  In this paper two formulations for the robust optimization of the size of the
permanent magnet in a synchronous machine are discussed. The optimization is
constrained by a partial differential equation to describe the electromagnetic
behavior of the machine. The need for a robust optimization procedure
originates from the fact that optimization parameters have deviations. The
first approach, i.e., \textcolor{red}{worst-case} optimization, makes use of
local sensitivities. The second approach takes into account expectation values
and standard deviations. The latter are associated with global sensitivities.
The geometry parametrization is elegantly handled thanks to the introduction of
an affine decomposition. Since the stochastic quantities are determined by
tools from uncertainty quantification (UQ) and thus require a lot of finite
element evaluations, model order reduction is used in order to increase the
efficiency of the procedure. It is shown that both approaches are equivalent if
a linearization is carried out. \textcolor{blue}{This finding is supported by
the application on an electric machine. The optimization algorithms used are
sequential quadratic programming, particle swarm optimization and genetic
algorithm}. While both formulations reduce the size of the magnets, the UQ
based optimization approach is less pessimistic with respect to deviations and
yields smaller magnets.
