MOBO-OSD: Batch Multi-Objective Bayesian Optimization via Orthogonal Search Directions
Lam Ngo, Huong Ha, Jeffrey Chan, Hongyu Zhang
Bayesian Optimization (BO) is a powerful tool for optimizing expensive black-box objective functions. Much research has been conducted on the single-objective optimization problem, while the multi-objective optimization problem remains challenging. In this paper, we propose NBI-MOBO, a multi-objective Bayesian Optimization algorithm inspired by the Normal Boundary Intersection framework. NBI-MOBO decomposes the multi-objective problem into a series of single-objective subproblems, referred to as NBI-MOBO subproblems, each constrained along a predefined search direction in the objective space. Solving these subproblems yields a set of Pareto-optimal candidate solutions. NBI-MOBO employs a well-distributed set of search directions across the objective space, which enhances solution diversity, hence improving hypervolume performance of selected solutions. Furthermore, to improve coverage of the Pareto-optimal candidate solutions without requiring a large number of subproblems, we leverage a Pareto Front Estimation technique that locally explores the neighborhood of each obtained candidate, generating additional Pareto-optimal candidates. Additionally, NBI-MOBO can scale to more than three objectives while maintaining good hypervolume performance. Our experiments and analysis on various synthetic and real-world benchmark functions with various objective functions, ranging from 2 to 6 objectives, show that NBI-MOBO can outperform the state of the arts.