Development of efficient global optimization method for discontinuous optimization problems with infeasible regions using classification method

Abstract

The objective of this research is to efficiently solve discontinuous optimization problems as well as optimization problems with large infeasible regions in the design variables space. Recently, major optimization targets have been changed to more complicated ones such as topology optimization problem, discontinuous optimization problem, robust optimization problem and high dimensional optimization problem. The aim of this research is to efficiently solve the complicated optimization problems by using machine learning technologies. In aerodynamic optimization problems at supersonic flow conditions, it is confirmed that aerodynamic objective functions have discontinuity due to shock waves and it needs to treat the discontinuous functions and large infeasible regions via strong shock waves. In this research, therefore, we develop an efficient global optimization method for discontinuous optimization problems with infeasible regions using classification method (EGODISC). The developed method is compared with a Bayesian optimization method using the Matern 5/2 kernel Gaussian process regression and a genetic algorithm to verify the usefulness of the developed method. The Bayesian optimization falls into an infinite loop in its optimization process by selecting an additional sample point in the infeasible regions. On the other hand, the developed method can work well with the infeasible regions in the design variables space. It is confirmed that EGODISC can be effectively used with discontinuous aerodynamic objective functions. It is also confirmed that EGODISC can be effectively used for a shape optimization problem with large infeasible regions by the negative thickness of airfoil.