  The compact Genetic Algorithm (cGA) is an Estimation of Distribution
Algorithm that generates offspring population according to the estimated
probabilistic model of the parent population instead of using traditional
recombination and mutation operators. The cGA only needs a small amount of
memory; therefore, it may be quite useful in memory-constrained applications.
This paper introduces a theoretical framework for studying the cGA from the
convergence point of view in which, we model the cGA by a Markov process and
approximate its behavior using an Ordinary Differential Equation (ODE). Then,
we prove that the corresponding ODE converges to local optima and stays there.
Consequently, we conclude that the cGA will converge to the local optima of the
function to be optimized.
