A non-uniform multi-point incremental Kriging facing with discrete response surfaces

The conventional Kriging model is widely employed for continuous response surface fitting. Nonetheless, when dealing with discrete response surfaces with non-uniform sample points, Kriging exhibits limited construction efficiency and lacks accuracy. In this regard, we analyze the influence that non-uniform training data and discrete response values bring to the Kriging model both theoretically and empirically. On this basis, a nonuniform multi-point incremental Kriging facing with discrete response surfaces (PRIK) is proposed, aiming at striking a balance between model accuracy and construction efficiency. PRIK employs the multiple sample points prescreening strategy to select training data from the sample pool that embodies both uncertainty and diversity. Subsequently, ridge regression Kriging is introduced to prevent the potential accuracy reductions stemming from local densely distributed sample points for discrete response surfaces. Lastly, a multi-point incremental updating method and control criterion are introduced to reduce the construction complexity of the ridge regression Kriging. Starting from benchmarks commonly used for surrogate model testing, we developed 10 test cases with discrete response values characterized by diverse input space dimensional, ranges, and landscape features, along with five evaluation metrics. We have performed extensive experiments on various numbers of sample points and parameter values. Experiment results illustrate that the prescreening strategy and the incremental updating method can significantly reduce Kriging's training time, calling time, and the number of calls to the original system. Ridge regression Kriging notably enhances Kriging's accuracy. By applying PRIK to a decision boundary search problem that needs to fit a discrete response surface with non-uniform sample points, it is found that the accuracy of the model constructed by PRIK is greatly improved compared with the original Kriging.