桥接可视化与优化：多模态大语言模型在图结构组合优化中的应用
Bridging Visualization and Optimization: Multimodal Large Language Models on Graph-Structured Combinatorial Optimization
AI总结：
本研究提出将图转换为图像，结合多模态大语言模型与简单搜索技术，以解决图结构组合优化问题，实验表明该方法具备卓越空间智能，可高效处理多种图任务。
摘要：
图结构组合挑战因其非线性和复杂性而固有地难以解决，往往使传统计算方法效率低下或成本高昂。然而，这些挑战可以通过视觉表示更自然地由人类处理，利用我们与生俱来的空间推理能力。在本研究中，我们提出将图转换为图像以准确保留其高阶结构特征，从而革新用于解决图结构组合任务的表示方式。这种方法使机器能够模拟人类在处理复杂组合挑战时的处理方式。通过将多模态大语言模型（MLLMs）驱动的创新范式与简单搜索技术相结合，我们旨在开发一种新颖且有效的框架来解决此类问题。我们对MLLMs的调查研究涵盖了多种基于图的任务，从影响力最大化等组合问题到网络瓦解中的序列决策，以及解决六个基本的图相关问题。我们的研究结果表明，MLLMs表现出卓越的空间智能和独特的问题处理能力，显著提升了机器以类似人类认知的深度和直觉来理解和分析图结构数据的潜力。这些结果还表明，将MLLMs与简单优化策略相结合，可以形成一种无需复杂推导、计算上昂贵的训练和微调即可导航图结构组合挑战的新颖高效方法。
英文摘要：
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.
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