Without local optimization, the "bare" GA is unable to locate the global minimum, whereas the MC algorithm requires a very large (> 10 5 ) number of steps. In contrast, algorithms assisted by the optimal-exchange algorithm are able to find the minimum requiring approximately two orders or magnitude fewer steps. We further note that the effect of the optimal-exchange scheme on performance is even more significant when increasing particle size. Such remarkable improvement allows to comfortably perform a large number of global optimizations for different particles on commodity compute architectures. Despite requiring a similar number of steps to find the global minimum, our implementation of the optimalexchange BH algorithm is faster in CPU time than the GA with optimal exchange relaxation (see Fig. in SI), and we therefore rely on the former to optimize the orderings of ensembles of Au n Pt 140-n particles with different shape and composition.