We first run a traditional GA (described in details in the Methods section) to baseline our benchmark and then describe the ML extensions and their results. When using the traditional GA, it is possible to locate the hull of local minima with ∼16,000 energy evaluations. This is significantly lower than the total number of homotops that are present, and thus the number of energy calculations required if a brute-force method was used (1.78 × 10 44 ). However, this is still typically above the number of energy calculations one would wish to perform if a more expensive energy calculator were being employed. To overcome inefficiencies in this method, the underlying search algorithm is optimized and coupled with machine learning selection. A GP regression model is used to predict excess energies of nanoparticles before employing electronic structure calculations. The squared exponential kernel was utilized for the mapping function, as in Equation .