The automated design of metasurface (MTS) antennas has been a subject of extensive research, encompassing both theoretical and practical aspects. The inherent complexity of these antennas, made by sub-wavelength scattering elements organized in a periodic lattice over large areas, has forced researchers to devise more efficient methods for addressing this challenge. Recent strategies have shifted towards fully numerical modelling, with solutions attained through either direct methods or optimization algorithms. Among the latter, recently the current-based approach has emerged as a promising avenue for tackling the design of large antennas. Nonetheless, like all non-linear and non-convex optimization problems, it encounters common issues such as slow convergence and the occurrence of local minima.