Optimal Transonic Aerodynamic Shape Design Using Simultaneous Perturbation Stochastic Approximation Method Coupled with Global and Local Optimization Methods

Abstract

Non-gradient based optimization methods such as Simultaneous Perturbation Stochastic Approximation (SPSA) and Simulated Annealing (SA) have been investigated by the authors in earlier studies on aerodynamic shape design optimisation. In this paper, hybrid methods are designed to exploit the high rate of reduction of the objective function at the inception of the design process using SPSA to drive the design towards the optimal design zone first, then followed by the use of other methods to perform the final stages of the convergence towards the optimal solutions. The design objective functions are determined by finite volume compressible viscous flow solvers. In this work SPSA method is used to find the optimal design zone followed by deterministic search method of BroydonFletcher-Goldfarb-Shanno (BFGS) for unconstrained design problems and Modified-Feasible-DirectionsAlgorithm (MFDA) for constrained design problems to perform the final search to optimal design. SPSA is also combined with SA method to perform the final search. The effects of switching from SPSA to SA and local optimisation methods are also considered. The optimal designs, performance and convergence obtained by hybrid SPSA-BFGS, SPSA-MFDA and SPSA-SA methods are compared for inverse airfoil design problem, airfoil drag minimization problem and design of the 3D leading edge of a transonic blade.