Investigating the Correlation Amongst the Objective and Constraints in Gaussian Process-Assisted Highly Constrained Expensive Optimization

Abstract

Expensive constrained optimization refers to problems where the calculation of the objective and/or constraint functions are computationally intensive due to the involvement of complex physical experiments or numerical simulations. Such expensive problems can be addressed by Gaussian process-assisted evolutionary algorithms. In many problems, the (single) objective and constraints are correlated to some extent. Unfortunately, existing works based on the Gaussian process for expensive constrained optimization treat the objective and multiple constraints as being statistically independent, typically for the ease of computation. To fill this gap, this article investigates the correlation among the objective and constraints. To be specific, we model the correlation amongst the objective and constraint functions using a multitask Gaussian process prior, and then mathematically derive a constrained expected improvement acquisition function that allows the correlation among the objective and constraints. The correlation between the objective and constraints can be captured and leveraged during the optimization process. The performance of the proposed method is examined on a set of benchmark problems and a real-world antenna design problem. On problems with high correlation amongst the objective and constraints, the experimental results show that leveraging the correlation yields improvements in both the optimization speed and the constraint-handling ability compared with the method that assumes the objective and constraints are statistically independent.