Phase retarders normally exhibit strong wavelength dependence. However, for use with polychromatic light, achromatic retarders, which exhibit ideally nearly identical characteristics over a wide wavelength region, are in demand. Designing such a superachromatic retarder is a challenging task for an optical system designer where retardation will be almost constant within a wide range of wavelengths. The present investigation considers a system consisting of wave plates made of different materials, which focus on near-infrared wavelength range, viz. 800 to 2000 nm. Here, a flower pollination algorithm has been used for this nonlinear optimization problem. With the help of the mentioned optimization technique, the optimal values of thicknesses of wave plates are calculated for which the system act as a quarter-wave plate. The obtained result shows a significant improvement in terms of maximum deviation of retardation for the above-mentioned wavelength range. The proposed methodology holds promise for optimizing the design of optical systems.