As a typical model-based evolutionary algorithm (EA), estimation of distribution algorithm (EDA) possesses unique characteristics and has been widely applied to global optimization. However, the common-used Gaussian EDA (GEDA) usually suffers from premature convergence which severely limits its search efficiency. This study first systematically analyses the reasons for the deficiency of the traditional GEDA, then tries to enhance its performance by exploiting its evolution direction, and finally develops a new GEDA variant named EDA2. Instead of only utilizing some good solutions produced in the current generation when estimating the Gaussian model, EDA2 preserves a certain number of high-quality solutions generated in previous generations into an archive and takes advantage of these historical solutions to assist estimating the covariance matrix of Gaussian model. By this means, the evolution direction information hidden in the archive is naturally integrated into the estimated model which in turn can guide EDA2 towards more promising solution regions. Moreover, the new estimation method significantly reduces the population size of EDA2 since it needs fewer individuals in the current population for model estimation. As a result, a fast convergence can be achieved. To verify the efficiency of EDA2, we tested it on a variety of benchmark functions and compared it with several state-of-the-art EAs, including IPOP-CMAES, AMaLGaM, three high-powered DE algorithms, and a new PSO algorithm. The experimental results demonstrate that EDA2 is efficient and competitive.

We modified some experiments in this manuscript that it has to be rewritten. With the agreement of my co-authors, we would like to withdraw this manuscript