Large language models for design structure matrix sequencing as combinatorial optimization

In complex engineering systems, the dependencies among components or development activities are often modeled and analyzed using the Design Structure Matrix (DSM). Reorganizing the sequence of elements within a DSM to minimize feedback loops, thereby improving process efficiency and reducing rework, 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 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 representative CO problem in this domain. Experiments on various DSM cases demonstrate that our proposed 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. This study demonstrates the potential of LLMs as a promising foundation for advancing knowledge-informed optimization in engineering design.