An efficient constrained global optimization algorithm with a clustering-assisted multiobjective infill criterion using Gaussian process regression for expensive problems

Abstract Constrained optimization problems trouble engineers and researchers because of their high complexity and computational cost. When the objective function and constraints are both expensive black-box problems, there are many difficulties in solving them due to the unknown mathematical expressions and limited computational resources. To address these difficulties, we propose an efficient constrained global optimization algorithm. In the proposed algorithm, Gaussian process regression models are used to approximate the expensive objective function and constraints. Differential evolution (DE) is adopted to find the minimum value of the constrained lower confidence bounding (LCB). To further improve the accuracy of the Gaussian process regression models for the objective and constraints simultaneously, a clustering-assisted multiobjective infill criterion is proposed. The multiobjective infill criterion is utilized to balance the exploration between the objective and constraints. The clustering selection method is used to maintain the diversity of the sample points. The experimental results show that the proposed algorithm is better than or at least comparable to classic algorithms and other state-of-the-art algorithms