  In the field of parametric partial differential equations, shape optimization
represents a challenging problem due to the required computational resources.
In this contribution, a data-driven framework involving multiple reduction
techniques is proposed to reduce such computational burden. Proper orthogonal
decomposition (POD) and active subspace genetic algorithm (ASGA) are applied
for a dimensional reduction of the original (high fidelity) model and for an
efficient genetic optimization based on active subspace property. The
parameterization of the shape is applied directly to the computational mesh,
propagating the generic deformation map applied to the surface (of the object
to optimize) to the mesh nodes using a radial basis function (RBF)
interpolation. Thus, topology and quality of the original mesh are preserved,
enabling application of POD-based reduced order modeling techniques, and
avoiding the necessity of additional meshing steps. Model order reduction is
performed coupling POD and Gaussian process regression (GPR) in a data-driven
fashion. The framework is validated on a benchmark ship.
