AI Insight
This paper presents a new Bayesian optimization algorithm for solving constrained optimization problems in high-dimensional spaces where function evaluations are expensive and gradients are unavailable. The method converts constrained problems into unconstrained ones using penalties, combines this with surrogate models that approximate the objective function, and restricts the search to local trust regions around current best solutions. Testing on synthetic and real-world problems demonstrates the approach finds high-quality feasible solutions with fewer function evaluations compared to existing methods.
Why it matters
This work addresses a common challenge in engineering design, hyperparameter tuning, and scientific experimentation where evaluating candidate solutions is costly and constraints must be satisfied. The improved sample efficiency could reduce computational costs and experimental time in applications such as materials discovery, robotics control, and industrial process optimization.
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⚠️ Preprint – Noch nicht peer-reviewed
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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.
Source: Trust Region Constrained Bayesian Optimization with Penalized Constraint Handling