Retrograde vaporization calculation is a hard problem, which possesses several solutions and demands a robust algorithm. In the present work, we solved the double retrograde vaporization problem by hybrid global-local optimization. In fact, we propose a new methodology that involves fuzzy clustering means together with Luus-Jaakola and Nelder-Mead algorithms. We applied the proposed methodology to solve the double retrograde vaporization problem for binary systems of methane + n-butane. For this mixture, the dew point curve exhibits an S-shape at temperatures slightly below the critical temperature of the more volatile component. This binary mixture was modeled using the original Peng-Robinson equation of state and the classical one-fluid van der Waals mixing rule.