The practical implementation of data augmentation for this work's optimization task is not straightforward and is of limited use in terms of combinatorial explosion when many variables are involved as well as data scaling limitations. This results in a high-cost scenario for possibly murky results and applicability to a more limited range of tasks (i.e. small data, few variables in the permutation constraint). Thus, we choose to focus on order constraints in this work. However, the effect of using data augmentation vs. order constraints on search space efficiency in combination with other constraints may be an interesting topic for future study.