Ordinary Kriging: A machine learning tool applied to mixed-integer multiparametric approach

The complexity of optimization problems of optimization problems increases along with the dimensions, non-linearity, and/or the required accuracy of the model constraints and objective functions. Additionally, for mixed-integer multiparametric problems, the discreet and uncertain nature of the variables and parameters to be considered, affect the complexity further more. Recently, machine learning or data-driven techniques have been proposed as alternatives for the solution of complex multiparametric programming problems. However, those methods presents as a main limitation its very high prediction error in variables that show discrete behavior and on the limits of the critical/local regions. This work extends this investigation line via proposing a novel machine learning method for solving these kind of problems based on an iterative process that use Ordinary Kriging as supervised learning tool to classify and model data. Furthermore, Ordinary Kriging can be also used, as an unsupervised tool to cluster data. The proposed methodology is applied to a benchmark case-study and the numerical results exhibits a significant improvements, up to 65% based on the normalized root-mean-square error, compared with reported information that used other modeling techniques.