Robust Multi-Objective Optimization in Aerodynamics using MGDA

Daigo Maruyama 1
1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : This study deals with robust design optimization strategies in aerodynamics, by considering geometric parameters as uncertainty factors, with application to transonic airfoil design. Mean and standard deviation of the aerodynamic coefficients are considered as cost functions for a multi-objective optimization problem. Statistical moments are evaluated using Monte-Carlo simulations (MCS), on the basis of Radial Basis Functions (RBF) surrogate models. The multi-objective optimization is achieved using the Multiple-Gradient Descent Algorithm (MGDA), which permits to find a descent direction for all criteria simultaneously, starting from a set of initial design points. The airfoil shape parameterization is carried out using the PARSEC approach to define significant design parameters. Moreover, the ANOVA (ANalysis Of Variance) technique is used to identify the most relevant parameters for aerodynamic criteria. The proposed approach is illustrated on a practical robust design problem involving four statistical cost functions.
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[Research Report] RR-8428, INRIA. 2013
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Daigo Maruyama. Robust Multi-Objective Optimization in Aerodynamics using MGDA. [Research Report] RR-8428, INRIA. 2013. 〈hal-00919215〉

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