Multi-objective airfoil shape optimization using an adaptive hybrid evolutionary algorithm

Abstract

In this study, multi-objective aerodynamic optimization problems were conducted with a hybrid evolutionary-adaptive directional local search method for convergence enhancement. The directional search operator includes selection of search direction and one-dimensional search. Probability for the directional operator is adaptively changed based on relative effectiveness of the directional search operator and evolutionary operators such as crossover and mutation. The adaptive directional operator is combined with a baseline evolutionary multi-objective algorithm (EMOA) such as NSGA-II or MOGA. Multi-objective airfoil shape optimization examples are defined as drag minimization/lift maximization and L/D maximization at high lift and cruise conditions in subsonic and transonic regimes. The CST method and the B-spline method were used for airfoil shape parameterization. Design examples with drag minimization and L/D maximization at cruise conditions are all found to have uni-modal design spaces, and the local search operator is effective for those examples. However, lift maximization and high angle of attack cases show multi-modality in the design spaces due to flow separations and thus the local search is not effective for those cases. Design results show that the adaptive directional search method significantly enhances convergence of problems in which the directional search is effective, and also minimizes unnecessary spending of computational budget for cases in which the directional search does not produce competitive solutions. The present method improves search performance for different airfoil parameterization methods and different baseline EMOAs. Statistical tests confirm that the adaptive hybrid method is superior to the baseline EMOA.