Advanced Optimization

Objectives

Minimize y1, y2, y3, and y4

Correlations

• y1 and y2 are correlated
• y1 is anticorrelated with y3
• y2 is anticorrelated with y3

Noise

y1, y2, and y3 are stochastic with heteroskedastic, parameter-free noise, whereas y4 is deterministic, but still considered 'black-box'. In other words, repeat calls with the same input arguments will result in different values for y1, y2, and y3, but the same value for y4.

Objective thresholds

If y1 is greater than 0.2, the result is considered "bad" no matter how good the other values are. If y2 is greater than 0.7, the result is considered "bad" no matter how good the other values are. If y3 is greater than 1800, the result is considered "bad" no matter how good the other values are. If y4 is greater than 40e6, the result is considered "bad" no matter how good the other values are.

Search Space

Fidelity

fidelity1 is a fidelity parameter. The lowest fidelity is 0, and the highest fidelity is 1. The higher the fidelity, the more expensive the evaluation, and the higher the quality.

NOTE: fidelity1 and y3 are correlated.

Constraints

• x₁₉ < x₂₀
• x₆ + x₁₅ ≤ 1.0

Parameter bounds

• 0 ≤ x_i ≤ 1 for i ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
• c₁ ∈ {c1_0, c1_1}
• c₂ ∈ {c2_0, c2_1}
• c₃ ∈ {c3_0, c3_1, c3_2}
• 0 ≤ fidelity1 ≤ 1

Notion of best

Thresholded Pareto front hypervolume vs. running cost for three different budgets, and averaged over 10 search campaigns.

References:

1. Baird, S. G.; Liu, M.; Sparks, T. D. High-Dimensional Bayesian Optimization of 23 Hyperparameters over 100 Iterations for an Attention-Based Network to Predict Materials Property: A Case Study on CrabNet Using Ax Platform and SAASBO. Computational Materials Science 2022, 211, 111505. https://doi.org/10.1016/j.commatsci.2022.111505.

2. Baird, S. G.; Parikh, J. N.; Sparks, T. D. Materials Science Optimization Benchmark Dataset for High-Dimensional, Multi-Objective, Multi-Fidelity Optimization of CrabNet Hyperparameters. ChemRxiv March 7, 2023. https://doi.org/10.26434/chemrxiv-2023-9s6r7.