A Bayesian view on the polynomial distribution model in estimation of distribution algorithms

Estimation of distribution algorithms(EDA) are a class of recently-developed evolutionary algorithms in which the probabilistic model are used to explicitly characterize the distribution of the population and to generate new individuals. The polynomial distribution is applied by discrete EDAs and continuous EDAs based on discretization of the domain such as histogram-based EDA. We can unify those kinds of EDA from their distribution and call them PolyEDA. In this paper, we theoretically analyze PolyEDA from a Bayesian analysis view. Our analysis is based on the assumption that the prior distribution of the parameters satisfies a Dirichlet distribution, because under this assumption the formulation can be analytically solved. Furthermore, we notice that the prior distribution is always overlooked by previous algorithms, so we follow this way and propose some strategies to improve the PolyEDA. The experimental results show that these new strategies can help the polynomial model based estimation of distribution algorithms achieve better convergence and diversity.