Multi-point Airfoil Optimization Using Evolution Strategies

The considered multi-point (multi-objective) optimization problem is characterized by a multi-modal, nonlinear topology and a highly sophisticated evaluation of the objective function, thus requiring an efficient, direct global optimization algorithm. Evolution strategies have shown their capabilities for solving complex optimization problems with continuous variables in a variety of applications. This paper reports on the application of evolution strategies to an airfoil optimization problem. The objective function which holds for this test case is described by the difference in pressure described for the different design points of an airfoil compared to predefined airfoil shapes and the corresponding pressure distribution. The design conditions for the two-point optimization problem involve a typical subsonic high-lift and a typical transonic low-drag airfoil. In particular, results for different algorithmic variants are presented. Some emphasis is put on the reduction of the number of function evaluations required for the algorithm. The results will include an assessment according to the influence of different geometryparameterization strategies and the dependence of CFD mesh fineness. The CFD analysis utilized a full Reynolds-averaged Navier-Stokes approach in order to achieve an accurate prediction of the different flow types involved.