Evolutionary multi-objective optimization assisted by metamodels, kernel PCA and multi-criteria decision making techniques with applications in aerodynamics

Abstract

This paper presents two methods which aim at improving the efficiency of evolutionary algorithms (EAs) and metamodel-assisted EAs (MAEAs) used to solve multi-objective optimization problems with computationally expensive evaluation tools. The EAs and MAEAs are accelerated by implementing the kernel principal component analysis (KPCA) during: (a) the application of the evolution operators, by processing the population members in a new/feature, rather than the standard design, space and/or (b) the metamodel training, to reduce the number of input units and, thus, get more accurate predictions. Over and above, a variant of EA (or MAEA) which takes the decision maker's (DM) preferences into consideration during the evolution is proposed. In contrast to standard multi-objective EAs which may insufficiently populate the preferred area(s) of the objective space, more non-dominated solutions are now driven towards them. This is achieved by using the multi-criteria decision making (MCDM) Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), which affects the parent selection and the non-dominated front trimming operators. The combined use of KPCA and TOPSIS is implemented, too. The proposed methods are evaluated by solving two computationally demanding aerodynamic shape optimization problems, with two objectives each.