Large Language Models for Combinatorial Optimization of Design Structure Matrix

ABSTRACT: Combinatorial optimization (CO) is essential for improving efficiency and performance in engineering applications. Traditional algorithms based on pure mathematical reasoning are limited and incapable to capture the contextual nuances for optimization. This study explores the potential of Large Language Models (LLMs) in solving engineering CO problems by leveraging their reasoning power and contextual knowledge. We propose a novel LLM-based framework that integrates network topology and contextual domain knowledge to optimize the sequencing of Design Structure Matrix (DSM) —a common CO problem. Our experiments on various DSM cases demonstrate that the proposed method achieves faster convergence and higher solution quality than benchmark methods. Moreover, results show that incorporating contextual domain knowledge significantly improves performance despite the choice of LLMs.