where s i and n represent log-normal shape parameter of the i-th particle type and number of particles, respectively. An alternative, though not particularly amenable to BO (at least when data scaling is an issue) and in general intractable when the number of permutations is large, is to perform data augmentation in the original search space by including the repeat permutation data at "no additional cost". Additionally, we did not choose to perform data augmentation due to the difficulty of simultaneously implementing both reparameterizations/constraints within an AxSearch first in, first out scheduler framework.