The deformable mirror adjusts the mirror surface shape to compensate the wavefront error in the adaptive optics system. Recently, the adaptive optics has been widely used in many applications, such as astronomical telescopes, high power laser systems, etc. These applications require large diameter deformable mirrors with large stroke, high speed and low cost. Thus, the bimorph piezoelectric deformable mirror, which is a good match for the applications, has attracted more and more attentions. In this paper, we use zeroth-order optimization method to optimize the physical parameters of a bimorph piezoelectric deformable mirror that consists of a metal reflective layer deposited on the top of a slim piezoelectric ceramic surface layer. The electrodes are deposited on the bottom of the piezoelectric ceramic layer. The physical parameters to be optimized include the optimal thickness ratio between the piezoelectric layer and reflective layer, inter-electrode distance, and so on. A few reasonable designs are obtained by a comparative study presented for three geometries of electrodes, which are circular, square and hexagon, respectively.