arXiv:2412.17629cs.NEcs.AI2024-12AAAI被引 36

用图神经网络捕捉全局关联,让进化算法更智能地平衡探索与利用。

Learn from Global Correlations: Enhancing Evolutionary Algorithm via Spectral GNN

  • 将种群建模为图,通过频谱GNN分解并过滤进化信号
  • 在球函数上平均解达3.07e-20,比传统算法优数个数量级
  • 无需手动调参,适合需自动调节的复杂优化场景

进化算法(EAs)模拟自然选择,但存在两大局限:一是极少基于全局关联更新个体,限制了全面学习;二是难以平衡探索与利用,过度利用导致早熟收敛,过度探索则降低搜索速度。此外,EAs常依赖人工调参,易破坏平衡。为此,提出图神经进化(GNE)框架。GNE将种群表示为图,节点为个体,边刻画其关系,实现全局信息利用。采用谱图神经网络(GNN)将进化信号分解为频率成分,通过滤波函数融合:高频成分捕捉多样全局信息,低频成分反映一致信息。该显式频率滤波策略直接通过频率控制全局特征,克服人工调参缺陷,使探索-利用控制更可解释、易管理。在九个基准函数(如Sphere、Rastrigin、Rosenbrock)上的测试表明,GNE在噪声干扰及最优解偏移等条件下均优于经典(GA、DE、CMA-ES)和先进算法(SDAES、RL-SHADE)。例如,在Sphere函数上平均解达3.07e-20,远超传统算法的1.51e-07。

原文摘要 · Abstract (English)

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).

进化算法图神经网络优化自适应

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