用图神经网络预测优化算法性能，比传统方法更准。
Geometric Learning in Black-Box Optimization: A GNN Framework for Algorithm Performance Prediction
- 构建包含问题、配置、性能的异构图结构建模复杂关系。
- 在24个BBOB问题上测试324种modCMA-ES和576种modDE变体。
- 相比表格式方法，均方误差降低36.6%，适合算法开发者使用。
黑盒优化中的自动化算法性能预测通常依赖于问题特征（如探索性景观分析特征），这些特征以表格形式输入机器学习模型。然而，这类方法常忽略算法配置这一关键影响因素。算法算子、参数、问题特性与性能结果之间的关系构成复杂结构，更适合用图表示。本文探索使用异构图数据结构与图神经网络，通过捕捉问题、算法配置与性能结果间的复杂依赖关系来预测优化算法性能。研究聚焦两个模块化框架：modCMA-ES 和 modDE，它们分别分解了两种广泛应用的无导数优化算法——协方差矩阵自适应进化策略（CMA-ES）与差分进化（DE）。我们在6种运行时预算、2种问题维度下，对324种modCMA-ES和576种modDE变体在24个BBOB问题上进行评估。结果显示，该方法在均方误差（MSE）上相较传统表格方法最高提升36.6%，凸显几何学习在黑盒优化中的潜力。
原文摘要 · Abstract (English)
Automated algorithm performance prediction in numerical blackbox optimization often relies on problem characterizations, such as exploratory landscape analysis features. These features are typically used as inputs to machine learning models and are represented in a tabular format. However, such approaches often overlook algorithm configurations, a key factor influencing performance. The relationships between algorithm operators, parameters, problem characteristics, and performance outcomes form a complex structure best represented as a graph. This work explores the use of heterogeneous graph data structures and graph neural networks to predict the performance of optimization algorithms by capturing the complex dependencies between problems, algorithm configurations, and performance outcomes. We focus on two modular frameworks, modCMA-ES and modDE, which decompose two widely used derivative-free optimization algorithms: the covariance matrix adaptation evolution strategy (CMA-ES) and differential evolution (DE). We evaluate 324 modCMA-ES and 576 modDE variants on 24 BBOB problems across six runtime budgets and two problem dimensions. Achieving up to 36.6% improvement in MSE over traditional tabular-based methods, this work highlights the potential of geometric learning in black-box optimization.
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