A number of different algorithms have been described in the literature for the decomposition of both convex binary morphological structuring elements and a specific subset of nonconvex ones. Nevertheless, up to now no deterministic solutions have been found to the problem of decomposing arbitrarily shaped structuring elements. This work presents a new stochastic approach based on genetic algorithms, in which no constraints are imposed on the shape of the initial structuring element nor assumptions are made on the elementary factors, which are selected within a given set.