Improved Genetic Algorithm In Nonlinear Equations

With the rapid development of science and technology.the computer is widely used in the field of mathematics.More and more problems we encounter in practice need to be wolved by establishing a mathematical model,which more often than not forms corresponding equation or eauations.For the research of various kinds of nonlinear equation issues is getting more and more attention,the nonlinear issue,which is formed by overlapping subjects,is becoming one of the central issues gradually.The nonlinear issue includes nonlinear FEM, nonlinear fracture,elastic-plastic issue and so on.There are two main directions in the research of nonlinear equation,one is the numerical method,which is represented by Newton method,another is non-numerical method,which is representd by evolutionary algorithm.When uesd to reslove the nonlinear equations,the numerical method is more complex,at the same time the numerical method often fall into the local optimal and have a lower definition.For the defects of the numerical method,we use the non-numerical method to resolve the nonlinear equations.In this paper we base on the evolutionary algorithm belonged to the classical evolutionary algorithm,optimize and improve the defects of the evolutionary algorithm,to make it more appropriate for resolving the nonlinear equations.Based on the previous achievements,this paper add the mountain climbing operator to the traditional evolutionary algorithm to improve the function of the traditional evolutionary algorithm,and avoid the defects mentioned above.We also use this algorithm in nonlinear equations,which are a kind of special equations formed by EM algorithm.The main contribution of this paper are as follows:●Prepare and introduce related knowledges according to the improvement requirements of evolutionary algorithm when resolve the nonlinear equations.This Paper introduces the basic concept,the basis principle,the related theory and application of evolutionary algorithm in the first place,then introduces the mode theorem of evolutionary algorithm and discusses the convergence of evolutionary algorithm based on the mode thorem.The paper also introduces the local search altorithm and the framework of the mountain climbing algorithm,analyze the defects of the mountain climbing algorithm.●According the defects of the tradtional evolutionary algorithm,we propose local mountain climbing algorithm. At the same time we make corresponding improvement to the evolutionary operation,including selection,crossion and variation operator.We propose improved evolutionary algorithm combined with excellent evolutionary strategy.The improved evolutionary algorithm improves the global and local search capability completely and adjust the search operator according to different situation.We program and perform simulation experiment.The result of the experiment shows that the improved evolutionary algorithm is easier to convergence,and has a higher accuracy when reslove the nonlinear equations compare to the traditional evolutionary algorithm.●For the special kind of nonlinear equations that is formed when we compute with the EM algorithm, the improve evolutionary algorithm is applied to EM algorithm. We make some improvements to the execution of traditonal EM algorithm, and provide examples to compare the two algorithm, the result shows that the improved EM algorithm has a large improvement in global convergence insufficiency and slow convergent rate.