Multi-Objective Evolutionary Algorithm NSGA-II for Variables Selection in Multivariate Calibration Problems

This paper proposes a multiobjective formulation for variable selection in multivariate calibration problems in order to improve the generalization ability of the calibration model. The authors applied this proposed formulation in the multiobjective genetic algorithm NSGA-II. The formulation consists in two conflicting objectives: minimize the prediction error and minimize the number of selected variables for multiple linear regression. These objectives are conflicting because, when the number of variables is reduced the prediction error increases. As study of case is used the wheat data set obtained by NIR spectrometry with the objective for determining a variable subgroup with information about protein concentration. The results of traditional techniques of multivariate calibration as the partial least square and successive projection algorithm for multiple linear regression are presented for comparisons. The obtained results showed that the proposed approach obtained better results when compared with a mono-objective evolutionary algorithm and with traditional techniques of multivariate calibration.