International Congress on Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems EUROGEN 2003 G. Bugeda, J.A.- D´ esid´ eri, J. Periaux, M. Schoenauer and G. Winter (Eds) c CIMNE, Barcelona, 2003 EXPERIMENTS WITH HYBRIDIZED GENETIC ALGORITHMS IN AERODYNAMICS Y. Berard, J-A. D´ esid´ eri, A. Habbal, A. Janka, L. Oulladji OPALE Project INRIA Sophia Antipolis 2004 route des Lucioles, BP 93 F–06902 Sophia Antipolis (France) Jean-Antoine.Desideri@sophia.inria.fr Abderrahmane.Habbal@sophia.inria.fr Key words: discrete functional gradient, genetic algorithm, lift and drag, supersonic bang, hybridization, clustering Abstract. This article is made of two parts. In the first, we solve an optimum shape design problem in aerodynamics. In the supersonic regime, we minimize a functional blending lift and drag constraints with a bang criterion and a geometrical penalty. The algorithm is a standard hybridization strategy consisting of operating a gradient-based op- timizer after a search by a genetic algorithm. This basic technique combines the robustness of genetic algorithms with the quality of convergence of a gradient-based method. In the second part, we report on our experiments with a technique of clustering used to construct a hybridized optimization method that we have applied to test problems de- fined by specified mathematical cost functionals. The aim of this technique is to reduce substantially the computational cost of fitness evaluations for individuals in a standard genetic algorithm. We use exact evaluation just for a few typical representants of the population (master individuals). The fitness of other individuals is being interpolated by a Taylor expansion using the values on master individuals together with their first deriva- tives. Presented numerical experiments for minimizing analytical functions in 2D clearly illustrate the advantage of the hybrid method over a classical genetic algorithm. Not only we reduced the computational cost of the optimization, but also we were able to better detect multiple global minima. 1