Genetic algorithms as a method for variable selection in multiple linear regression and partial least squares regression, with applications to pyrolysis mass spectrometry

Four optimising methods for variable selection in multivariate calibration have been described: one for determining the optimal subset of variables to give the best possible root-mean-square error of prediction (RMSEP) in a multiple linear regression (MLR) model, the second for determining the optimal subset of variables which produce a model with RMSEP less than or equal to a given value. Algorithms three and four were identical to algorithms one and two, respectively, except that this time they use a cost function derived from a partial least squares (PLS) model rather than an MLR model. Applied to a typical set of pyrolysis mass spectrometry data the first variable selection method is shown to reduce the RMSEP of the optimal MLR or PLS model significantly when the number of variables is decreased by approximately half. Alternatively, the number of variables may be reduced substantially (> 10-fold) with no loss in RMSEP.