In general, the constrained search spaces tend to have better performance than the bounds-only search space. For example, the "comp-order", ) and best in-sample results (Table and Figure ) exhibited higher mean packing fractions than bounds-only. In the case of validation results for "comp" and "order", the difference in distribution mean relative to bounds-only had t-test pvalues of 0.19 and 0.20 (Figure ). We interpret this to mean that the true means for "comp" and "order" are likely to be greater than the boundsonly case. However, the p-value for "comp-order" was much higher (0.59), indicating less certainty that the means of the two distributions are unequal. Likewise, "comp-order" and "order" exhibited lower model error than bounds-only, though "comp" typically had a larger model error. This indicates that the model has a more difficult time accurately predicting objective function values when permutation symmetries are left unreduced; however, it is interesting that the same behavior is not reflected in the optimization performance.