Evolutionary algorithms (EAs) have proven effective in exploring the vast solution spaces typical of graph-structured combinatorial problems. However, traditional encoding schemes, such as binary or numerical representations, often fail to straightforwardly capture the intricate structural properties of networks. Through employing the image-based encoding to preserve topological context, this study utilizes multimodal large language models (MLLMs) as evolutionary operators to facilitate structure-aware optimization over graph data. To address the visual clutter inherent in large-scale network visualizations, we leverage graph sparsification techniques to simplify structures while maintaining essential structural features. To further improve robustness and mitigate bias from different sparsification views, we propose a cooperative evolutionary optimization framework that facilitates cross-domain knowledge transfer and unifies multiple sparsified variants of diverse structures. Additionally, recognizing the sensitivity of MLLMs to network layout, we introduce an ensemble strategy that aggregates outputs from various layout configurations through consensus voting. Finally, experiments on real-world networks through various tasks demonstrate that our approach improves both the quality and reliability of solutions in MLLM-driven evolutionary optimization.

翻译：进化算法（EAs）已被证明在探索图结构组合问题典型的广阔解空间方面具有有效性。然而，传统的编码方案（如二进制或数值表示）往往无法直观地捕捉网络的复杂结构特性。本研究通过采用基于图像的编码来保留拓扑上下文，利用多模态大语言模型（MLLMs）作为进化算子，以促进对图数据的结构感知优化。针对大规模网络可视化中固有的视觉杂乱问题，我们利用图稀疏化技术来简化结构，同时保持关键的结构特征。为了进一步提高鲁棒性并减轻不同稀疏化视角带来的偏差，我们提出了一种协同进化优化框架，该框架促进了跨领域知识迁移，并统一了多样结构的多个稀疏化变体。此外，认识到MLLMs对网络布局的敏感性，我们引入了一种集成策略，通过共识投票聚合来自不同布局配置的输出。最后，通过多种任务在真实世界网络上的实验表明，我们的方法在MLLM驱动的进化优化中提高了解决方案的质量和可靠性。