We target PtyOx clusters with y = 3 or 6 and x = 0 -2y. Both free-standing and CeO2(111)-supported structures are evaluated. For the CeO2(111)-supported structures, only the supported particles are globally optimized, whereas the atoms of the CeO2 surface are kept in their bulk-terminated positions. The structural characterization of each targeted stoichiometry consists on obtaining the configuration with the lowest internal energy, i.e. the Global Minimum (GM). Once the GM has been characterized for all the considered stoichiometries of the system, AITD is used to evaluate the free energies of each system and to generate the corresponding phase diagrams. In this section, we describe the global optimization strategy using GOFEE, the DFT calculations, and the AITD approach used.