The most compact search space is not always the most efficient: A case study on maximizing solid rocket fuel packing fraction via constrained Bayesian optimization

Would you rather search for a line inside a cube or a point inside a square? This type of solution degeneracy often exists in physics-based simulations and wet-lab experiments, but constraining these degeneracies is often unsupported or difficult to implement in many optimization packages, requiring additional time and expertise. So, are the possible improvements in efficiency worth the cost of implementation? We demonstrate that the compactness of a search space (to what extent and how degenerate solutions and non-solutions are removed) can significantly affect Bayesian optimization search efficiency via the Ax platform. 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. We assess a total of eight search space types which range from none up to all three constraint types imposed simultaneously. We find that leaving the search space unconstrained leads to a large variance in the outcome and that on average, the most constrained search space is not always the most efficient. Likewise, the least constrained search space is not always the least efficient. We recommend that optimization practitioners in the physical sciences carefully consider the impact of removing search space degeneracies on search efficiency before running expensive optimization campaigns.