On the Use of Symmetry in Optimal Design of Experiments

Soloviov, Vladimir

doi:10.1007/978-1-4612-1318-5_13

Cited by 1 publication

(2 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is well-known in the mathematical programming (optimization) community that problem formulations can introduce degeneracy or symmetry [35]. Moreover, alternate model formulations that break symmetry/degeneracy are essential for many integer programming (optimization) algorithms [36]. Much effort in the operations research community focuses on how to model problems to avoid degeneracy/symmetry and how these features can impact algorithm performance.…”

Section: Related Workmentioning

confidence: 99%

“…Much effort in the operations research community focuses on how to model problems to avoid degeneracy/symmetry and how these features can impact algorithm performance. Likewise, symmetries have also been addressed for traditional de-sign of experiments 3 [36] (e.g., using discrete search spaces with constraints imposed in advance). In a similar vein, we devote attention to avoiding degeneracy and symmetry in a materials-specific context.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Compactness Matters: Improving Bayesian Optimization Efficiency of Materials Formulations through Invariant Search Spaces

Baird

Hall

Sparks

2023

Preprint

View full text Add to dashboard Cite

Would you rather search for a line inside a cube or a point inside a square? Physics-based simulations and wet-lab experiments often have symmetries (degeneracies) that allow reducing problem dimensionality or search space, 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) affects Bayesian optimization search efficiency. Here, we use the Adaptive Experimentation (Ax) Platform by Meta and a physics-based particle packing simulation with eight or nine tunable parameters, depending on the search space compactness. These parameters represent three truncated log-normal distributions of particle sizes which exhibit compositional-invariance and permutation-invariance characteristic of formulation problems (e.g., chemical formulas, composite materials, alloys). We assess a total of four search space types which range from none up to both constraint types imposed simultaneously. In general, the removal of degeneracy through problem reformulation (as seen by the optimizers surrogate model) improves optimization efficiency. We recommend that optimization practitioners in the physical sciences carefully consider the trade-off between implementation cost and search efficiency before running expensive optimization campaigns.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%