Aerodynamic shape design using evolutionary algorithms and new gradient-assisted metamodels

Abstract

Aerodynamic shape design and optimization problems based on evolutionary algorithms and surrogate evaluation tools, i.e., the so-called metamodels, have recently found widespread use. Using metamodels, trained either separately from or during the optimization loop, a considerable reduction in the overall computing cost can be achieved. To support metamodel-based evolutionary algorithms, a class of new metamodels which utilize both known responses and response gradients for their training is proposed. The new gradient-assisted metamodels are extensions of standard multi-layer perceptrons and radial basis function networks. To demonstrate the prediction capabilities of the proposed metamodels and investigate different implementation modes within search algorithms along with the relevant CPU cost, a number of 2D and 3D aerodynamic shape (namely airfoils and turbomachinery blades) design problems are analyzed. Single- and two-objective problems, aiming at designing shapes that reproduce known pressure distributions at specific operating points, are considered. The exact evaluation tool is a numerical solver of the compressible fluid flow equations. The necessary gradient of the objective function is obtained by formulating and numerically solving adjoint equations.