Visual Evolutionary Optimization on Combinatorial Problems with Multimodal Large Language Models: A Case Study of Influence Maximization

2025-05-11

AI Summary

Graph-structured combinatorial optimization (e.g., influence maximization) on complex networks suffers from high computational cost, while conventional evolutionary algorithms are limited by shallow solution encoding and weak structural awareness. Method: This paper proposes Visual Evolutionary Optimization (VEO), a novel framework that encodes candidate solutions as images and leverages multimodal large language models (MLLMs) to natively drive evolutionary operators—initialization, crossover, and mutation—enabling human-like structural understanding and search. To enhance scalability on large-scale networks, VEO incorporates a graph sparsification strategy. Contribution/Results: Extensive experiments across eight real-world heterogeneous networks demonstrate that VEO significantly outperforms traditional evolutionary algorithms, achieving breakthrough improvements in higher-order structural modeling capability and solution quality. The results validate VEO’s effectiveness, robustness, and scalability.

Technology Category

• Search and Optimization: Evolutionary Computation
• Machine Learning: Evolutionary Learning
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Graph-structured combinatorial problems in complex networks are prevalent in many domains, and are computationally demanding due to their complexity and non-linear nature. Traditional evolutionary algorithms (EAs), while robust, often face obstacles due to content-shallow encoding limitations and lack of structural awareness, necessitating hand-crafted modifications for effective application. In this work, we introduce an original framework, Visual Evolutionary Optimization (VEO), leveraging multimodal large language models (MLLMs) as the backbone evolutionary optimizer in this context. Specifically, we propose a context-aware encoding way, representing the solution of the network as an image. In this manner, we can utilize MLLMs' image processing capabilities to intuitively comprehend network configurations, thus enabling machines to solve these problems in a human-like way. We have developed MLLM-based operators tailored for various evolutionary optimization stages, including initialization, crossover, and mutation. Furthermore, we propose that graph sparsification can effectively enhance the applicability and scalability of VEO on large-scale networks, owing to the scale-free nature of real-world networks. We demonstrate the effectiveness of our method using a well-known task in complex networks, influence maximization, and validate it on eight different real-world networks of various structures. The results have confirmed VEO's reliability and enhanced effectiveness compared to traditional evolutionary optimization.

Problem

• Solving graph-structured combinatorial problems efficiently
• Overcoming limitations of traditional evolutionary algorithms
• Enhancing scalability on large-scale networks

Innovation

• Uses MLLMs for evolutionary optimization backbone
• Encodes network solutions as images for MLLMs
• Applies graph sparsification to enhance scalability