  Global optimization is an active area of research in atomistic simulations,
and many algorithms have been proposed to date. A prominent example is basin
hopping Monte Carlo, which performs a modified Metropolis Monte Carlo search to
explore the potential energy surface of the system of interest. These
simulations can be very demanding due to the high-dimensional configurational
search space. The effective search space can be reduced by utilizing grids for
the atomic positions, but at the cost of possibly biasing the results if fixed
grids are employed. In this paper, we present a flexible grid algorithm for
global optimization that allows to exploit the efficiency of grids without
biasing the simulation outcome. The method is general and applicable to very
heterogeneous systems, such as interfaces between two materials of different
crystal structure or large clusters supported at surfaces. As a benchmark case,
we demonstrate its performance for the well-known global optimization problem
of Lennard-Jones clusters containing up to 100 particles. In spite of the
simplicity of this model potential, Lennard-Jones clusters represent a
challenging test case, since the global minima for some "magic" numbers of
particles exhibit geometries that are very different from those of clusters
with only a slightly different size.
