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Mixture models (including latent class analysis and latent profile analysis) have been increasingly used in educational research to identify latent classes of individuals who differ with respect to model parameters. For data obtained from system logs of virtual learning environments, the number of potential indicators of latent classes is often too large, leading to model non-convergence. Thus, there is a need for developing methods to automate simultaneous variable selection and latent class enumeration for mixture models. We use the ant colony optimization algorithm to automate simultaneous selection of latent classes and indicators for latent class analysis. Results show that the proposed method is able to select a set of non-redundant indicators and identify the correct number of classes.