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Recently, we introduced the sorted Gaussian mixture models (SGMMs) algorithm providing the means to tradeoff performance for operational speed and thus permitting the speed-up of GMM-based classification schemes. The performance of the SGMM algorithm depends on the proper choice of the sorting function, and the proper adjustment of its parameters. In the present work, we employ particle swarm optimization (PSO) and an appropriate fitness function to find the most advantageous parameters of the sorting function. We evaluate the practical significance of our approach on the text-independent speaker verification task utilizing the NIST 2002 speaker recognition evaluation (SRE) database while following the NIST SRE experimental protocol. The experimental results demonstrate a superior performance of the SGMM algorithm using PSO when compared to the original SGMM. For comprehensiveness we also compared these results with those from a baseline Gaussian mixture model-universal background model (GMM-UBM) system. The experimental results suggest that the performance loss due to speed-up is partially mitigated using PSO-derived weights in a sorted GMM-based scheme.