)

In the high-cost simulation-driven design domain, translating ambiguous design requirements into a mathematical optimization formulation is a bottleneck for optimizing product performance. This process is time-consuming and heavily reliant on expert knowledge. While large language models (LLMs) offer potential for automating this task, existing approaches either suffer from poor formalization that fails to accurately align with the design intent or rely on solver feedback for data filtering, which is unavailable due to the high simulation costs. To address this challenge, we propose APF, a framework for solver-independent, automated problem formulation via LLMs designed to automatically convert engineers' natural language requirements into executable optimization models. The core of this framework is an innovative pipeline for automatically generating high-quality data, which overcomes the difficulty of constructing suitable fine-tuning datasets in the absence of high-cost solver feedback with the help of data generation and test instance annotation. The generated high-quality dataset is used to perform supervised fine-tuning on LLMs, significantly enhancing their ability to generate accurate and executable optimization problem formulations. Experimental results on antenna design demonstrate that APF significantly outperforms the existing methods in both the accuracy of requirement formalization and the quality of resulting radiation efficiency curves in meeting the design goals.