  Bayesian optimization (BO) is an efficient and flexible global optimization
framework that is applicable to a very wide range of engineering applications.
To leverage the capability of the classical BO, many extensions, including
multi-objective, multi-fidelity, parallelization, latent-variable model, have
been proposed to improve the limitation of the classical BO framework. In this
work, we propose a novel multi-objective (MO) extension, called srMO-BO-3GP, to
solve the MO optimization problems in a sequential setting. Three different
Gaussian processes (GPs) are stacked together, where each of the GP is assigned
with a different task: the first GP is used to approximate the single-objective
function, the second GP is used to learn the unknown constraints, and the third
GP is used to learn the uncertain Pareto frontier. At each iteration, a MO
augmented Tchebycheff function converting MO to single-objective is adopted and
extended with a regularized ridge term, where the regularization is introduced
to smoothen the single-objective function. Finally, we couple the third GP
along with the classical BO framework to promote the richness and diversity of
the Pareto frontier by the exploitation and exploration acquisition function.
The proposed framework is demonstrated using several numerical benchmark
functions, as well as a thermomechanical finite element model for flip-chip
package design optimization.
