We optimize a silica-encapsulated silicon L3 photonic crystal cavity for ultra-high quality factor by means of a global optimization strategy, where the closest holes surrounding the cavity are varied to minimize out-of-plane losses. We find an optimal value of Qc=4.33×107, which is predicted to be in the 2 million regime in presence of structural imperfections compatible with state-of-the-art silicon fabrication tolerances.