  We develop and apply a novel shape optimization exemplified for a two-blade
rotor with respect to the figure of merit ($FM$). This topologically assisted
optimization (TAO) contains two steps. First a global evolutionary optimization
is performed for the shape parameters and then a topological analysis reveals
the local and global extrema of the objective function directly from the data.
This non-dimensional objective function compares the achieved thrust with the
required torque. Rotor blades have a decisive contribution to the performance
of quadcopters. A two-blade rotor with pre-defined chord length distribution is
chosen as the baseline model.The simulation is performed in a moving reference
frame with a $k-\omega$ turbulence model for the hovering condition.The rotor
shape is parameterized by the twist angle distribution.The optimization of this
distribution employs a genetic algorithm. The local maxima are distilled from
the data using a novel topological analysis inspired by discrete scalar-field
topology. We identify one global maximum to be located in the interior of the
data and five further local maxima related to errors from non-converged
simulations.The interior location of the global optimum suggests that small
improvements can be gained from further optimization.The local maxima have a
small persistence, i.e., disappear under a small $\varepsilon$ perturbation of
the figure of merit values. In other words, the data may be approximated by a
smooth mono-modal surrogate model. Thus, the topological data analysis provides
valuable insights for optimization and surrogate modeling.
