Convergence behaviours of genetic algorithms for aerodynamic optimisation problems Online publication date: Sat, 30-Aug-2014
by Paola Cinnella; Pietro Marco Congedo
International Journal of Engineering Systems Modelling and Simulation (IJESMS), Vol. 5, No. 4, 2013
Abstract: 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.
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