Research On Differential Evolution Algorithm About A Class Of Inverse Problem Of Partial Differential Equation

As a branch of evolutionary algorithms, Differential Evolution algorithm has been developed in recent years. Differential Evolutionary algorithm (DE) has made a great progress in the algorithm since the evolutionary algorithm appeared. In fact, DE is the fastest algorithm which is convergent to global optimum solution to solve optimization problems with continuous arguments faster and more stably.At present, researches about the inverse problem have been already quite mature at home and abroad. The theory and solving solution of the inverse problem with a wider range are more difficult than the direct problem because the inverse problem is nonlinear and ill-posed. Now, there are many methods for solving inverse problem at home and abroad, such as select method, para-solution method, Tikhonov regularization method, pulse spectrum technique, the best perturbation method and enhance Lagrange method. But, each of them has its shortage.The standard Differential Evolution algorithm can only solve the unconstrained optimization with continuous arguments. The practical application problems generally with constraints are more complex. In this paper, the special Differential Evolution algorithm with constraints was proposed which was based on the standard Differential Evolution algorithm and the solution of the constraints in order to overcome the deficiencies of other existing methods. The new approach can be used to solve the inverse problem of partial differential equation and point-wise source. The results of numerical simulation show that the new approach is effective and feasible which has high accuracy and good stability when solving the inverse problems.