  Optimization and control of complex unsteady flows remains an important
challenge due to the large cost of performing a function evaluation, i.e. a
full computational fluid dynamics (CFD) simulation. Reducing the number of
required function evaluations would help to decrease the computational cost of
the overall optimization procedure. In this article, we consider the stochastic
derivative-free surrogate-model based Dynamic COordinate search using Response
Surfaces (DYCORS) algorithm and propose several enhancements: First, the
gradient information is added to the surrogate model to improve its accuracy
and enhance the convergence rate of the algorithm. Second, the internal
parameters of the radial basis function employed to generate the surrogate
model are optimized by minimizing the leave-one-out error in the case of the
original algorithm and by using the gradient information in the case of the
gradient-enhanced version. We apply the resulting optimization algorithm to the
minimization of the total pressure loss through a linear cascade of blades, and
we compare the results obtained with the stochastic algorithms at different
Reynolds numbers with a gradient-based optimization algorithm. The results show
that stochastic optimization outperforms gradient-based optimization even at
very low $Re$ numbers, and that the proposed gradient-enhanced version improves
the convergence rate of the original algorithm. An open-source implementation
of the gradient-enhanced version of the algorithm is available.
