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 mu ltiple objective design optimization of internal aerodynamic shape operatin g with transonic flow. The distributed optimization strategy discussed here and inspired from Lions' new distributed control approach (J.L. Lions, Dis tributed active control approach for pde systems, Fourth WCCM CD-ROM, Bueno s Aires, Argentina, 1998) relies on genetic algorithms (GAs). GAs are diffe rent from traditional optimization tools and based on digital imitation of biological evolution. Game theory replaces here a global optimization probl em by a non-cooperative game based on Nash equilibrium with several players solving local constrained sub-optimization tasks. The transonic flow simul ator uses a full potential solver taking advantage of domain decomposition methods and GAs for the matching of non-linear local solutions. The main id ea developed here is to combine domain decomposition methods for the flow s olver with the geometrical optimization procedure using local shape paramet erization. Numerical results are presented for a simple nozzle inverse prob lem with subsonic and transonic shocked flows. A comparison of the nozzle r econstruction using domain decomposition method (DDM) or not for the simula tion of the flow is then presented through evolutionary computations and co nvergence of the two surface parts of the throat is discussed. The above re sults illustrate the robustness and primising inherent parallelism of GAs f or mastering the complexity of 3D optimizations. (C) 2001 Published by Else vier Science B.V.