Effects of Solver Fidelity on a Parallel Search Algorithm's Performance for Airfoil Shape Optimization Problems

Abstract

Stochastic search algorithms are known to computationally time intensive for shape optimization problems. In order to reduce the computational time, it is att ractive to incorporate variable fidelity solution schemes within stochastic search methods. Such methods are guided by low fidelity computations during the initial exploratory phases of search and high fidelity computations towards the end of the search. I n this paper, we present a stochastic parallel search algorithm that is embedded with a decaying variable perturbation mechanism and a multigrid Euler solver that can perform low, medium, high and variable fidelity computations. The performance of the para llel stochastic search algorithm has been studied on two airfoil shape optimization problems. The results obtained using the variable fidelity solution scheme (one that progressively uses low, medium and high fidelity computations) are compared with the r esults obtained using a low fidelity, medium fidelity and a high fidelity solution scheme on two well -studied airfoil design examples. The study provides insights on the effects solver fidelity on the progress of the parallel stochastic search and the qual ity of the final solution. It highlights that the use of variable fidelity solution schemes can lead to substantial savings in the computational time without significant compromise on the quality of the final solution. The results also suggest that in orde r to successfully use a reduced level of fidelity to guide a stochastic search, care should be taken to ensure a rank correspondence between the high fidelity and the reduced fidelity schemes.