# Large Language Models for Combinatorial Optimization of Design Structure Matrix

arXiv: https://arxiv.org/abs/2411.12571 · HTML: https://mlsanity.com/paper/2411.12571/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 79 references that are in the map.
- First posted on arXiv 19 Nov 2024.

## Builds on (most cited first, 14 of 14)

- [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)
- [Resource Optimization of Product Development Projects with Time-Varying Dependency Structure](https://mlsanity.com/paper/1903.09964/) (2019)

## Built on by (most cited first, 8 of 8)

- [Large Language Models as End-to-end Combinatorial Optimization Solvers](https://mlsanity.com/paper/2509.16865/) (2025)
- [A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving](https://mlsanity.com/paper/2509.08269/) (2025)
- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [ACEvo: Adversarial Co-Evolution of Problem Distributions and Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2506.02594/) (2025)
- [Intelligent Design 4.0: Paradigm Evolution Toward the Agentic AI Era](https://mlsanity.com/paper/2506.09755/) (2025)
- [EvoOpt-LLM: Evolving industrial optimization models with large language models](https://mlsanity.com/paper/2602.01082/) (2026)
- [Design Structure Matrix Modularization with Large Language Models](https://mlsanity.com/paper/2604.28018/) (2026)
- [Large Language Models as Optimizers: A Survey of Direct vs. Tool-Augmented Approaches and Their Performance Frontiers](https://mlsanity.com/paper/2606.15577/) (2026)

## Abstract (arXiv)

Combinatorial optimization (CO) is essential for improving efficiency and performance in engineering applications. As complexity increases with larger problem sizes and more intricate dependencies, identifying the optimal solution become challenging. When it comes to real-world engineering problems, algorithms based on pure mathematical reasoning are limited and incapable to capture the contextual nuances necessary 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 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. These findings highlight the potential of LLMs in tackling complex real-world CO problems by combining semantic and mathematical reasoning. This approach paves the way for a new paradigm in in real-world combinatorial optimization.