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We present solutions to two problems that prevent the effective use of population-based algorithms in clustering problems. The first solution presents a new representation for arbitrary covariance matrices that allows independent updating of individual parameters while retaining the validity of the matrix. The second solution involves an optimization formulation for finding correspondences between different parameter orderings of candidate solutions. The effectiveness of the proposed solutions are demonstrated on a novel clustering algorithm based on particle swarm optimization for the estimation of Gaussian mixture models.