# Large Language Models for Combinatorial Optimization of Design Structure Matrix

arXiv: https://arxiv.org/abs/2506.09749 · HTML: https://mlsanity.com/paper/2506.09749/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 79 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 15 of 15)

- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [Large Language Models as Evolutionary Optimizers](https://mlsanity.com/paper/2310.19046/) (2023)
- [Rethinking Interpretability in the Era of Large Language Models](https://mlsanity.com/paper/2402.01761/) (2024)
- [ReplanVLM: Replanning Robotic Tasks with Visual Language Models](https://mlsanity.com/paper/2407.21762/) (2024)
- [Generative Transformers for Design Concept Generation](https://mlsanity.com/paper/2211.03468/) (2022)
- [Data-Driven Design-by-Analogy: State of the Art and Future Directions](https://mlsanity.com/paper/2106.01592/) (2021)
- [AutoTRIZ: Automating Engineering Innovation with TRIZ and Large Language Models](https://mlsanity.com/paper/2403.13002/) (2024)
- [Generative Optimization: A Perspective on AI-Enhanced Problem Solving in Engineering](https://mlsanity.com/paper/2412.13281/) (2024)
- [Resource Optimization of Product Development Projects with Time-Varying Dependency Structure](https://mlsanity.com/paper/1903.09964/) (2019)

## Abstract (arXiv)

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.