Micropumps play a crucial role in various drug delivery applications. Non-mechanical micropumps offer simplicity by eliminating moving parts. These pumps operate by displacing small volumes of fluid, prompting the exploration of innovative enhancement ideas. In this research, a piezoelectric actuator generates vibrations to drive the micropump. The proposed micropump design includes a piezoelectric plate, a diaphragm plate, an inlet, and two outlets. The novelty of this study lies in developing an innovative model of a non-mechanical piezoelectric micropump using finite element method (FEM) and genetic algorithm (GA) codes. The resulting displacement vector is used as an input for fluid-solid interaction analysis. Geometric specifications and optimization processes for the micropump's design are discussed. A simulation model with appropriate parameters is developed, and applying a sinusoidal voltage to the piezoelectric actuator is evaluated to propose an innovative model. Four parameters, including diameter, divergence angle, nozzle-diffuser length, and piezo thickness, are examined in sensitivity analyses. The results demonstrate that increasing the micropump diameter and reducing the actuator plate thickness leads to higher flow rates. The maximum flow rate is achieved with a 1.2 mm nozzle-diffuser length and an optimal angle of 10 degrees in the end equation is observed.