Large Language Models for Combinatorial Optimization of Design Structure Matrix
Shuo Jiang, Min Xie, Jianxi Luo
TL;DR
This work tackles DSM sequencing, a combinatorial optimization problem in engineering design, by introducing a knowledge-informed LLM framework that jointly leverages network topology and contextual domain knowledge. The method initializes with random solutions, iteratively generates candidates via in-context learning, and evaluates them using a DSM-specific feedback-loop metric, achieving superior convergence and solution quality against stochastic and deterministic baselines. Key findings show that incorporating domain knowledge consistently improves outcomes across multiple DSM cases and LLM backbones, with Claude-3.5-Sonnet often delivering the best performance. The results suggest a promising new paradigm for engineering design optimization where semantic reasoning and mathematical structure are integrated through LLMs, with implications for planning, modularization, and decision support, and trajectories toward multimodal extensions and integration into commercial DSM tools.
Abstract
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.