21st Congress of International Council of the Aeronautical Sciences, Melbourne, Australia, 13-18 September, 1998
Paper ICAS-98-2.9.1

MULTI-OBJECTIVE STRATEGIES FOR COMPLEX OPTIMIZATION PROBLEMS IN AERODYNAMICS USING GENETIC ALGORITHMS

Periaux J., Sefrioui M.*, Montel B.
Dassault Aviation, France; * Universite Paris VI, France

Keywords: multi-objective strategies,complex optimization problems, aerodynamics, genetic algorithms

Deterministic optimizers are powerful tools for solving optimization problems dealing with smooth, unimodal objective functions. They require few objective function evaluations, particularly if compared to stochastic optimization methods. However, deterministic methods face serious problems for search spaces with rugged landscapes. Genetic Algorithms (GAs) are a stochastic derivative-free search procedures running on a natural selection mode. A decisive advantage for Gas in complex industrial environment is robustness and simplicity. Indifference to problem specifics, codings of decision variables, process of population, randomized crossover and mutation operators are the main characteristics which contribute to the robustness of Gas. There are three main sections in this paper. The first section introduces the fundamentals of (1) genetic algorithms with binary or floating point codings and (2) game theory and multiple objective optimization (cooperative and no cooperative) . The second section presents two CFD applications: inverse problem in optimum shape design for a transonic Euler flow condition using Bezier spline parametrization of the airfoil population and lift maximization for a multielement landing configuration. The third section deals with single and multi objective optimization of scattered waves by active control elements. The problem in finding optimal distribution of active control elements in order to minimize the RCS of perfectly conducting reflectors Electromagnetics. Both problems are solved by means of Genetic Algorithms via a fitness evaluation through the solution of the Maxwell equations corresponding to the RCS of the radar illumination. Pareto and Nash solutions are computed and compared using a combination of Gas and Games Theory. It is shown through numerical experiments that Nash Gas are faster and more robust than Pareto Gas, although Pareto solutions are better.

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