Effect of reducible and irreducible search space representations on adaptive design efficiency: a case study on maximizing packing fraction for solid rocket fuel propellant simulations

Would you rather search for a point inside of a line or a line inside of a rectangle? This is a type of solution degeneracy that often exists physics-based simulations and wetlab experiments, but constraining these degeneracies is often unsupported or difficult-to-implement in many optimization packages, requiring additional time and expertise. So, is the increase in efficiency worth the cost of implementation? We demonstrate that the compactness of a search space (to what extent degenerate solutions and nonsolutions are removed) can have a significant effect on Bayesian optimization search efficiency via the Ax platform. As our optimization task, we use a physics-based particle packing simulation with seven to nine tunable parameters, depending on the search space compactness, that represent three truncated, discrete log-normal distributions of particle sizes. This physics-based simulation exhibits three qualitatively different degeneracy types: size-invariance, compositional-invariance, and permutation-invariance. The degeneracies are reflected in the outcomes being identical when: 1. all particle sizes are multiplied by a constant factor, 2. the fractional prevalences of the particle types sum to unity, and 3. sets of log-normal distribution parameters are swapped with each other, respectively. This simulation provides fertile ground for assessing the impact of multiple constraints on search efficiency, with a total of eight search space types which ranges from none up to all three constraints imposed simultaneously. Contrary to intuition, we find that, on average, the most compact search space performs worse than the least compact search space ((0.692 ± 0.036) vs. (0.699 ± 0.016) , respectively) over 50 iterations due to the interactions of the non-linear size-invariance degeneracy with other degeneracy types. The most efficient search space in terms of both predicted and validated outcomes is the combination of the composition and permutation constraints, resulting in a mean packing fraction of (0.728±0.010) over 50 iterations, where randomly sampled volume fractions are typically no less than 0.6. We recommend that optimization practitioners in the physical sciences carefully consider the impact of removing search space degeneracies on search efficiency prior to running expensive optimization campaigns.