  High current storage rings, such as the Z-pole operating mode of the FCC-ee,
require accelerating cavities that are optimized with respect to both the
fundamental mode and the higher order modes. Furthermore, the cavity shape
needs to be robust against geometric perturbations which could, for example,
arise from manufacturing inaccuracies or harsh operating conditions at
cryogenic temperatures. This leads to a constrained multi-objective shape
optimization problem which is computationally expensive even for axisymmetric
cavity shapes. In order to decrease the computation cost, a global sensitivity
analysis is performed and its results are used to reduce the search space and
redefine the objective functions. A massively parallel implementation of an
evolutionary algorithm, combined with a fast axisymmetric Maxwell eigensolver
and a frequency-tuning method is used to find an approximation of the Pareto
front. The computed Pareto front approximation and a cavity shape with desired
properties are shown. Further, the approach is generalized and applied to
another type of cavity.
