Efficient global optimization method via clustering/classification methods and exploration strategy

Abstract

The objective of this research is to efficiently solve complicated high dimensional optimization problems by using machine learning technologies. Recently, major optimization targets have been changed to more complicated ones such as discontinuous and high dimensional optimization problems. It is necessary to solve the high-dimensional optimization problems to obtain an innovate design from topology design optimizations that have enormous numbers of design variables in order to express various topologies/shapes. In this research, therefore, an efficient global optimization method via clustering/classification methods and exploration strategy (EGOCCS) is developed to efficiently solve the high dimensional optimization problems without using probabilistic values as standard deviation, that are generally given/utilized in Gaussian process, and to reduce the construction cost of response surface models. Two optimization problems are solved to verify the usefulness of the developed method of EGOCCS. First optimization is executed to demonstrate the validity of the EGOCCS in 2, 10, 40, 80 and 160-dimensional analytic function problems that are also solved by the Bayesian optimization for comparison purposes. It is confirmed that the EGOCCS with radial basis function interpolation approach can obtain the best solutions in many analytic function problems with larger numbers of design variables. Second optimization is executed to examine the effect of the EGOCCS in high dimensional aerodynamic shape optimization problems for a two-dimensional biconvex airfoil that are also solved by a genetic algorithm for comparison purposes. It is confirmed that the EGOCCS can be efficiently used in the high dimensional aerodynamic shape optimization problems.