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

*(English)*Zbl 1178.76310Summary: 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.

##### MSC:

76N25 | Flow control and optimization for compressible fluids and gas dynamics |

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

65K10 | Numerical optimization and variational techniques |

##### Keywords:

Shape optimization; Evolutionary algorithms; Adjoint formulation; Artificial neural networks; Turbomachinery; Aerodynamics
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\textit{K. C. Giannakoglou} et al., Comput. Methods Appl. Mech. Eng. 195, No. 44--47, 6312--6329 (2006; Zbl 1178.76310)

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