An optical aperture synthesis telescope such as the LBT will suffer from phase errors unless the apertures are aligned to within a small fraction of a wavelength. A phase diversity wave-front sensor can measure phase errors brought by a misaligned aperture synthesis telescope. The Phase Diversity is formulated in the context of nonlinear programming where a metric is developed and then minimized. We here introduce a novel Genetic Algorithms (GAs), evaluate the different Zernike coefficients to obtain the wave-front error. The results of the computer simulations performed with simulated data including the effects of noise are shown for the case of random misalignment phase errors on each of three sub-telescope.