Multi-Objective Bayesian Optimization Supported by Gaussian Process Classifiers and Conditional Probabilities

Abstract

In the last years, there has been an increasing effort to develop Bayesian methodologies to solve multi-objective optimization problems. Most of these methods can be classified in two groups: infilling criterion-based methods and aggregation-based methods. The first group employs an index that quantifies the gain that a new design can produce in the current Pareto front while the last group uses a (possibly non-linear) aggregation function and a weighting vector to identify a Pareto design. Most infilling-based methods have been developed to solve two-objective optimization problems. Aggregation-based methods enable the solution of many-objective optimization problems but their performance depends on the set of weighting vectors, which are often selected randomly. This study proposes a novel multi-objective Bayesian framework that exploits the rich probabilistic information that can be extracted from Gaussian process (GP) classifiers and the ability of conditional probabilities to capture design preferences. In the proposed framework, a GP classifier is trained to identify design zones that potentially contain Pareto designs. The training process involves the inference of a latent GP that encodes input-space interactions that describe a Pareto design. This latent GP enables the solution of many-objective optimization problems with any standard acquisition function and without the prescription of a weighting vector. Conditional probabilities are utilized to define design goals that promote a uniform expansion of the Pareto front. The proposed approach is demonstrated with two benchmark analytical problems and the design optimization of sandwich composite armors for blast mitigation, which involves expensive finite element simulations.