Parallelization of a Modified Firefly Algorithm using GPU for Variable Selection in a Multivariate Calibration Problem

1. Introduction

Multivariate calibration refers to construction procedure of a mathematical model that establishes the relationship between the properties measured by a instrument and the concentration of a sample to be determined (Brown et al., 1994). The building of a model from a subset of explanatory variables usually involves two conflicting objectives:

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  Extracting as much information from a measured data with many possible independent variables;

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  Decreasing the cost of obtaining data by using the smallest set of independent variables that results in a model with high accuracy and low variance.

The balance between these two commitments is achieve using variable selection techniques. The application of multivariate calibration had a breakthrough and nowadays are very popular (Ferreira et al., 1999). One of the most interesting features of modern instrumental methods is the number of variables that can be measured in a single sample. Recently, devices as spectrophotometers have generated large amount of data with thousands of variables. As a consequence, the development of efficient algorithms for variable selection is important in order to deal with data even larger (George, 2000; Coifman & Wickerhauser, 1992; Paula et al., 2013). Furthermore, a high-performance computing framework can significantly contribute to efficiently construct an accurate model (Chau et al., 2004). In this context, this paper proposes an implementation of a modified Firefly Algorithm (FA) for variable selection in a multivariate calibration problem (George, 2000; Westad, 2000; Coifman & Wickerhauser, 1992; Filho et al., 2011).

The FA is a metaheuristic inspired by the flashing behaviour of fireflies (Yang, 2008). Recent works have used FA to solve various types of problems. For instance, Yang (2009) provides a detail description of a new FA for multimodal optimization applications. Lukazik and Zak (2009) provide an implementation of the FA for constrained continuous optimization. Yang (2010) shows the use of the FA for nonlinear design problems. Senthilnath et al. (2011) use the FA for clustering on benchmark problems and compares its performance with other nature-inspired techniques. Gandomi et al. (2011) use the FA for mixed-continuous and discrete-structural optimization problems. Jati et al. (2011) apply the FA for travelling salesman problem. Banati and Monika (2011) propose a new feature selection approach that combines the Rough Set Theory with the nature-inspired FA to reduce the dimensionality of data containing large number of features. Horng (2012) proposes a new method based on the FA to construct the codebook of vector quantization for image compression. Finally, Abdullah et al. (2013) introduce a new hybrid optimization method incorporating the FA and the evolutionary operation of the differential evolution method.