Study And Application Of CMA-ES Algorithm Based On Cloud Model

In order to solve various optimization problems encountered in this realworld, various optimization algorithms appear one after another. Generallyspeaking, optimization algorithms can be divided into deterministic andprobabilistic optimization algorithms. Traditional optimization algorithmsachieve the extreme value of target function based on its mathematical form, butwhen the target function is discontinuous and undifferentiable, deterministicalgorithms are powerlessness and greatly limited. Inspired by the nature,probabilistic algorithms based on various natural mechanisms have become themainstream of development of optimization algorithms, such as simulatedannealing algorithm(SA) based on physical mechanisms, artificial ant colonyalgorithm (ACO) based on swarm intelligence mechanisms, evolutionaryalgorithms(EAs) based on evolutionary mechanisms, and so on. Althoughly,these algorithms show satisfactory problem-solving performance to some extent,however, there still exist some common problems, such as slow convergence,poor search ability, premature convergence, when solving some of optimizationproblems. Currently, no one algorithm can well solve all of optimizationproblems, according to the characteristic of specific problem, it is a verymeaningful job that designing or improving the mechanism of algorithm to solve different kinds of optimization problems.As an important part of probabilistic algorithms, evolutionary algorithmshave become an important research field of optimization. As one of the branchesof evolutionary algorithms, evolution strategy shows superior performance insolving continuous real-valued optimization problems, in particular, covariancematrix adaptation evolution strategy (CMA-ES) has the advantages ofinsensitive to population size, fast convergence with small populations, goodglobal performance with large populations, which attracts great concern in thefield of continuous real-valued optimization. However, the same as otherevolutionary algorithms, there are still the disadvantages of falling into localoptimum easily and poor problem-solving precision when CMA-ES is employedto solve some of optimization problems.Cloud model is an effective tool for dealling with uncertainty problems, canwell achieve uncertainty modeling and reasoning. The evolutionary process is acomplex process full of a lot of uncertainty, many concepts and behaviors ofwhich are uncertain. The step-size control process of CMA-ES employs thehistorical feedback information of “evolution path”, which makes theevolutionary process highly efficient, but the step-size is changed bydeterministic function mapping, to some extent, which ignores the uncertainty ofthe evolutionary process. As for this problem, this paper is based on the goodcapability of cloud model in dealing with uncertainty, step-size control processof CMA-ES is improved, then an improved CMA-ES algorithm based on cloud reasoning is proposed. Firstly, the cloud reasoning model of step-size control isestablished based on the process of CMA-ES; secondly, the step-size iscontrolled using uncertainty reasoning method of cloud model; finally, theproblem-solving performance of the improved CMA-ES algorithm is tested andverified on63test functions. Experimental results show that: the improvedCMA-ES algorithm has a strong global optimization ability than basic CMA-ESalgorithm, can improve the success rate, at the same time, further improve theproblem-solving precision and convergence speed, and has also betteroptimization stability.It has a great impact on the performance of Support Vector Machine (SVM)for its model parameters selection. We employ the improved CMA-ESalgorithm to optimize the parameters of SVM, and then a method of SVMparameters selection based on improved CMA-ES is proposed. Compared withthe methods based on genetic algorithm (GA) and particle swarm optimization(PSO), and through training and prediction of common UCI datasets, theexperimental results show that: the classification accuracy and convergencespeed of SVM parameters optimization selection based on the improvedCMA-ES algorithm are significantly improved.