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 analyzed 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. To check the validity of the proposed framework, a reference single-objective optimisation problem, namely, wave drag minimization for a non-lifting transonic flow past a symmetric airfoil is considered. Several optimisations runs are performed at different flow conditions using a GA coupled with a compressible flow solver. The results show that GA-hardness is greater for flow problems characterized by very weak shocks, and is strongly affected by numerical inaccuracies in the evaluation of the objective function. Then, some possible cures to GA-hardness are proposed and numerically verified. An efficient objective-function evaluation procedure based on Richardson extrapolation is introduced, which drastically reduces GA-hardness with a very moderate increase (and sometimes a slight decrease) in computational cost of optimisation runs. Finally, an application of the proposed strategy to a multi-objective optimisation problem is provided, clearly demonstrating the advantages deriving by the use of the proposed technique.