Student-t Process Assisted Covariance Matrix Adaptation Evolution Strategy Research And Its Application

Evolutionary algorithms(EAs)is a gradient-free stochastic optimization method that has been successfully applied to a wide spectrum of engineering problems.Covariance matrix adaptation evolutionary strategy algorithm as an advanced evolutionary algorithm,it's considered one of the most competitive evolutionary algorithm in real value optimization.CMA-ES approximate the contour lines of the objective function through covariance matrix adaptation,enables evolutionary strategy algorithm to have invariance to any invertible linear transformation of the search space,and to have outstanding capability for solving the ill conditioned or highly none-separable problems.But as any other EAs,CMA-ES may suffer from insufficient convergence speed where the budget of objective function evaluations is limited,it takes quite much evaluations to explore the function because of the search information is only provided by evaluated the function,a set of candidate solutions(populations)can free choose,while means greater search information,prevents from using CMA-ES on computationally expensive problems.And CMA-ES is a local search optimization algorithm,there are some disadvantages of CMA-ES such as the weakening ability of global searching,the easily occurring phenomenon of early mature and so on.Then,this thesis put forward a better algorithm to solve those problems,called a student-t process assisted covariance matrix adaptation evolution strategy optimization algorithm.The kernel function used in the algorithm is constructed by the covariance matrix.Take advantage of the student-t process,which plays a key role in both online learning about the historic experience and predicting the promising region contained globally optimal solution,the frequency of calculating fitness function in the algorithm is reduced markedly.Meanwhile,in order to improve the efficiency of the algorithm,the algorithm is sampling in the trust region,to provide more high-quality sample points to further modify the student-t process model.So it has rapid convergence and good global search capacity.Finally,in order to verify the effectiveness of the algorithm,the search efficiency and search precision of different algorithms are compared by numerical simulation.Results show that the student-t process assisted CMA-ES algorithm compared to the basic CMA-ES and Gaussian process assisted CMA-ES algorithm have stronger global search ability,decrease number of cost function evaluations at the same time,further improves the solution accuracy and robustness.On the other hand,a case study of medical image registration is examined to demonstrate the ability and applicability of the proposed algorithm,and experiment results show that modified algorithm is proper for medical image registration than CMA-ES,and it receives a better effect on the precision of registration while reducing the numbers of calculation of the fitness function.