Bayesian Optimization via Exact Penalty

Constrained optimization problems pose challenges when the objective function and constraints are nonconvex and their evaluation requires expensive black-box simulations. Recently, hybrid optimization methods that integrate statistical surrogate modeling with numerical optimization algorithms have shown great promise, as they inherit the properties of global convergence from statistical surrogate modeling and fast local convergence from numerical optimization algorithms. However, the computational efficiency is not satisfied by practical needs under limited budgets and in the presence of equality constraints. In this article, we propose a novel hybrid optimization method, called exact penalty Bayesian optimization (EPBO), which employs Bayesian optimization within the exact penalty framework. We model the composite penalty function by a weighted sum of Gaussian processes, where the qualitative components of the constraint violations are smoothed by their predictive means. The proposed method features (i) closed-form acquisition functions, (ii) robustness to initial designs, (iii) the capability to start from infeasible points, and (iv) effective handling of equality constraints. We demonstrate the superiority of EPBO to state-of-the-art competitors using a suite of benchmark synthetic test problems and two real-world engineering design problems.