Convergence behaviours of genetic algorithms for aerodynamic optimisation problems
Paola Cinnella, Pietro Marco Congedo · International Journal of Engineering Systems Modelling and Simulation · 2013
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.