Hierarchical Surrogate-Assisted Evolutionary Multi-Scenario Airfoil Shape Optimization

For multi-scenario airfoil shape optimization problems, an evaluation of a single airfoil is based on its full-scenario drag landscape. To obtain the full-scenario drag landscape, a large number of computational fluid dynamic simulations for different operating conditions must be conducted. Since a single computational fluid dynamic simulation is often time-consuming, evaluations for multi-scenario airfoil shape optimization will be computationally highly intensive. Although surrogate-assisted evolutionary algorithms have been widely applied to expensive optimization problems, existing surrogate-assisted evolutionary algorithms cannot be directly applied to multi-scenario airfoil shape optimization due to the lack of training data. Instead of using surrogate models to directly approximate the multi-scenario evaluations, we employ a hierarchical surrogate model consisting of a K-nearest neighbors classifier and a Kriging model to approximate the full-scenario drag landscape for each candidate design during the optimization. Then, the fitness of the candidate design is evaluated based on the approximated drag landscape to reduce the computational cost. The proposed hierarchical surrogate model is embedded in the covariance matrix adaptation evolution strategy and applied to the RAE2822 airfoil design problem. Our experimental results show that the proposed algorithm is able to obtain an airfoil design with limited computational cost that perform well in different operating conditions.