Evaluating the Risk of Local Optima in Aerodynamic Shape Optimization

Abstract

A gradient-based multistart method based on a set of 17 to 33 random initial geometries is used to examine the risk associated with multimodality when applying gradient-based optimization to aerodynamic shape optimization. Aerodynamic shape optimization problems typical of detailed, preliminary, and exploratory design are shown to consistently present design spaces with multiple local optima. In the case of detailed design, the risk of converging to a local optimum with performance significantly inferior to that of the best local optimum found is reduced due to the ability of a well-designed initial geometry, which is often available for such problems, to converge to a well-performing local optimum. In problems permitting increased geometric freedom typical of preliminary design, the risk associated with multimodality is much higher. This risk is further exacerbated in exploratory cases where high geometric freedom is combined with limited knowledge of the design space in question and hence greater differences between available initial geometries and the optimal geometry. Therefore, for preliminary and exploratory design, allocating resources toward addressing multimodality can significantly reduce the risk of overlooking a superior optimum.