Anisotropic adaptive variance scaling for Gaussian estimation of distribution algorithm

A novel ensemble estimation of distribution algorithm with distribution modification strategies

The canonical estimation of distribution algorithm (EDA) easily falls into a local optimum with an ill-shaped population distribution, which leads to weak convergence performance and less stability when solving global optimization problems. To overcome this defect, we explore a novel EDA variant with an ensemble of three distribution modification strategies, i.e., archive-based population updating (APU), multileader-based search diversification (MSD), and the triggered distribution shrinkage (TDS) strategy, named E3-EDA. The APU strategy utilizes historical population information to rebuild the search scope and avoid ill-shaped distributions. Moreover, it continuously updates the archive to avoid overfitting the distribution model. The MSD makes full use of the location differences among populations to evolve the sampling toward promising regions. TDS is triggered when the search stagnates, shrinking the distribution scope to achieve local exploitation. Additionally, the E3-EDA performance is evaluated using the CEC 2014 and CEC 2018 test suites on 10-dimensional, 30-dimensional, 50-dimensional and 100-dimensional problems. Moreover, several prominent EDA variants and other top methods from CEC competitions are comprehensively compared with the proposed method. The competitive performance of E3-EDA in solving complex problems is supported by the nonparametric test results.

An Adaptive Covariance Scaling Estimation of Distribution Algorithm

Optimization problems are ubiquitous in every field, and they are becoming more and more complex, which greatly challenges the effectiveness of existing optimization methods. To solve the increasingly complicated optimization problems with high effectiveness, this paper proposes an adaptive covariance scaling estimation of distribution algorithm (ACSEDA) based on the Gaussian distribution model. Unlike traditional EDAs, which estimate the covariance and the mean vector, based on the same selected promising individuals, ACSEDA calculates the covariance according to an enlarged number of promising individuals (compared with those for the mean vector). To alleviate the sensitivity of the parameters in promising individual selections, this paper further devises an adaptive promising individual selection strategy for the estimation of the mean vector and an adaptive covariance scaling strategy for the covariance estimation. These two adaptive strategies dynamically adjust the associated numbers of promising individuals as the evolution continues. In addition, we further devise a cross-generation individual selection strategy for the parent population, used to estimate the probability distribution by combing the sampled offspring in the last generation and the one in the current generation. With the above mechanisms, ACSEDA is expected to compromise intensification and diversification of the search process to explore and exploit the solution space and thus could achieve promising performance. To verify the effectiveness of ACSEDA, extensive experiments are conducted on 30 widely used benchmark optimization problems with different dimension sizes. Experimental results demonstrate that the proposed ACSEDA presents significant superiority to several state-of-the-art EDA variants, and it preserves good scalability in solving optimization problems.

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

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.