In this study, two new techniques are proposed for accelerating the multi-point optimization of an airfoil shape by genetic algorithms. In such multi-point evolutionary optimization, the objective function has to be evaluated several times more than a single-point optimization. Thus, excessive computational time is crucial in these problems particularly, when computational fluid dynamics is used for fitness function evaluation. Two new techniques of preadaptive range operator and adaptive mutation rate are proposed. An unstructured grid Navier-Stokes flow solver with a two-equation k À " turbulence model is used to evaluate the objective function. The new methods are applied for optimum design of a transonic airfoil at two speed conditions. The results show that using the new methods can increase the aerodynamic efficiency of optimum airfoil at each operating condition with about 30% less computational time in comparison with the conventional genetic algorithm approach.

Abstract. Two new techniques are proposed to enhance the estimation abilities of the conventional Neural Network (NN) method in its application to the tness function estimation of aerodynamic shape optimization with the Genetic Algorithm (GA). The rst technique is pre-processing the training data in order to increase the training accuracy of the Multi-Layer Perceptron (MLP) approach. The second technique is a new structure for the network to improve its quality through a modi ed growing and pruning method. Using the proposed techniques, one can obtain the best estimations from the NN with less computational time. The new methods are applied for optimum design of a transonic airfoil and the results are compared with those obtained from the accurate Computational Fluid Dynamics (CFD) tness evaluator and with the conventional MLP NN approach. The numerical experiments show that using the new method can reduce the computational time signi cantly while achieving improved accuracy.