An efficient estimation of distribution algorithm with rank-one modification and population reduction

Abstract

As a type of model-based metaheuristic, estimation of distribution algorithms (EDAs) show certain advantages over other metaheuristics by using statistical learning method to estimate the distribution of promising solutions. However, the commonly-used Gaussian EDAs (GEDAs) usually suffer from premature convergence that severely limits their efficiency. In this paper, we first attempt to enhance the performance of GEDA by improving its model estimation method. The new estimation method shifts the weighted mean of high-quality solutions towards the fitness improvement direction and estimates the covariance matrix by taking the shifted mean as the center. Theoretical analyses show that the new covariance matrix is essentially a rank-one modification (R1M) of the original one. It could effectively adjust both the search scope and the search direction of GEDA, and thus improving the search efficiency. Furthermore, considering the importance of the population size tuning in GEDA, we develop a population reduction (PR) strategy which linearly reduces the population size throughout the evolution. By this means, the exploration and exploitation ability of GEDA could be balanced better in different search stages and a more proper utilization of limited computation resource can be achieved. Combining GEDA with the R1M and PR strategies, a novel EDA variant named EDA-R1M-PR is developed. The performance of EDA-R1M-PR was comprehensively evaluated and compared with that of several state-of-the-art evolutionary algorithms. Experimental results indicate that the R1M and PR strategies effectively enhance the global optimization ability of GEDA and the resultant EDA-R1M-PR significantly outperforms its competitors on a set of benchmark functions.