Design of a matrix hydraulic turbine using a metamodel-assisted evolutionary algorithm with PCA-driven evolution operators

The Objective Space and the Formulation of Design Requirement in Natural Laminar Flow Optimization

“…PCA can solve that problem by providing new linear combinations of the original variables representing orthogonal eigenvectors of principal component axes in space, each of which with different variances [23,24]. The first principal component is associated with the largest variance, and the following ones are perpendicular to the previous ones [52].…”

Efficient PCA-driven EAs and metamodel-assisted EAs, with applications in turbomachinery

“…In Single-Objective Optimization (SOO) problems, the Pareto front can be replaced by an elite set formed by the current optimal and a few near-optimal solutions. The result of the principal components analysis, as applied in this article, is used (a) to guide the application of evolution operators which, with the new design space coordinates resulting from the last PCA, has been proved (Kyriacou, Weissenberger, and Giannakoglou 2012) to improve the performance of the EA and (b) to reduce the dimension of the problem during the training of metamodels which possess a much smaller number of sensory units. The latter, along with the fact that the use of metamodels starts much earlier, leads to much better performing MAEAs (or EAs).…”

Low-cost metamodel-assisted evolutionary algorithms with applications in shape optimization in fluid dynamics

“…Linear PCA The PCA can be either Linear (LPCA) or Kernel (KPCA). EAs and MAEAs assisted by LPCA were firstly presented in [113] and [114]. The covariance matrix (P) for the LPCA is computed as P N ×N = 1 M BB T , where M is the number of observations (herein, the number of offspring, M = λ) and N the number of design variables.…”