srMO-BO-3GP: A sequential regularized multi-objective constrained Bayesian optimization for design applications

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.

aphBO-2GP-3B: A budgeted asynchronously-parallel multi-acquisition for known/unknown constrained Bayesian optimization on high-performing computing architecture

High-fidelity complex engineering simulations are highly predictive, but also computationally expensive and often require substantial computational efforts. The mitigation of computational burden is usually enabled through parallelism in high-performance cluster (HPC) architecture. In this paper, an asynchronous constrained batch-parallel Bayesian optimization method is proposed to efficiently solve the computationally-expensive simulation-based optimization problems on the HPC platform, with a budgeted computational resource, where the maximum number of simulations is a constant. The advantages of this method are three-fold. First, the efficiency of the Bayesian optimization is improved, where multiple input locations are evaluated massively parallel in an asynchronous manner to accelerate the optimization convergence with respect to physical runtime. This efficiency feature is further improved so that when each of the inputs is finished, another input is queried without waiting for the whole batch to complete. Second, the method can handle both known and unknown constraints. Third, the proposed method considers several acquisition functions at the same time and sample based on an evolving probability mass distribution function using GP-Hedge scheme, where parameters are corresponding to the performance of each acquisition function. The proposed framework is termed aphBO-2GP-3B, which corresponds to asynchronous parallel hedge Bayesian optimization with two Gaussian processes and three batches. The aphBO-2GP-3B framework is demonstrated using two high-fidelity expensive industrial applications, where the first one is based on finite element analysis (FEA) and the second one is based on computational fluid dynamics (CFD) simulations.