Research On Hybrid Grey Wolf Optimizers And Their K-means Clustering Optimization

In the real world,there are optimization problems all the time and everywhere.With the development of society,the optimization problems that need to be dealt with are becoming more diverse and more complex.For example,K-means clustering and image segmentation are typical complex optimization problems.However,traditional mathematical methods such as Newton's method and gradient descent method cannot solve these optimization problems well.Therefore,many researchers have created various bionic intelligent computing models and proposed many Intelligent Optimization Algorithms(IOAs),such as Grey Wolf Optimizer(GWO),Differential Evolution(DE)and Coyote Optimization Algorithm(COA),etc.GWO is a novel IOA proposed by Mirjalili et al in 2014.It has the advantages of simple principle,strong exploitation capacity and few adjustable parameters,but it has shortcomings such as easy to fall into local optima and poor performance to solve complex optimization problems.Therefore,many scholars have conducted research and improvement on it,of which hybrid improvement is one of the most effective improved methods and has become a research hotspot in the field of intelligent optimization.A single IOA has its own advantages and disadvantages.Hybrid improvement can make the advantages of two IOAs complement each other and overcome their shortcomings.Therefore,this paper conducts an in-depth study on GWO,and uses the most classic IOA representative—DE and the most novel IOA representative—COA to be hybridized with GWO respectively to obtain two effective hybrid algorithms.They are used to solve the optimization problems of K-means clustering and image segmentation.The main research contents of this paper are as follows:(1)Aiming at the poor performance of GWO in solving complex optimization problems,a hybrid GWO and COA algorithm(Hybrid GWO with COA,HGWOC)is proposed.Firstly,the improved COA(Improved COA,ICOA)is obtained: on the one hand,a Gaussian global-best growing operator is proposed to improve search efficiency and convergence speed;on the other hand,a dynamic adjustment scheme of coyote number in each group is proposed to enhance the global search ability in the early stage and the local search ability in the late stage as well as the operability.Secondly,in order to improve the operability of the original GWO and simplify its operation,a simplified GWO(Simplified GWO,SGWO)is proposed.Finally,a sine crossover strategy is used to fuse SGWO and ICOA to obtain HGWOC.The experimental results of a large number of classical functions and CEC 2017 complex functions show that HGWOC has higher search efficiency,stronger operability and better universality than COA and GWO.(2)In order to make up for the poor exploration ability of GWO,a hybrid algorithm of GWO and DE(Hybrid GWO with DE,HGWOD)is proposed.First of all,GWO is improved: First,a new random learning operator is embedded into GWO to obtain random learning GWO(RGWO);second,the global-best opposition-learning operator is randomly integrated into RGWO to obtain global-best opposition-learning RGWO(GRGWO);third,Levy flight is randomly integrated into GRGWO to obtain LGRGWO.The addition of the first three operators greatly enhances the global search capability of GWO.Then,in order to improve the stability,diversity and running speed of GWO,a static DE is proposed.Finally,this static DE is combined with LGRGWO to form HGWOD.A large number of experiments have been conducted on a series of classic benchmark functions and complex functions of CEC2014 test set.The experimental results show that the performance of the HGWOD is better than GWO and other state-of-the-art algorithms.(3)In order to verify the ability of the two GWO hybrid algorithms to solve practical optimization problems,they are applied to the K-means clustering problem to solve the shortcomings of sensitive initial clustering center and easy to fall into local optimal.Specifically,HGWOC is applied to K-means clustering and HGWOD is applied to image segmentation based on histogram K-means.Experiments show that compared with comparison algorithms,HGWOC based K-means clustering and HGWOD based histogram K-means image segmentation methods have respectively better clustering and segmentation performance,and can better solve the problem of K-means clustering and image segmentation.