Based on the concept of the cloak generating function, we propose a numerical method
to compute the invisibility performance of various quadratic spherical cloaks and
obtain optimal invisibility results. A non-ideal discrete model is used to calculate
and optimize the total scattering cross-sections of different profiles of the generating
function. A bell-shaped quadratic spherical cloak is found to be the best candidate,
which is further optimized by controlling design parameters involved. Such improved
invisibility is steady even when the model is highly discretized.