Penalization method to convert Bayesian optimization methods into batch multi-objective Bayesian optimization methods

Abstract

Bayesian optimization is a surrogate-based global optimization method that is increasingly being used for engineering design. However, most methods are designed to be sequential, and in optimization problems where the functional evaluation can be easily parallelized, batch methods are more effective at reducing real-time computation. While existing batch multi-objective Bayesian optimization (B-MOBO) methods achieve strong performance, they are typically purpose-built from scratch, limiting ability to leverage the extensive library of proven sequential acquisition functions for parallel settings. In this paper, a generalizable transformation methodology is developed that converts compatible single- or multi-objective sequential Bayesian optimization methods into B-MOBO methods. The key innovation is a Euclidean distance-based composite acquisition function with multi-objective penalization averaging, which combines multiple sequential acquisition functions while incorporating objective-wise penalization information from all objectives and preventing redundant sampling in batch selection. To demonstrate the schema, this methodology is applied to two representative sequential acquisition strategies, the expected improvement method (single-objective) and the quality metrics method (multi-objective), to develop two new B-MOBO variants. These new methods are then compared against their sequential counterparts and established B-MOBO methods using both computation time and real-time analysis. Results show that the new B-MOBO methods are as effective as existing methods at solving optimization problems in terms of solution quality and show improvements when real-time is considered.