Modeling dynamics of a real-coded CHC algorithm in terms of dynamical probability distributions

Abstract

Some theoretical models have been proposed in the literature to predict dynamics of real-coded evolutionary algorithms. These models are often applied to study very simplified algorithms, simple real-coded functions or sometimes these make difficult to obtain quantitative measures related to algorithm performance. This paper, trying to reduce these simplifications to obtain a more useful model, proposes a model that describes the behavior of a slightly simplified version of the popular real-coded CHC in multi-peaked landscape functions. Our approach is based on predicting the shape of the search pattern by modeling the dynamics of clusters, which are formed by individuals of the population. This is performed in terms of dynamical probability distributions as a basis to estimate its averaged behavior. Within reasonable time, numerical experiments show that is possible to achieve accurate quantitative predictions in functions of up to 5D about performance measures such as average fitness, the best fitness reached or number of fitness function evaluations.