To solve the problem of the optimization of gamma irradiation facilities given by an objective function (throughput), which is to be maximized, and by constraints (in terms of nonlinear inequalities and of linear equations) a computer program was developed based on the evolution method, a combination of a stochastic search and an aim-oriented step-by-step procedure. The applicability of the alogrithm implemented on an ES 1040 computer to the maximization of the throughput as well as to the improvement of the dose field homogeneity is demonstrated by different examples especially related to the irradiation of onions.