The use of Kernel PCA in evolutionary optimization for computationally demanding engineering applications

Abstract

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.