Design of a matrix hydraulic turbine using a metamodel-assisted evolutionary algorithm with PCA-driven evolution operators
by Stylianos A. Kyriacou; Simon Weissenberger; Kyriakos C. Giannakoglou
International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO), Vol. 3, No. 1/2, 2012

Abstract: To overcome the excessive CPU cost of evolutionary algorithms (EAs) which make use of demanding evaluation models, metamodel-assisted EAs (MAEAs) have been devised and used in either single-objective (SOO) or multi-objective (MOO) problems. MAEAs are based on low-cost surrogate evaluation models that screen out non-promising individuals during the evolution and exclude them from the expensive, problem-specific evaluation. This paper proposes a new technique that further reduces the computational cost of MAEAs. This technique is based on the principal-component-analysis (PCA) of the non-dominated individuals (in MOO) within each generation, to identify dependences among the design variables and, through appropriate rotations, use this piece of information to efficiently 'drive' the application of the evolution operators. The proposed technique is used to perform the multi-operating point design of a matrix hydraulic turbine, where each evaluation is based on a 3D computational fluid dynamics (CFD) code; this is a highly constrained optimisation problem with many objectives, which is herein handled as a two-objective one. Some convincing mathematical function minimisation problems are also worked out using PCA-driven EAs; it is, thus, shown that the PCA-driven evolution operators can be used with or without metamodels.

Online publication date: Wed, 20-Aug-2014

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