Surrogate models are often used to reduce the cost of design optimization problems that involve computationally costly models, such as computational fluid dynamics simulations. However, the number of evaluations required by surrogate models usually scales poorly with the number of design variables, and there is a need for both better constraint formulations and multimodal function handling. To address this issue, we developed a surrogate-based gradient-free optimization algorithm that can handle cases where the function evaluations are expensive, the computational budget is limited, the functions are multimodal, and the optimization problem includes nonlinear equality or inequality constraints. The proposed algorithm-super efficient global optimization coupled with mixture of experts (SEGOMOE)can tackle complex constrained design optimization problems through the use of an enrichment strategy based on a mixture of experts coupled with adaptive surrogate models. The performance of this approach was evaluated for analytic constrained and unconstrained problems, as well as for a multimodal aerodynamic shape optimization problem with 17 design variables and an equality constraint. Our results showed that the method is efficient and that the optimum is much less dependent on the starting point than the conventional gradient-based optimization.
Aircraft shape optimization must be performed with multiple flight conditions in order to produce a robust aerodynamic design. Under these flight conditions, the aircraft is subjected to different aerodynamic loads which translate into different static aeroelastic equilibria. As the optimization proceeds, the external shape is modified and consequently alters each aerostructural coupling. Modeling the latter in the adjoint-based optimization process therefore appears necessary to properly take flexibility effects into consideration, not only to get the right state variables but also to compute consistent coupled sensitivities. Nonetheless, relying on a coupled-adjoint increases the wall-clock time of the optimization process with respect to a more classical uncoupled aerodynamic approach. This paper therefore assesses the benefits of the coupled approach with respect to an uncoupled one, by quantifying them on an industrially-representative long range aircraft test case. A high-fidelity 5-point optimization problem is considered, relying on RANS CFD for the aerodynamics and on a FEM model of the aircraft for the structural analysis. The optimizations consist in minimizing the weighted drag coefficient subject to lift, pitching moment and geometrical constraints with respect to 110 variables controlling the twist law and cross-sectional camber laws. The two approaches are compared on cost efficiency, geometrical proximity and by analyzing the far-field drag breakdown improvements for each point of the problem.
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