  Anticipating the low energy arrangements of atoms in space is an
indispensable scientific task. Modern stochastic approaches to searching for
these configurations depend on the optimisation of structures to nearby local
minima in the energy landscape. In many cases these local minima are relatively
high in energy, and inspection reveals that they are trapped, tangled, or
otherwise frustrated in their descent to a lower energy configuration.
Strategies have been developed which attempt to overcome these traps, such as
classical and quantum annealing, basin/minima hopping, evolutionary algorithms
and swarm based methods. Random structure search makes no attempt to avoid the
local minima, and benefits from a broad and uncorrelated sampling of
configuration space. It has been particularly successful in the first
principles prediction of unexpected new phases of dense matter. Here it is
demonstrated that by starting the structural optimisations in a higher
dimensional space, or hyperspace, many of the traps can be avoided, and that
the probability of reaching low energy configurations is much enhanced.
Excursions into the extra dimensions are progressively eliminated through the
application of a growing energetic penalty. This approach is tested on hard
cases for random search - clusters, compounds, and covalently bonded networks.
The improvements observed are most dramatic for the most difficult ones. Random
structure search is shown to be typically accelerated by two orders of
magnitude, and more for particularly challenging systems. This increase in
performance is expected to benefit all approaches to structure prediction that
rely on the local optimisation of stochastically generated structures.
