MOBO-OSD: Batch Multi-Objective Bayesian Optimization via Orthogonal Search Directions

TL;DR

MOBO-OSD introduces a novel multi-objective Bayesian optimization method that employs orthogonal search directions and Pareto front estimation to efficiently generate diverse Pareto optimal solutions, outperforming existing algorithms.

Contribution

The paper proposes MOBO-OSD, a new multi-objective Bayesian optimization algorithm using orthogonal search directions and Pareto front estimation for improved solution diversity and performance.

Findings

Outperforms state-of-the-art algorithms on benchmark functions.

Provides broad coverage of the objective space with diverse solutions.

Supports batch optimization for faster convergence.

Abstract

Bayesian Optimization (BO) is a powerful tool for optimizing expensive black-box objective functions. While extensive research has been conducted on the single-objective optimization problem, the multi-objective optimization problem remains challenging. In this paper, we propose MOBO-OSD, a multi-objective Bayesian Optimization algorithm designed to generate a diverse set of Pareto optimal solutions by solving multiple constrained optimization problems, referred to as MOBO-OSD subproblems, along orthogonal search directions (OSDs) defined with respect to an approximated convex hull of individual objective minima. By employing a well-distributed set of OSDs, MOBO-OSD ensures broad coverage of the objective space, enhancing both solution diversity and hypervolume performance. To further improve the density of the set of Pareto optimal candidate solutions without requiring an excessive number of subproblems, we leverage a Pareto Front Estimation technique to generate additional solutions in the neighborhood of existing solutions. Additionally, MOBO-OSD supports batch optimization, enabling parallel function evaluations to accelerate the optimization process when resources are available. Through extensive experiments and analysis on a variety of synthetic and real-world benchmark functions with two to six objectives, we demonstrate that MOBO-OSD consistently outperforms the state-of-the-art algorithms. Our code implementation can be found at https://github.com/LamNgo1/mobo-osd.