We propose an evolutionary optimization method for maximum likelihood and approximate maximum likelihood estimation of discrete latent variable models. The proposal is based on modified versions of the expectation–maximization (EM) and variational EM (VEM) algorithms, which are based on the genetic approach and allow us to accurately explore the parameter space, reducing the chance to be trapped into one of the multiple local maxima of the log-likelihood function. Their performance is examined through an extensive Monte Carlo simulation study where they are employed to estimate latent class, hidden Markov, and stochastic block models and compared with the standard EM and VEM algorithms. We observe a significant increase in the chance to reach global maximum of the target function and a high accuracy of the estimated parameters for each model. Applications focused on the analysis of cross-sectional, longitudinal, and network data are proposed to illustrate and compare the algorithms.