Modern Metaheuristic with Multi-Objective Formulation for the Variable Selection Problem

Abstract

The development of efficient algorithms for variable selection becomes important to deal with large and complex datasets. Most works in quantitative chemical analysis have used Genetic Algorithms (GAs) as a reference method to select variables. On the other hand, new advances in metaheuristic techniques provide novel possibilities in this task Moreover, the application of Multi-Objective Optimization (MOO) may significantly contribute to efficiently construct an accurate model in the context of multivariate calibration. MOO has showed itself as an efficiently and successful tool to dealing with conflicting objective-functions. For instance, the use of MOO may be considered as a good choice to treat the reducing of prediction error and the number of selected variables in a calibration model. In this paper, we present a modern metaheuristic implementation called Multi-Objective Firefly Algorithm (MOFA) for variable selection in multivariate calibration models. The goal is to propose an optimization to reduce the prediction error of the property of interest in the analysed sample as well as reducing the number of selected variables. However, the outcomes are remarkably promising compared with the previous work. Based on the results obtained, it is possible to demonstrate that our proposal is a viable alternative in order to deal with such conflicting objectives. Additionally, we compare MOFA with a traditional GA implementation and show that MOFA is more efficient for the variable selection problem.