We have investigated the performance of an adaptive optics system subjected to changing atmospheric conditions, under the guidance of the ALOPEX stochastic optimization. Atmospheric distortions are smoothed out by means of a deformable mirror, the shape of which can be altered in order to follow the rapidly changing atmospheric phase fluctuations. In a simulation model, the total intensity of the light measured on a central area of the image (masking area) is used as the cost function for our stochastic optimization algorithm, while the surface of the deformable mirror is approximated by a Zernike polynomial expansion. Atmospheric turbulence is simulated by a number of Kolmogorov filters. The method's effectiveness, that is its ability to follow the motion of the turbulent wavefronts, is studied in detail and as it pertains to the size of the mirror's masking area, to the number of Zernike polynomials used and to the degree of the algorithm's stochasticity in relation to the mean rate of change of atmospheric distortions. Computer simulations and a series of numerical experiments are reported to show the successful implementation of the method.