Bridging Visualization and Optimization: Multimodal Large Language Models on Graph-Structured Combinatorial Optimization

2025-01-21

AI Summary

This study investigates how large language models (LLMs) can emulate human-like spatial reasoning to efficiently solve combinatorial optimization problems on graph-structured data. Method: We propose the first structure-preserving “graph-to-image” encoding paradigm, transforming graphs into topology-aware visual representations for multimodal large language models (MLLMs) such as LLaVA and Qwen-VL. Our approach integrates zero-shot prompting with lightweight heuristic search—requiring no fine-tuning or training. Contribution/Results: We provide the first systematic empirical validation that MLLMs possess intrinsic spatial intelligence and strong zero-shot generalization capability in combinatorial optimization. Evaluated across six diverse graph tasks—including influence maximization and network dismantling—our method significantly outperforms classical solvers while matching the performance of domain-specific algorithms. The results demonstrate human-like intuitive graph understanding, establishing MLLMs as viable, interpretable, and general-purpose solvers for structured combinatorial problems.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Computer Vision: Large Vision Models
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Graph-structured combinatorial challenges are inherently difficult due to their nonlinear and intricate nature, often rendering traditional computational methods ineffective or expensive. However, these challenges can be more naturally tackled by humans through visual representations that harness our innate ability for spatial reasoning. In this study, we propose transforming graphs into images to preserve their higher-order structural features accurately, revolutionizing the representation used in solving graph-structured combinatorial tasks. This approach allows machines to emulate human-like processing in addressing complex combinatorial challenges. By combining the innovative paradigm powered by multimodal large language models (MLLMs) with simple search techniques, we aim to develop a novel and effective framework for tackling such problems. Our investigation into MLLMs spanned a variety of graph-based tasks, from combinatorial problems like influence maximization to sequential decision-making in network dismantling, as well as addressing six fundamental graph-related issues. Our findings demonstrate that MLLMs exhibit exceptional spatial intelligence and a distinctive capability for handling these problems, significantly advancing the potential for machines to comprehend and analyze graph-structured data with a depth and intuition akin to human cognition. These results also imply that integrating MLLMs with simple optimization strategies could form a novel and efficient approach for navigating graph-structured combinatorial challenges without complex derivations, computationally demanding training and fine-tuning.

Problem

• Large Language Models
• Graph Structured Problems
• Enhanced Efficiency

Innovation

• Visualization Technology
• Optimization Algorithm
• Multimodal Large Model