To overcome these limitations, we have developed a relaxation and basin-climbing approach that can improve the efficiency of algorithms that globally optimize the chemical ordering in bimetallic NPs. This approach relies on approximations to the local energy of each metal atom derived from eq. 1, which reveal optimal permutations to be carried out by the optimization algorithm. The identification of optimal permutations implemented here is analogous to the deterministic search scheme proposed by Schebarchov and Wales , which was itself based on the heuristic approaches for partitioning graphs .