A hierarchical optimization strategy based on cluster characteristics for aerodynamic shape optimization

As an efficient method for aerodynamic shape optimization, the performance of hierarchical optimization strategy largely depends on the convergence criteria for non-final layers and the selection of the design space for the next layer. This paper proposes an efficient hierarchical optimization strategy based on cluster characteristics for aerodynamic shape optimization, aiming to enhance optimization efficiency while maintaining desirable results. In the proposed strategy, a convergence criterion based on the convergence characteristics of clusters (also called populations) is used to effectively identify the termination point for each non-final layer. In addition, a dynamic adjustment method redefines the design space for the next layer based on convergence results from the current non-final layer, directing the search towards the potential optimal region. The proposed strategy is validated using two test functions and two typical cases: airfoil drag reduction optimization and inverse design. Compared to traditional optimization methods, it demonstrates high efficiency in these aerodynamic optimization problems while yielding comparable results. Specifically, the overall optimization efficiency is improved by 75.67 % in the drag reduction case and 67.79 % in the inverse design space.