Research On Large Scale Optimization Problem Using Covariance Matric Adaptive Evolution Strategy

The real-value optimization problem is a kind of problem that has been widely used in industrial,engineering,and daily life.With the development of science and technology,the system that need to be optimized is becoming more and more complex,and the parameters or decision variables that need to be optimized in the problem are also increasing.As the time,the search space of the problem solution will also increase exponentially,and the "dimensional disaster" will appear.If the dimension is too high,the optimization performance and speed of the algorithm will decrease sharply when solving large-scale optimization problems,which will make the search ability and convergence speed of the algorithm greatly challenged.Therefore,studying the large-scale real-value optimization problem has certain theoretical significance and important practical application significance.This paper has carried out research on an improved Covariance Matrix Adaptation Evolution Strategy(CMAES)based on a collaborative co-evolutionary framework and a global differential grouping method.Firstly,in order to solve the problem of weak early exploration ability of CMAES,an improved research on CMAES was carried out,and a covariance matrix adaptive evolution strategy(D-CMAES algorithm)for efficient eigenvalue selection was proposed.This improvement enhanced the algorithm's "exploration" and "exploitation." The covariance matrix C is an important parameter that affects the performance of the CMAES.This paper improves the optimization performance of the algorithm by improving the eigenvalue of the parameter covariance matrix C.Four improvement methods for eigenvalues are proposed.The improved algorithm corresponding to the value selection method is compared and analyzed on the test function set.The simulation results show that the D-CMAES is excellent in solving unimodal and multimodal functions,and the optimization results of the D-CMAES are compared with the existing optimization algorithms.The results show that the D-CMAES has a good performance in optimization.Secondly,this paper studies the global differential grouping method.Because the threshold selection method of the global differential grouping has a great influence on the variable grouping result,this paper improves the method of selecting the threshold value.Finally,based on the collaborative co-evolution framework,an algorithm(CC-D-CMAES algorithm)combining the global differential grouping method with an improved covariance matrix adaptive evolution strategy is proposed to solve large-scale optimization problems.For the problem of large-scale optimization problems with too large dimensions,the improved global difference grouping method is used to judge the correlation of variables and group the variables.A large problem is decomposed into some sub-problems,D-CMAES is used to optimize each sub-problem,and then the final result is obtained.Simulation results show that the CC-D-CMAES proposed in this paper has good performance on the large-scale optimization problem of CEC2010,and has good performance on 1000-dimensional separable and inseparable problems.