Large Language Models for Combinatorial Optimization of Design Structure Matrix

• URL: http://arxiv.org/abs/2411.12571v1
• Date: Tue, 19 Nov 2024 15:39:51 GMT
• Title: Large Language Models for Combinatorial Optimization of Design Structure Matrix
• Authors: Shuo Jiang, Min Xie, Jianxi Luo,
• Abstract summary: Combinatorial optimization (CO) is essential for improving efficiency and performance in engineering applications. 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.
• Score: 4.513609458468522
• License:
• Abstract: 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.

Related papers

• Improving Existing Optimization Algorithms with LLMs [0.9668407688201361]
  This paper investigates how Large Language Models (LLMs) can enhance existing optimization algorithms. Using their pre-trained knowledge, we demonstrate their ability to propose innovative variations and implementation strategies. Our results show that an alternative proposed by GPT-4o outperforms the expert-designed of CMSA.
  arXiv  Detail & Related papers  (2025-02-12T10:58:57Z)
• Bridging Visualization and Optimization: Multimodal Large Language Models on Graph-Structured Combinatorial Optimization [56.17811386955609]
  Graph-structured challenges are inherently difficult due to their nonlinear and intricate nature. In this study, we propose transforming graphs into images to preserve their higher-order structural features accurately. By combining the innovative paradigm powered by multimodal large language models with simple search techniques, we aim to develop a novel and effective framework.
  arXiv  Detail & Related papers  (2025-01-21T08:28:10Z)
• A Survey on Inference Optimization Techniques for Mixture of Experts Models [50.40325411764262]
  Large-scale Mixture of Experts (MoE) models offer enhanced model capacity and computational efficiency through conditional computation. deploying and running inference on these models presents significant challenges in computational resources, latency, and energy efficiency. This survey analyzes optimization techniques for MoE models across the entire system stack.
  arXiv  Detail & Related papers  (2024-12-18T14:11:15Z)
• Deep Insights into Automated Optimization with Large Language Models and Evolutionary Algorithms [3.833708891059351]
  Large Language Models (LLMs) and Evolutionary Algorithms (EAs) offer promising new approach to overcome limitations and make optimization more automated. LLMs act as dynamic agents that can generate, refine, and interpret optimization strategies. EAs efficiently explore complex solution spaces through evolutionary operators.
  arXiv  Detail & Related papers  (2024-10-28T09:04:49Z)
• Learning Joint Models of Prediction and Optimization [56.04498536842065]
  Predict-Then-Then framework uses machine learning models to predict unknown parameters of an optimization problem from features before solving. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by joint predictive models.
  arXiv  Detail & Related papers  (2024-09-07T19:52:14Z)
• When Large Language Model Meets Optimization [7.822833805991351]
  Large language models (LLMs) facilitate intelligent modeling and strategic decision-making in optimization. This review outlines the progress and potential of combining LLMs with optimization algorithms.
  arXiv  Detail & Related papers  (2024-05-16T13:54:37Z)
• How Multimodal Integration Boost the Performance of LLM for Optimization: Case Study on Capacitated Vehicle Routing Problems [33.33996058215666]
  Large language models (LLMs) have positioned themselves as capable tools for addressing complex optimization challenges. We propose to enhance the optimization performance using multimodal LLM capable of processing both textual and visual prompts.
  arXiv  Detail & Related papers  (2024-03-04T06:24:21Z)
• SEGO: Sequential Subgoal Optimization for Mathematical Problem-Solving [64.38649623473626]
  Large Language Models (LLMs) have driven substantial progress in artificial intelligence. We propose a novel framework called textbfSEquential subtextbfGoal textbfOptimization (SEGO) to enhance LLMs' ability to solve mathematical problems.
  arXiv  Detail & Related papers  (2023-10-19T17:56:40Z)
• An Interactive Knowledge-based Multi-objective Evolutionary Algorithm Framework for Practical Optimization Problems [5.387300498478744]
  This paper proposes an interactive knowledge-based evolutionary multi-objective optimization (IK-EMO) framework. It extracts hidden variable-wise relationships as knowledge from evolving high-performing solutions, shares them with users to receive feedback, and applies them back to the optimization process to improve its effectiveness. The working of the proposed IK-EMO is demonstrated on three large-scale real-world engineering design problems.
  arXiv  Detail & Related papers  (2022-09-18T16:51:01Z)
• Neural Combinatorial Optimization: a New Player in the Field [69.23334811890919]
  This paper presents a critical analysis on the incorporation of algorithms based on neural networks into the classical optimization framework. A comprehensive study is carried out to analyse the fundamental aspects of such algorithms, including performance, transferability, computational cost and to larger-sized instances.
  arXiv  Detail & Related papers  (2022-05-03T07:54:56Z)
• A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs [91.07247251502564]
  We propose a hybrid approach to combine the best of the two worlds, in which a bi-level framework is developed with an upper-level learning method to optimize the graph. Such a bi-level approach simplifies the learning on the original hard CO and can effectively mitigate the demand for model capacity.
  arXiv  Detail & Related papers  (2021-06-09T09:18:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.