with n i classes in each categorical variable Z i , i = 1, . . . , n d . We assume both x and y are bounded, i.e., ℓ x ≤ x ≤ u x and ℓ y ≤ y ≤ u y , and n i is finite, for i = 1, . . . , n d . In (1), f is the objective function that maps the optimization vector X to a scalar value in R.