Natural photonic structures exhibit remarkable color effects such as metallic appearance and iridescence. A rigorous study of the electromagnetic response of such complex structures requires to accurately determine some of their relevant optical parameters, such as the refractive indices of the materials involved. In this paper, we apply different heuristic optimization strategies to retrieve the real and imaginary parts of the refractive index of the materials comprising natural multilayer systems. Through some examples, we compare the performances of the inversion methods proposed and show that these kinds of algorithms have a great potential as a tool to investigate natural photonic structures. © 2013 Optical Society of America.