Optimization of engineering systems is essential for efficient operation and enhanced lifespan of these systems. Owing to their complex designs, multiple design parameters, and their operation under stochastic conditions, optimization of such systems becomes difficult. The absence of a well-defined mathematical relation between the input and the output of such systems prevents the conventional gradient based methods from providing meaningful solutions. To optimize such problems, we use black-box optimization techniques. Multiple black-box optimization techniques have been developed, which have been shown to perform well for low and medium dimensional problems. ScoutND, a black-box optimization algorithm is shown to perform well for high dimensional problems as well as stochastic problems. The present work extends ScoutND to perform shape optimization of the PitzDaily problem, a test case problem in Computational Fluid Dynamics. We propose methods to perform Constrained and Unconstrained optimization of the Pitzdaily problem. We perform optimization under stochastic and non-stochastic conditions. We compare the results of our shape optimization problem from ScoutND with other optimizers such as Nelder-Mead, SLSQP, COBYLA, and L-BFGS-B. We show that ScoutND successfully optimizes the problem for stochastic and non-stochastic conditions and outperforms all other optimizers in the case of stochastic conditions.