Title: Convergence behaviours of genetic algorithms for aerodynamic optimisation problems

Authors: Paola Cinnella; Pietro Marco Congedo

Addresses: Arts et Métiers ParisTech, Laboratoire DynFluid, 151 bd de l'Hopital, France ' Team Bacchus, INRIA Bordeaux Sud-Ouest, 351, cours de la Libération, 33405 Talence Cedex, France

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.

Keywords: transonic aerodynamics; shape optimisation; genetic algorithms; GA hardness; numerical errors; convergence behaviour; aerodynamic optimisation; transonic flows; ideal gases; dense gases; drag minimisation; transonic airfoils.

DOI: 10.1504/IJESMS.2013.056782

International Journal of Engineering Systems Modelling and Simulation, 2013 Vol.5 No.4, pp.197 - 216

Published online: 30 Aug 2014 *

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