Multi-objective Genetic Algorithm for Variable Selection in Multivariate Classification Problems: A Case Study in Verification of Biodiesel Adulteration

Abstract

This paper proposes multi-objective genetic algorithm for the problem of variable selection in multivariate calibration. We consider the problem related to the classification of biodiesel samples to detect adulteration, Linear Discriminant Analysis classifier. The goal of the multi--objective algorithm is to reduce the dimensionality of the original set of variables; thus, the classification model can be less sensitive, providing a better generalization capacity. In particular, in this paper we adopted a version of the Non-dominated Sorting Genetic Algorithm (NSGA-II) and compare it to a mono-objective Genetic Algorithm (GA) in terms of sensitivity in the presence of noise. Results show that the mono-objective selects 20 variables on average and presents an error rate of 14%. One the other hand, the multi-objective selects 7 variables and has an error rate of 11%. Consequently, we show that the multi-objective formulation provides classification models with lower sensitivity to the instrumental noise when compared to the mono-objetive formulation