Enhancing boundary optimality in constrained Bayesian optimization via exterior barrier functions

Abstract

In Bayesian optimization frameworks, expected performance indicator-based acquisition functions, such as Expected Improvement and Expected Hypervolume Improvement, are among the most widely adopted approaches for both single- and multi-objective problems, and are readily extensible to constrained problems through surrogate-based feasibility predictions. However, the intrinsic characteristics of these formulations introduce challenges in convergence, particularly when optimal solutions lie on the boundary of the feasible region. Firstly, the accuracy refinement inherent in these formulations leads to a highly localized subproblem, characterized by broadly flat regions with only narrow peaks near the global optimum, resembling a needle-in-a-haystack problem that poses significant challenges for any optimizer. Secondly, uncertainty in constraint predictions should be explicitly accounted for to avoid overly conservative optimization that limits exploration. In this study, we examine the challenges associated with the constrained forms of expected indicator types and propose an acquisition strategy that combines constraint relaxation at the subproblem level with barrier type exterior penalization. The proposed approach yields a more tractable subproblem, which enhances exploration in promising regions of the feasibility space, leading to improved convergence and more reliable feasibility prediction, particularly for solutions with active constraints. Superior performance is demonstrated on several single- and multi-objective benchmark problems, as well as an engineering-relevant aerodynamic optimization case.