Improved Grey Wolf Algorithm And Its Applications In Ordinary Differential Equations

Grey wolf optimizer(GWO)is a kind of intelligent optimization algorithm which imitates the hierarchical system and predatory behavior of grey wolf group in nature to achieve the purpose of optimization search.Compared with other swarm intelligence optimization algorithms,gray wolf optimization algorithm has the advantages of simple principle,less parameters to be adjusted and easy to implement,so gray wolf algorithm has been widely concerned by scholars at home and abroad.With the in-depth study of gray wolf optimization algorithm,scholars found that the gray wolf optimization algorithm has some shortcomings,such as low precision of the final optimization results,slow convergence speed in the later stage of the algorithm,easy to fall into the local optimum and unable to jump out.These shortcomings seriously affect and limit the application of gray wolf optimization algorithm in the field of science and engineering.The application of ordinary differential equations is very extensive.In physics,the dynamics of variable forces,chemistry and other natural subjects are inseparable from the study of ordinary differential equations.In the process of studying natural science problems or solving engineering problems,we often need to use ordinary differential equations to abstract and establish mathematical models.Therefore,the application of algorithms in ordinary differential equations has important value.In this thesis,the shortcomings of gray wolf optimization algorithm are improved,and the improved algorithm is applied to the study of ordinary differential equations.In view of the limitations of the original gray wolf algorithm,such as the low precision of the final optimization results,the slow convergence speed of the algorithm in the late running stage,and it is easy to fall into the local optimum and can not jump out,the corresponding improvements are made in the aspects of population initialization,convergence factor and location update formula,and the improved gray wolf algorithm based on Gaussian Cauchy mixture mutation(GCGWO)and an improved grey wolf optimization algorithm based on dynamic reverse search for update position are proposed,and the effectiveness of the improved algorithm is verified by simulation experiments.Finally,the improved gray wolf optimization algorithm is applied to the ordinary differential equation.The improved DAGWO-LSSVM algorithm is used to improve the accuracy of the approximate solution of ordinary differential equations.The corresponding examples of first-order constant coefficient linear ordinary differential equations,first-order variable coefficient ordinary differential equations,second-order variable coefficient ordinary differential equations and ordinary differential equations without analytical solution are solved and simulated,It is verified that DAGWO algorithm can effectively improve the accuracy of the approximate solutions of the above ordinary differential equations;The improved dagwo algorithm is used to optimize the parameters of the dynamic ordinary differential equation.Through the parameter fitting of the dynamic ordinary differential equation in the example,the effectiveness of the improved dagwo algorithm in optimizing the parameters of the dynamic ordinary differential equation is verified.