Structure-Aware Cooperative Ensemble Evolutionary Optimization on Combinatorial Problems with Multimodal Large Language Models
Jie Zhao, Kang Cheong
While evolutionary algorithms (EAs) have proven effective in exploring the vast solution spaces characteristic of such problems, traditional encoding schemes, such as binary or numerical representations, often fail to capture the intricate structural properties of networks. Through employing image-based encodings 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 representations while maintaining essential structural features. To further enhance robustness and mitigate biases introduced by any single sparsification view, we propose a cooperative evolutionary framework that operates across multiple sparsified variants from diverse structural perspectives to achieve knowledge transfer among various domains. Additionally, acknowledging 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, illustrated through the classical influence maximization task, demonstrate that our approach substantially improves both the quality and resilience of solutions in MLLM-driven evolutionary optimization.