The direct density functional theory global optimization of MgO(100)-supported AuIr sub-nanoalloys is performed using the Birmingham parallel genetic algorithm (BPGA). The BPGA is a pool-based genetic algorithm for the structural characterization of nanoalloys. The parallel pool methodology utilized within the BPGA allows the code to characterize the structures of N = 4–6 AunIrN–n clusters in the presence of the MgO(100) surface. The use of density functional theory allows the code to capture quantum size effects in the systems, which determine their structures. The searches reveal significant differences in structure and chemical ordering between the surface-supported and gas-phase global minimum structures.