In complex engineering systems, the dependencies among components or development activities are often modeled and analyzed using Design Structure Matrix (DSM). Reorganizing elements within a DSM to minimize feedback loops and enhance modularity or process efficiency constitutes a challenging combinatorial optimization (CO) problem in engineering design and operations. As problem sizes increase and dependency networks become more intricate, traditional optimization methods that rely solely on mathematical heuristics often fail to capture the contextual nuances and struggle to deliver effective solutions. In this study, we explore the potential of Large Language Models (LLMs) to address such CO problems by leveraging their capabilities for advanced reasoning and contextual understanding. We propose a novel LLM-based framework that integrates network topology with contextual domain knowledge for iterative optimization of DSM sequencing-a common CO problem. Experiments on various DSM cases demonstrate that our method consistently achieves faster convergence and superior solution quality compared to both stochastic and deterministic baselines. Notably, incorporating contextual domain knowledge significantly enhances optimization performance regardless of the chosen LLM backbone. These findings highlight the potential of LLMs to solve complex engineering CO problems by combining semantic and mathematical reasoning. This approach paves the way towards a new paradigm in LLM-based engineering design optimization.

翻译：在复杂工程系统中，组件或开发活动间的依赖关系常通过设计结构矩阵（DSM）进行建模与分析。对DSM中的元素进行重排以最小化反馈回路、提升模块化程度或流程效率，构成了工程设计及运维中的一项具有挑战性的组合优化（CO）问题。随着问题规模的扩大与依赖网络复杂性的增加，仅依赖数学启发式算法的传统优化方法往往难以捕捉上下文细节，且难以提供有效解决方案。本研究探索利用大语言模型（LLMs）的高级推理与上下文理解能力解决此类组合优化问题的潜力。我们提出一种基于大语言模型的新框架，该框架将网络拓扑结构与上下文领域知识相结合，用于DSM排序这一常见组合优化问题的迭代优化。在多种DSM案例上的实验表明，与随机及确定性基线方法相比，我们的方法始终能实现更快的收敛速度与更优的解质量。值得注意的是，无论选用何种大语言模型主干架构，融入上下文领域知识均能显著提升优化性能。这些发现揭示了LLMs通过融合语义与数学推理来解决复杂工程组合优化问题的潜力，为基于大语言模型的工程设计优化开辟了新范式。