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Searching a probabilistic model for differential evolution population

The probabilistic behavior study of Evolutionary Algorithms (EA) in every generation is relevant to perform exploratory analysis, in order to summarize, monitor, and to formulate a hypothesis about observed data. For the purpose of understanding better how the population evolves along the generations, we made a descriptive analysis of Differential Evolution (DE) evolving population. The objective was to find a probabilistic model to fit the population over the generation. This probabilistic model can be a known probability distribution or a latent variable model, i.e., Gaussian mixture model. In this work, we conducted different adhesion tests for known continuous distributions defined for real variables, namely, Students t, Laplace, and Normal distributions. Among them, the latter showed the highest number of occurrences, hence we conducted a further study over the probability populations distribution based on this result. We used Henze and Zirkler hypothesis tests to verify multivariate normal distribution and a version of the multivariate Kolmogorov test aiming to assess the adjustment to other known multivariate continuous distributions. The probabilistic behavior analysis of the population generated by the DE was made over the single-objective box-constrained continuous optimization problems, the CEC13 benchmarks.