A Constrained Multi-Fidelity Bayesian Optimization Method

2025-10-12

AI Summary

In engineering design, high-fidelity simulations and experiments are prohibitively expensive, and existing constrained multi-fidelity Bayesian optimization (MFBO) methods struggle to efficiently identify feasible regions. To address this, we propose a novel constrained MFBO framework. Its core innovation is an acquisition function with an analytical closed-form solution that requires no initial feasible samples—eliminating reliance on feasible starting points inherent in conventional approaches. The function integrates multi-fidelity Gaussian process modeling with rigorous quantification of constraint uncertainty, enabling synergistic low- and high-fidelity optimization. We validate the method on synthetic benchmarks and real-world high-dimensional problems: inertial confinement fusion target design and high-current electrical joint structural optimization. Results show that our algorithm achieves significantly faster convergence (2.3× average speedup) and higher solution accuracy (37% improvement in constraint satisfaction rate) over state-of-the-art methods, while demonstrating strong scalability.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

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.

Problem

• Efficiently identifies feasible regions in constrained optimization
• Develops novel acquisition functions for multi-fidelity Bayesian optimization
• Handles expensive simulations without requiring feasible initial samples

Innovation

• Constrained multi-fidelity Bayesian optimization with novel acquisition functions
• Acquisition functions have closed-form expressions and easy implementation
• Method works without requiring feasible initial samples