Learn from Global Correlations: Enhancing Evolutionary Algorithm via Spectral GNN

TL;DR

Traditional evolutionary algorithms suffer from limited use of global population correlations and poorly controlled exploration–exploitation balance. Graph Neural Evolution (GNE) reinterprets the evolutionary process as spectral graph filtering by constructing a population graph with adjacency $\mathbf{A}$ and applying a polynomial filter to the normalized Laplacian spectrum $\widehat{\mathbf{L}}$, yielding interpretable control over exploration and exploitation. Empirically, GNE outperforms classical and advanced EAs on nine benchmarks (e.g., Sphere, Rastrigin, Rosenbrock), including under noise and optimum deviations, with notable gains in accuracy and robustness. The approach provides a principled, globally informed EA framework with potential applications in engineering design and neural network optimization, and points to further work in scaling and reducing spectral complexity.

Abstract

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).

Figures (4)

• Figure 1: The relationship between spatial and spectral domain graph neural networks.
• Figure 2: The framework of the proposed GNE method. It begins by constructing the population's adjacency matrix to capture global relationships, which is computed using cosine similarities between individual nodes.The obtained adjacency matrix is further transformed into the graph Laplacian. Through this process, GNE extracts frequency components that characterize population diversity (high-frequency) and consistency (low-frequency). Furthermore, exploration–exploitation balance is achieved by modulating the weights of these frequency components with a polynomial filter, while a sampling function resamples the population in feature space to optimize overall fitness.
• Figure 3: Visualizing the relationship between consistent traits (low-frequency) and diverse traits (high-frequency) in the Boat.
• Figure 4: Comparison of the runtime and Friedman ranking of different algorithms on the benchmark function