For each system a large number of structures were evaluated with DFT (up to 1613 for a single run of the most complex system -ceria supported Pt6O12) in order to locate the GM. Each stoichiometry is run at least twice, and if the minimum energy structures of the runs don't coincide a third run of the algorithm is performed, which ensures that the obtained most stable structures are the best guess for each stoichiometry. After subsequent relaxations at increasing levels of theory, ~ 10 structures per stoichiometry are recalculated at the final HSE06 level.