A Class Of Evolutionary Algorithm And Its Application Based On Domain Decomposition

Domain Decomposition method is an effective numericalmethod for partial differential equations. Using it, we candivide the complex and large area into some small areas andget solutions on them respectively, thenthe real solution onthe whole area can be gained through iteration of precedingsolutions we have got. This method can transform large probleminto small one and can change complex area into simple one.When it comes to functions optimization, evolutionaryalgorithms perform faily well. But there also exist somelimitations of its applications: firstly, evolutionaryalgorithms is too slow for solving certain problems; secondly,it is apt to run into local optima and have no robustness forfunction optimization problems with single peak. However, someresearches showed that better results for functionoptimization can be get through crossover operators. Sorecently many researchers try their best to search effectivecrossover operators.In this paper, we introduce the basic structure and currentdevelopment of evolutionary algorithms and analyze theiradvantages and disadvantages. Especially, we analyze guotaocrossover operator, improve it and put forward a new algorithm for nonlinear equations set. We also introduce the boundaryproblems of ordinary differential equation and some popularnumerical methods for it, and the principle of Finite Elementmethod and Domain Decomposition method. Furthermore, to onedimension boundary problem of ordinary differential equation,we present the discretization procedure and specific algorithmtaking advantage of Domain Decomposition method associatedwith Finite Element method.In the numerical experiment part, we present tables andgraphs of several typical examples we have computed. Analysisfor these results is given, too.The great contribution of this paper is that we improve theguotao algorithm, which makes search space and populationself-regulating on the evolutionary process in order toaccelerate convergence to exact solution. Based on thisimproved guotao algorithm, we put forward an new evolutionaryalgorithm for boundary problems of ordinary differentialequation.