A gradient-improved sampling plan for surrogate-based aerodynamic shape optimization using discontinuous Galerkin methods

Surrogate-based optimization (SBO) is a powerful approach for global optimization of high-dimensional expensive black-box functions, commonly consisting of four modules: design of experiment, function evaluation, surrogate construction, and infill sampling criterion. This work develops a robust and efficient SBO framework for aerodynamic shape optimization using discontinuous Galerkin methods as the computational fluid dynamics evaluation. Innovatively, the prior adjoint gradient information of the baseline shape is used to improve the performance of the sampling plan in the preliminary design of the experiment stage and further improve the robustness and efficiency of the construction of surrogate(s). Specifically, the initial sample points along the direction of objective rise have a high probability of being transformed into feasible points in a subspace of objective descending. Numerical experiments verified that the proposed gradient-improved sampling plan is capable of stably exploring the design space of objective descending and constraint satisfaction even with limited sample points, which leads to a stable improvement of the resultant aerodynamic performance of the final optimized shape.