Differential Evolution Algorithm Based On Opposition-Based Learning Strategies

As a new stochastic optimization algorithm based on population,differential evolution algorithm has rapidly attracted the attention of researchers from different fields because of its advantages such as simple operation,strong robustness and fewer control parameters.However,the traditional differential evolution algorithm often shows the shortcomings of premature convergence and slow convergence speed when solving complex problems.As a result,many DE variants have been developed to improve their optimization performance.Opposition-based learning(OBL)is a new concept in machine learning,which is inspired by the antagonistic relationships between entities in the real world.The performance of many soft computing algorithms has been greatly improved by the use of opposition-based learning,and the opposition-based differential evolution(ODE)is a typical representative of them.However,OBL,ODE and their variants still have some shortcomings,such as poor ability to search for high quality solutions,lack of population diversity and falling into local traps easily.Therefore,this paper will make a profound study on OBL and DE on this basis.The main research work of this paper is as follows:(1)Based on the ODE algorithm,a neighborhood opposition-based differential evolution algorithm with Gaussian perturbation(GODE)based on Gaussian perturbation is proposed.The employment of Gaussian perturbation strategy,the search neighborhood can be established with the opposition candidate solution as the center,which provides an opportunity to find a better candidate solution in the neighborhood,and also effectively enhances the population diversity.In the Gaussian perturbation strategy,three adaptive standard deviation models are proposed by making full use of the dynamic interval boundary information of individual dimension in the population.In addition,a multi-stage perturbation strategy is designed for different evolutionary stages of the population to balance the capabilities of exploration and exploitation.(2)To verify the effectiveness of GODE,extensive simulation experiments and result analysis are conducted on the CEC-2014 benchmark function suite.In different dimensions,GODE is fully compared with DE,ODE and other 8 recent state-of-the-art algorithms using OBL.Not only the test function mean value,the average optimal function value convergence curves and the boxplot are compared and analyzed,but also two non-parametric statistical test methods,namely Wilcoxon signed-ranks test and Friedman test,which are used to test the significance of the experimental result data.Thus,the excellent performance of GODE algorithm and the effectiveness of Gaussian perturbation strategy are verified.(3)After verifying the effectiveness of the Gaussian perturbation strategy,an extended study is carried out.A new version of OBL is proposed,namely the OBL strategy based on the stochastic centroid opposition,and then the Gaussian perturbation strategy is combined with 4 different OBL strategies and embedded in DE,and then the Gaussian perturbation strategy combined with different types of OBL strategies in the DE algorithm are studied and analyzed.