  The optimal mixing evolutionary algorithms (OMEAs) have recently drawn much
attention for their robustness, small size of required population, and
efficiency in terms of number of function evaluations (NFE). In this paper, the
performances and behaviors of OMEAs are studied by investigating the mechanism
of optimal mixing (OM), the variation operator in OMEAs, under two scenarios --
one-layer and two-layer masks. For the case of one-layer masks, the required
population size is derived from the viewpoint of initial supply, while the
convergence time is derived by analyzing the progress of sub-solution growth.
NFE is then asymptotically bounded with rational probability by estimating the
probability of performing evaluations. For the case of two-layer masks,
empirical results indicate that the required population size is proportional to
both the degree of cross competition and the results from the one-layer-mask
case. The derived models also indicate that population sizing is decided by
initial supply when disjoint masks are adopted, that the high selection
pressure imposed by OM makes the composition of sub-problems impact little on
NFE, and that the population size requirement for two-layer masks increases
with the reverse-growth probability.
