A low-sample-count, high-precision Pareto front adaptive sampling algorithm based on multi-criteria and Voronoi

In this paper, a Pareto front (PF)-based sampling algorithm, PF-Voronoi sampling method, is proposed to solve computationally intensive multi-objective problems of medium size. The Voronoi diagram is introduced to classify the region containing PF prediction points into Pareto front cells (PFCs). Valid PFCs are screened according to the maximum crowding criterion (MCC), Maximum leave-one-out error criterion (MLEC), and maximum mean mean-square-error (MSE) criterion (MMMSEC). Sampling points are selected among the valid PFCs based on the Euclidean distance. The PF-Voronoi sampling method is applied to the coupled Kriging and NSGA-II models, and its validity is verified on the ZDT mathematical cases. The results show that the MCC criterion helps to improve the distribution diversity of PF. The MLEC criterion and the MMMSEC criterion reduce the number of training samples by 38.9