Adaptive ensemble of metamodels for the solution of modelling and global optimization problems

The metamodeling approach is increasingly popular and has been shown to be useful in the analysis and optimization of computationally expensive simulation-based models in, for example, the aerospace, automotive and oil industries. Nevertheless, the problem of finding a metamodel that approximates a function (the original numeric model) from a sample of points (data), is inverse and nonlinear so that there are frequently multiple models that offer a reasonable fit to the data. This work proposes a method of modeling and global optimization with restrictions using an adaptive ensemble of metamodels (i.e., Radial Basis Functions, Kriging and Polynomial Regression), and its effectiveness is assessed comparing its performance (on 6 recognized test functions and an industrial application) with the individual use of the members of the ensemble. The performance of the proposed ensemble was robust: i) the average R-2 per sample size is one of the two highest with one of the two smallest variances (modeling) and ii) in most case studies the metamodel exhibited one of the two best results (modeling and optimization).