Evolutionary algorithms (EAs) are optimization algorithms that simulate natural selection and genetic mechanisms. Despite advancements, existing EAs have two main issues: (1) they rarely update next-generation individuals based on global correlations, thus limiting comprehensive learning; (2) it is challenging to balance exploration and exploitation, excessive exploitation leads to premature convergence to local optima, while excessive exploration results in an excessively slow search. Existing EAs heavily rely on manual parameter settings, inappropriate parameters might disrupt the exploration-exploitation balance, further impairing model performance. To address these challenges, we propose a novel evolutionary algorithm framework called Graph Neural Evolution (GNE). Unlike traditional EAs, GNE represents the population as a graph, where nodes correspond to individuals, and edges capture their relationships, thus effectively leveraging global information. Meanwhile, GNE utilizes spectral graph neural networks (GNNs) to decompose evolutionary signals into their frequency components and designs a filtering function to fuse these components. High-frequency components capture diverse global information, while low-frequency components capture more consistent information. This explicit frequency filtering strategy directly controls global-scale features through frequency components, overcoming the limitations of manual parameter settings and making the exploration-exploitation control more interpretable and effective. Extensive evaluations on nine benchmark functions (e.g., Sphere, Rastrigin, and Rosenbrock) demonstrate that GNE consistently outperforms both classical algorithms (GA, DE, CMA-ES) and advanced algorithms (SDAES, RL-SHADE) under various conditions, including original, noise-corrupted, and optimal solution deviation scenarios. GNE achieves solution quality several orders of magnitude better than other algorithms (e.g., 3.07e-20 mean on Sphere vs. 1.51e-07).

This paper proposes an innovative optimization framework, Dynamic Graph Neural Evolution (DGNE), integrating Graph Neural Networks (GNNs) with Evolutionary Algorithms (EAs). Building on the foundation of Graph Neural Evolution (GNE), DGNE introduces a dynamic filtering mechanism and adaptive Gaussian sampling functions to dynamically adjust the population distribution during the optimization process, achieving a balance between global exploration and local exploitation. By emphasizing high-frequency information in the early stages to enhance population diversity and low-frequency information in the later stages to promote convergence, DGNE effectively optimizes the search process. Experiments were conducted on the CEC2017 benchmark suite across 30, 50, and 100 dimensions, comparing DGNE with advanced algorithms (LSHADE, LSHADE_cnEpSin, MadDE, SaDE, EA4eig) and classic algorithms (DE and CMA-ES). Statistical analyses using the Wilcoxon rank-sum test and Friedman mean rank test demonstrate that DGNE achieves the best average ranking in 50 and 100 dimensions and ranks third in 30 dimensions. However, it achieves the highest overall average performance ranking across all dimensions, showcasing its stability and significant advantages in different scenarios. While its performance in low-dimensional tasks is slightly less competitive compared to high-dimensional ones, DGNE still exhibits strong competitiveness. Additionally, we explored the impact of population size. DGNE was evaluated across population sizes of 20, 30, 50, and 100. The results highlight DGNE’s robustness, maintaining competitive rankings across all population sizes, with top rankings for smaller population sizes (20 and 30) and strong results at larger sizes (50 and 100). These findings confirm DGNE’s adaptability to varying configurations and further validate its effectiveness as a robust optimization framework. Overall, DGNE demonstrates great potential as an optimization method, offering a promising direction for further research and applications in artificial intelligence and optimization fields. Its ability to remain competitive across diverse tasks and configurations underscores its versatility and scalability.