Learn from Global Correlations: Enhancing Evolutionary Algorithm via Spectral GNN
This addresses optimization problems for researchers and practitioners by improving evolutionary algorithms, though it is incremental as it builds on existing methods with a novel hybrid approach.
The paper tackles limitations in evolutionary algorithms, such as poor global correlation usage and exploration-exploitation imbalance, by proposing Graph Neural Evolution (GNE), which uses spectral GNNs to filter frequency components for better control, achieving solutions several orders of magnitude better on benchmark functions (e.g., 3.07e-20 mean on Sphere vs. 1.51e-07).
Evolutionary algorithms (EAs) simulate natural selection but have two main limitations: (1) they rarely update individuals based on global correlations, limiting comprehensive learning; (2) they struggle with balancing exploration and exploitation, where excessive exploitation causes premature convergence, and excessive exploration slows down the search. Moreover, EAs often depend on manual parameter settings, which can disrupt the exploration-exploitation balance. To address these issues, we propose Graph Neural Evolution (GNE), a novel EA framework. GNE represents the population as a graph, where nodes represent individuals, and edges capture their relationships, enabling global information usage. GNE utilizes spectral graph neural networks (GNNs) to decompose evolutionary signals into frequency components, applying a filtering function to fuse these components. High-frequency components capture diverse global information, while low-frequency ones 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 manageable. Tests on nine benchmark functions (e.g., Sphere, Rastrigin, Rosenbrock) show that GNE outperforms classical (GA, DE, CMA-ES) and advanced algorithms (SDAES, RL-SHADE) under various conditions, including noise-corrupted and optimal solution deviation scenarios. GNE achieves solutions several orders of magnitude better (e.g., 3.07e-20 mean on Sphere vs. 1.51e-07).