This paper approaches the question of multi-objective inverse problem for optimum shape design inaerodynamics using deterministic method and Game Theory. The employed basic optimizer is agradient-based control theory, more precisely an adjoint method. This method requires the solutionof adjoint problem, in addition to the analysis problem, to evaluate the gradient of cost function. Thecomplexity of the adjoint problem is equivalent to that of the analysis problem, therefore thecomputational cost of this method is approximately twice the evaluation of aerodynamic function,regardless of the number of design parameters, and is well suited to shape design problem.In a multi-objective optimization problem, there is non unique optimal solution but a whole set ofpotential solutions since in general no solution is optimal with respect to all criteria simultaneously,instead, one identifies a set of non-dominated solution referred to as the Pareto optimal front. Aftermaking these concepts precise, deterministic optimization method can be implemented by combiningmulti-objective functions using weighting constants into a single objective function. A differentchoice of weighting constant will result in a different optimum shape. The optimum shapes shouldnot dominated each other, and therefore lie on the Pareto front, where no improvement can beachieved in one objective component that doesn’t lead to degradation in the remaining component.Therefore, by vary the weighting constant, it is possible to compute the Pareto front [2]. Then anumerical experimentation is conducted to reconstruct simultaneously two pressure distributions,one is the high lift pressure distribution in subsonic regime the other is the low drag pressuredistribution in transonic regime [1]. Flows are analyzed by Eulerian computation.Finally, we have also computed both Nash and Stackelberg equilibria of the same optimizationproblem with two conflicting and hierarchical targets under different parameterizations using thedeterministic optimization method. The numerical results show clearly that all the equilibriasolutions lie within the Pareto surface. The non-dominated Pareto Front are obtained, this is due tothe factor that the best non-dominated solution by cooperative strategy however the CPU cost tocapture a set of solutions makes the Pareto Front an expensive to the designer engineer.
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