A high reflectivity and polarization selective high contrast grating mirror has been designed with the use of an automated optimization algorithm. Through a precise study of the tolerance of the different lengths of the structure, the robustness with respect to the fabrication errors has been enhanced to high tolerance values between 5 % and 210 %. This adjustment of the dimensions of the structure leads to a 250 nm large bandwidth mirror well adapted for a VCSEL application at λ = 2.65 µm and can easily be scaled for other wavelengths.