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.

翻译：高维黑箱环境下的约束优化因评估成本高昂、梯度信息缺失及可行域复杂而颇具挑战。本文提出一种融合惩罚函数、代理模型与信任域策略的贝叶斯优化方法。通过惩罚约束违例将原约束问题转化为无约束形式，构建统一建模框架。信任域将搜索范围限制在当前最优解邻近区域，有效提升高维场景下的稳定性与效率。在该区域内，采用期望改进采集函数，平衡优化潜力与不确定性以选取评估点。所提出的信任域方法将基于惩罚的约束处理与局部代理建模有机结合，在保持采样效率的同时实现可行域的高效探索。在合成与真实高维约束优化问题上与前沿方法的对比结果表明，该方法能以更少评估次数获得高质量可行解，并在不同场景下保持稳定性能。