Extending Population Based Incremental Learning using Dirichlet Processes

The unimodal Gaussian has been the distribution of choice for many extensions in Estimation of Distribution Algorithms (EDA). Some groups have used clustering algorithms, like k-means, to use multimodal distributions in different modifications of EDA. Most proposals use a fixed number of groups or clusters, and other works use heuristic approaches to find the right number of clusters in the search space without any previous information. The heuristic methods, however, lack the mathematical rigor required in the inference of a probability distribution´s parameters. In this work, we propose the use of the Nonparametric Bayesian Model known as Dirichlet Process to fit the number of clusters given the data in a modified Population Based Incremental Learning (PBIL) model. We compare our approach with similar techniques that also use multimodal probability distributions to enhance the quality of the search in other EDA approaches. Our approach shows improvements by reducing the number of generations needed to find good results that are comparable to the state of the art in clustered EDA.