Across all substitution levels the energy of the system decreases as the run progresses. The Mn-0.25 and Mn-0.50 runs find the normal ground state structures for N Zn = 4, 5. By finding the ground state, it is shown that the algorithm can start from the highest energy structure possible and evolve the system to find the lowest energy structure. The ground state is not found for the Mn-0.75, most probably due to the small number of swapping steps attempted in the 100 structure run. The true ground state is also not found starting from the inverse ZnFe 2 O 4 structure although many structures with 1 tetrahedral Fe atom are found (Figure . This suggests that more than 100 structures may need to be sampled in order to find the true ground state structure.