  Successful computer studies of glass-forming materials need to overcome both
the natural tendency to structural ordering and the dramatic increase of
relaxation times at low temperatures. We present a comprehensive analysis of
eleven glass-forming models to demonstrate that both challenges can be
efficiently tackled using carefully designed models of size polydisperse
supercooled liquids together with an efficient Monte Carlo algorithm where
translational particle displacements are complemented by swaps of particle
pairs. We study a broad range of size polydispersities, using both discrete and
continuous mixtures, and we systematically investigate the role of particle
softness, attractivity and non-additivity of the interactions. Each system is
characterized by its robustness against structural ordering and by the
efficiency of the swap Monte Carlo algorithm. We show that the combined
optimisation of the potential's softness, polydispersity and non-additivity
leads to novel computer models with excellent glass-forming ability. For such
models, we achieve over ten orders of magnitude gain in the equilibration
timescale using the swap Monte Carlo algorithm, thus paving the way to
computational studies of static and thermodynamic properties under experimental
conditions. In addition, we provide microscopic insights into the performance
of the swap algorithm which should help optimizing models and algorithms even
further.
