One of the characteristics that stands out is the large standard deviations for many of the features. In other words, separate optimization runs did not necessarily assign the same features as being most important, and this behavior was observed across many search spaces. The large variances observed for many of the search spaces indicate that no one parameter is universally important for the simulations. This can be explained by the representation of parameters as fractional contributions of distributions. Since we know that the physicsbased simulation takes an intermediate representation of the combined, discrete particle size distribution (Eq. ( )), and each parameter affects this final distribution, there are strong dependencies between parameters. Additionally, in the cases where the permutation constraint is not imposed, the model is just as likely to assign one set of distribution parameters as important compared with another. We would have expected that for search spaces with the best predicted and validated outcomes, the feature importances would have tighter standard deviations than others; however, this does not appear to be the case. This may be reflective of the interactions of the problem formulations with the mechanics of the physics-based particle packing simulation, where the parameters are highly interdependent.