Application And Research Of Algorithm In Inverse Problem

This thesis is concerned with the application of optimization in inverse Stefan problems.In this paper, the advantage and disadvantage of traditional optimization algorithms are analyzed firstly, then the function of inverse Stefan problem are introduced. For this multivariable function, if the variables are changed linearly, the single variable function will be got, by its curve the new function is discussed.GA is based on evolution, in the algorithm the solution are described as chromosome, according to "survival of the fittest", GA choose the better chromosome ,after the operation of reproduction, crossover, mutation, the new generation of chromosome are formed, by evolution, finally the best chromosome are found. The difficulty of GA is encode the chromosome, this paper use real-number encoding. In order to save the better chromosome, the mutation ratio are given adaptively, the best fitness has the lowest mutation.PSO originated from the research of bird, the basic thought of PSO is to find the best solution by all the particles share their information and cooperation. In this paper the author discussed the influence of each parameter such as particle number, maximum velocity, acceleration coefficient, inertia weight, iterations. After the discussion, the author list the best parameter and solution.The result of solve multivariable function of inverse Stefan shows both PSO and GA have a better precision, but that need too much time. As for the single variable function, this paper also use different algorithm to solve it, including PSO, GA and some traditional algorithms. The outcome display convert the multivariable function to single variable is feasible, especial for some real-time occasion, such as the real-time trace.Compared the algorithm used, the author put forward two combined algorithm, GA+Gradient, PSO+Gradient. Use them to solve the function, compared with the GA and PSO, the combined algorithm give a better solution,especial GA+Gradient.In the end, this paper changed the simulation data, use the same algorithm to solve it, the outcome is still acceptable,Gradien, Bisection, PSO are suitable for this function.