Structure-Aware Cooperative Ensemble Evolutionary Optimization on Combinatorial Problems with Multimodal Large Language Models

2025-10-24

AI Summary

Traditional evolutionary algorithms for graph-structured combinatorial optimization suffer from inadequate encoding of topological properties; large-scale network visualizations become cluttered and uninformative; and multimodal large language models (MLLMs) exhibit layout sensitivity, undermining optimization robustness. Method: We propose a structure-aware, MLLM-driven cooperative evolutionary framework. It (i) encodes graphs as topology-preserving images; (ii) integrates graph sparsification with multi-layout ensemble generation to produce complementary sparse visual representations; and (iii) employs MLLMs as learnable evolutionary operators, leveraging consensus voting across layouts to enable robust, structure-guided search. Results: Experiments on real-world network datasets demonstrate significant improvements in solution quality and optimization stability over conventional encoding schemes and single-layout MLLM-based baselines.

Technology Category

• Search and Optimization: Evolutionary Computation
• Machine Learning: Graph-based Machine Learning
• Planning, Routing, and Scheduling: Planning with Language Models

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
• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work

Abstract

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.

Problem

• Optimizing graph problems using multimodal language models as evolutionary operators
• Addressing visual clutter in networks through graph sparsification techniques
• Improving solution reliability with ensemble strategies across layout configurations

Innovation

• Uses multimodal LLMs as evolutionary operators
• Leverages graph sparsification to simplify structures
• Introduces ensemble strategy with layout consensus voting