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A Constrained Multi-Fidelity Bayesian Optimization Method

Jingyi Wang, Nai-Yuan Chiang, Tucker Hartland, J. Luc Peterson, Jerome Solberg, Cosmin G. Petra

Abstract

Recently, multi-fidelity Bayesian optimization (MFBO) has been successfully applied to many engineering design optimization problems, where the cost of high-fidelity simulations and experiments can be prohibitive. However, challenges remain for constrained optimization problems using the MFBO framework, particularly in efficiently identifying the feasible region defined by the constraints. In this paper, we propose a constrained multi-fidelity Bayesian optimization (CMFBO) method with novel acquisition functions. Specifically, we design efficient acquisition functions that 1) have analytically closed-form expressions; 2) are straightforward to implement; and 3) do not require feasible initial samples, an important feature often missing in commonly used acquisition functions such as expected constrained improvement (ECI). We demonstrate the effectiveness of our algorithms on synthetic test problems using different combinations of acquisition functions. Then, we apply the proposed method to a data-driven inertial confinement fusion (ICF) design problem, and a high-current joint design problem using finite element simulations with computational contact mechanics.

A Constrained Multi-Fidelity Bayesian Optimization Method

Abstract

Recently, multi-fidelity Bayesian optimization (MFBO) has been successfully applied to many engineering design optimization problems, where the cost of high-fidelity simulations and experiments can be prohibitive. However, challenges remain for constrained optimization problems using the MFBO framework, particularly in efficiently identifying the feasible region defined by the constraints. In this paper, we propose a constrained multi-fidelity Bayesian optimization (CMFBO) method with novel acquisition functions. Specifically, we design efficient acquisition functions that 1) have analytically closed-form expressions; 2) are straightforward to implement; and 3) do not require feasible initial samples, an important feature often missing in commonly used acquisition functions such as expected constrained improvement (ECI). We demonstrate the effectiveness of our algorithms on synthetic test problems using different combinations of acquisition functions. Then, we apply the proposed method to a data-driven inertial confinement fusion (ICF) design problem, and a high-current joint design problem using finite element simulations with computational contact mechanics.

Paper Structure

This paper contains 15 sections, 40 equations, 17 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Constrained Bayesian optimization
  3. Gaussian process
  4. Expected improvement and upper confidence bound
  5. Expected constrained improvement
  6. Expected Merit Improvement
  7. Additive expected constrained improvement
  8. Constrained upper confidence bound
  9. Constrained multi-fidelity Bayesian optimization
  10. Numerical Experiments
  11. Synthetic examples
  12. An ICF design optimization problem
  13. A high-current joint design problem
  14. Conclusions
  15. Numerical example

Figures (17)

  • Figure 1: Contour plots of example 1 to 4. Feasible regions are indicated by the absence of parallel black lines.
  • Figure 2: Low- (left) and high-fidelity (right) contour plots of example 5 and 6. Feasible regions are indicated by the absence of parallel black lines.
  • Figure 3: CMFBO optimization history for example 1 and 2.
  • Figure 4: CMFBO solution for example 3 and 4.
  • Figure 5: CMFBO optimization history for example 5 and 6.
  • ...and 12 more figures