Visual Evolutionary Optimization on Graph-Structured Combinatorial Problems with MLLMs: A Case Study of Influence Maximization

TL;DR

This paper introduces visual evolutionary optimization (VEO), a novel framework that uses multimodal large language models to solve complex graph-structured problems by representing solutions as images, improving scalability and effectiveness.

Contribution

The work presents a new VEO framework leveraging MLLMs with a context-aware image encoding scheme for graph problems, enhancing structural understanding and scalability.

Findings

VEO outperforms traditional evolutionary algorithms in influence maximization tasks.

Graph sparsification improves VEO's scalability on large networks.

VEO demonstrates high reliability across diverse real-world networks.

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 scheme, 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 develop 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 confirm VEO's reliability and enhanced effectiveness compared to traditional evolutionary optimization.