  Bayesian optimization is a promising methodology for analog circuit
synthesis. However, the sequential nature of the Bayesian optimization
framework significantly limits its ability to fully utilize real-world
computational resources. In this paper, we propose an efficient parallelizable
Bayesian optimization algorithm via Multi-objective ACquisition function
Ensemble (MACE) to further accelerate the optimization procedure. By sampling
query points from the Pareto front of the probability of improvement (PI),
expected improvement (EI) and lower confidence bound (LCB), we combine the
benefits of state-of-the-art acquisition functions to achieve a delicate
tradeoff between exploration and exploitation for the unconstrained
optimization problem. Based on this batch design, we further adjust the
algorithm for the constrained optimization problem. By dividing the
optimization procedure into two stages and first focusing on finding an initial
feasible point, we manage to gain more information about the valid region and
can better avoid sampling around the infeasible area. After achieving the first
feasible point, we favor the feasible region by adopting a specially designed
penalization term to the acquisition function ensemble. The experimental
results quantitatively demonstrate that our proposed algorithm can reduce the
overall simulation time by up to 74 times compared to differential evolution
(DE) for the unconstrained optimization problem when the batch size is 15. For
the constrained optimization problem, our proposed algorithm can speed up the
optimization process by up to 15 times compared to the weighted expected
improvement based Bayesian optimization (WEIBO) approach, when the batch size
is 15.
