Trust Region Constrained Bayesian Optimization with Penalized Constraint Handling

TL;DR

This paper introduces a Bayesian optimization approach that combines penalty methods, surrogate modeling, and trust regions to efficiently solve high-dimensional constrained black-box problems with fewer evaluations.

Contribution

It presents a novel trust region constrained Bayesian optimization method that effectively handles complex constraints via penalty formulation and local surrogate modeling.

Findings

Achieves high-quality solutions with fewer evaluations.

Maintains stable performance across various high-dimensional problems.

Outperforms existing methods on synthetic and real-world benchmarks.

Abstract

Constrained optimization in high-dimensional black-box settings is difficult due to expensive evaluations, the lack of gradient information, and complex feasibility regions. In this work, we propose a Bayesian optimization method that combines a penalty formulation, a surrogate model, and a trust region strategy. The constrained problem is converted to an unconstrained form by penalizing constraint violations, which provides a unified modeling framework. A trust region restricts the search to a local region around the current best solution, which improves stability and efficiency in high dimensions. Within this region, we use the Expected Improvement acquisition function to select evaluation points by balancing improvement and uncertainty. The proposed Trust Region method integrates penalty-based constraint handling with local surrogate modeling. This combination enables efficient exploration of feasible regions while maintaining sample efficiency. We compare the proposed method with state-of-the-art methods on synthetic and real-world high-dimensional constrained optimization problems. The results show that the method identifies high-quality feasible solutions with fewer evaluations and maintains stable performance across different settings.