  We consider a composite medium, which consists of a homogeneous matrix
containing a statistically homogeneous set of multimodal spherical inclusions.
This model is used to represent the morphology of heterogeneous solid
propellants (HSP) that are widely used in the rocket industry. The
Lubachevsky-Stillinger algorithm is used to generate morphological models of
HSP with large polydisperse packs of spherical inclusions. We modify the
algorithm by proposing a random shaking procedure that leads to the
stabilization of a statistical distribution of the simulated structure that is
homogeneous, highly mixed, and protocol independent (in sense that the
statistical parameters estimated do not depend on the basic simulation
algorithm). Increasing the number of shaking has a twofold effect. First, the
system becomes more homogeneous and well-mixed. Second, the stochastic
fluctuations of statistical parameters (such as e.g. radial distribution
function, RDF), estimated by averaging of these structures, tend to diminish.
