Design problem of APF accelerator for ensure enough high quality of output beam is considered. As we know, this problem is not easy because we have to achieve stability of longitudinal and transversal motions simultaneously. One of the first significant results in this subject were obtained by V. V. Kushin [1]. In the work [2] the problems of optimizations of ion beam are considered. The optimization approaches for some beam characteristics improving (acceleration and transmission ratios) are considered. Obtained results are confirmed by particle in cell simulations.