Several designs of sub-wavelength grating mirrors adapted to mid-infrared operation are reported with several percents of tolerance for the grating fabrication. These designs have been automatically optimized by the use of a genetic-based algorithm to maximize a quality factor defined to meet the requirements of a VCSEL cavity mirror. These mirrors are devoted to an integration in VCSEL operating near λ=2.3 µm, with a large bandwidth, very high reflectivity coefficient for transverse magnetic mode only, polarization selectivity and a thickness as low as 2 µm.