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

2025-12-21

AI Summary

In high-cost simulation-driven design, automatically translating natural language requirements into executable mathematical optimization models remains a critical bottleneck. Method: This paper proposes a solver-agnostic Automated Problem Formulation (APF) framework that integrates large language model (LLM) supervised fine-tuning, formal natural-language-to-optimization-model mapping, synthetic data generation, and semantic consistency verification. Crucially, APF introduces the first pipeline for generating and annotating training data without requiring real simulation feedback. Contribution/Results: Evaluated on antenna design tasks, APF achieves significantly higher requirement formalization accuracy and radiation efficiency curve compliance rates than state-of-the-art methods, demonstrating strong practicality, generalizability, and robustness. To our knowledge, this is the first work enabling end-to-end, fully automated translation from ambiguous engineering requirements to executable optimization models—eliminating reliance on domain experts and manual modeling.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• 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

Abstract

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.

Problem

• Automates conversion of natural language design requirements into optimization models
• Generates high-quality data for fine-tuning LLMs without solver feedback
• Enhances accuracy and efficiency in simulation-driven design formulation

Innovation

• Automated problem formulation via LLMs without solver dependency
• High-quality data generation pipeline for fine-tuning without solver feedback
• Supervised fine-tuning enhances LLMs for accurate optimization models