Multimodality and Global Optimization in Aerodynamic Design
Two optimization algorithms are presented that are capable of finding a global optimum in a computationally efficient manner: a gradient-based multistart algorithm based on Sobol sampling and a hybrid optimizer combining a genetic algorithm with a gradient-based algorithm. The optimizers are used to investigate multimodality in aerodynamic-shape-optimization problems. The performance of each algorithm is tested on an analytical test function as well as several aerodynamic-shape-optimization problems in two and three dimensions. In each problem the primary objectives are to classify the problem according to the degree of multimodality and to identify the preferred optimization algorithm for the problem. The results show that multimodality should not always be assumed in aerodynamic-shape-optimization problems. Typical two-dimensional airfoil-optimization problems are unimodal. Three-dimensional shape-optimization problems may contain local optima. The number of local optima tends to increase with increasin...