核主成分分析在进化优化中对计算要求高的工程应用的应用

D. Kapsoulis, K. Tsiakas, V. Asouti, K. Giannakoglou
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引用次数: 11

摘要

本文提出了两种进一步提高进化算法(EAs)效率的技术,即使这些技术已经通过实现替代评估模型或元模型来克服大量昂贵的评估,也可以提高进化算法的效率。两者都依赖于设计空间的核主成分分析(核PCA或KPCA)的使用,因为这反映了每一代的后代种群。PCA确定了一个特征空间,在这个空间中应该更好地应用进化算子。此外,在元模型辅助EA (maea)中,PCA可以减少元模型的感觉单元数量。由于后者,元模型能更好地逼近目标函数值。本文扩展了作者先前基于线性PCA的工作,用于相同的目的。在本文中,使用核(而不是线性)PCA的优越性,特别是在实际应用中,被证明。在单目标和双目标数学优化问题中对所提出的方法进行了评估,最后在计算成本昂贵的评估软件中对气动形状优化问题进行了展示。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The use of Kernel PCA in evolutionary optimization for computationally demanding engineering applications
Two techniques to further enhance the efficiency of Evolutionary Algorithms (EAs), even those which have already been accelerated by implementing surrogate evaluation models or metamodels to overcome a great amount of costly evaluations, are presented. Both rely upon the use of a Kernel Principal Component Analysis (Kernel PCA or KPCA) of the design space, as this reflects upon the offspring population in each generation. The PCA determines a feature space where the evolution operators should preferably be applied. In addition, in Metamodel-Assisted EA (MAEAs), the PCA can reduce the number of sensory units of metamodels. Due to the latter, the metamodels yield better approximations to the objective function value. This paper extends previous work by the authors which was based on Linear PCA, used for the same purposes. In the present paper, the superiority of using the Kernel (rather than the Linear) PCA, especially in real-world applications, is demonstrated. The proposed methods are assessed in single- and two-objective mathematical optimization problems and, finally, showcased in aerodynamic shape optimization problems with computationally expensive evaluation software.
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