Convergence behaviours of genetic algorithms for aerodynamic optimisation problems

The convergence behaviour of genetic algorithms (GAs) applied to aerodynamic optimisation problems for transonic flows of ideal and dense gases is analysed using a statistical approach. To this purpose, the concept of GA-hardness, i.e., the capability of converging more or less easily toward the global optimum for a given problem, is introduced, as well as a statistical GA-hardness indicator. For GA-hard problems, reduced convergence rate and high sensitivity to the choice of the starting population are observed. The validity of the proposed framework is initially verified for a reference optimisation problem, namely, minimisation of drag over a transonic airfoil. Numerical examples allow to identify sources of GA-hardness for aerodynamic problems. Numerical errors in the representation of the objective function contribute to increase GA-hardness. A simple and effective strategy based on Richardson extrapolation is proposed as a cure to this problem.