Combining game theory and genetic algorithms with application to DDM-nozzle optimization problems

The goal of this paper is to discuss a new evolutionary strategy for the multiple objective design optimization of internal aerodynamic shape operating with transonic flow. The distributed optimization strategy discussed here and inspired from Lions' new distributed control approach (J.L. Lions, Distributed active control approach for pde systems, Fourth WCCM CD-ROM, Buenos Aires, Argentina, 1998) relies on genetic algorithms (GAs). GAs are different from traditional optimization tools and based on digital imitation of biological evolution. Game theory replaces here a global optimization problem by a non-cooperative game based on Nash equilibrium with several players solving local constrained sub-optimization tasks. The transonic flow simulator uses a full potential solver taking advantage of domain decomposition methods and GAs for the matching of non-linear local solutions. The main idea developed here is to combine domain decomposition methods for the flow solver with the geometrical optimization procedure using local shape parameterization. Numerical results are presented for a simple nozzle inverse problem with subsonic and transonic shocked flows. A comparison of the nozzle reconstruction using domain decomposition method (DDM) or not for the simulation of the flow is then presented through evolutionary computations and convergence of the two surface parts of the throat is discussed. The above results illustrate the robustness and primising inherent parallelism of GAs for mastering the complexity of 3D optimizations. (C) 2001 Published by Elsevier Science B.V.