Research of multi-point infill criteria based on multi-objective optimization front and its application on aerodynamic shape optimization

Abstract

In this article, efficient multi-point infill criteria based on multi-objective optimization front and its applications on analytic functions and airfoil aerodynamic shape optimization are researched. In the expensive optimization, an excellent infill algorithm should meet the demand of local exploitation and global exploration at the same time, which stand for the optimization accuracy and efficiency, respectively. In the proposed infill criteria, the predicted value and a statistic variable are chosen as objectives to implement optimization, and the obtained front stands for the points which strike a balance between local optimization accuracy and global optimization efficiency. The test results of four analytic functions, which has 2 to 20 variables, show that compared with expected improvement algorithm, the proposed multi-point infill algorithm can save 85% iteration times, so the computation efficiency could be increased remarkably. The airfoil optimization design is adopted to test the validity and efficiency of the proposed infill criteria. In the airfoil optimization design, the computational fluid dynamic method is employed to obtain the aerodynamic forces of airfoils, and the Kriging surrogate model is introduced to reduce the computational cost. The global optimization is implemented by adopting multi-objective evolutionary algorithm based on decomposition as optimization algorithm, and the drag coefficient and section area of the airfoil are taken as optimization objectives. The proposed infill method and expected improvement method are employed to implement the optimization design process. With roughly equal times of aerodynamic computation, both of the algorithms can obtain the reliable Pareto front; however, the number of infill iteration of proposed infill method is only 17% of that of expected improvement method.