| This work focuses on an investigation of multi-modality in typical aerodynamic shape optimization problems and development of optimization algorithms that can find a global optimum. First, a classification of problems based on the degree of multi-modality is introduced. Then, two optimization algorithms are described that can find a global optimum in a computationally efficient manner: a gradient-based multi-start Sobol algorithm, and a hybrid optimization algorithm. Two additional algorithms are considered as well: a gradient-based optimizer and a genetic algorithm. Finally, we consider a set of typical aerodynamic shape optimization problems. In each problem, the primary objectives are to classify the problem according to the degree of multi-modality, and to select the preferred optimization algorithm for the problem. We find that typical two-dimensional airfoil shape optimization problems are unimodal. Three-dimensional shape optimization problems may contain local optima. In these problems, the gradient-based multi-start Sobol algorithm is the most efficient algorithm. |
