  Good agreement was found between experimental Vickers hardnesses,
$H_\text{v}$, of a wide range of materials and those calculated by three
macroscopic hardness models that employ the shear and/or bulk moduli obtained
from: (i) first principles via AFLOW-AEL (AFLOW Automatic Elastic Library), and
(ii) a machine learning (ML) model trained on materials within the AFLOW
repository. Because $H_\text{v}^\text{ML} $ values can be quickly estimated,
they can be used in conjunction with an evolutionary search to predict stable,
superhard materials. This methodology is implemented in the XtalOpt
evolutionary algorithm. Each crystal is minimized to the nearest local minimum,
and its Vickers hardness is computed via a linear relationship with the shear
modulus discovered by Teter. Both the energy/enthalpy and $H_\text{v,
Teter}^{\text{ML}}$ are employed to determine a structure's fitness. This
implementation is applied towards the carbon system, and 43 new superhard
phases are found. A topological analysis reveals that phases estimated to be
slightly harder than diamond contain a substantial fraction of diamond and/or
lonsdaleite.
