A Genetic Algorithm approach for selecting Tikhonov regularization parameter

This paper presents a genetic algorithm approach for selecting a Tikhonov regularization parameter. In using Tikhonov parameters regularization for solving ill problems, in terms of inverse problems of the first category, we could first apply discrete regularization method to transfer it into linear algebraic equations, and then get regular solutions by solving of Euler equations which is of minimum functional equivalence for Tikhonov. As to the selection of regularization parameter, this paper choose a genetic algorithm approach, which takes Morozov deviation equation as fitness function for genetic algorithm approach, and dynamically selects regularization parameter by designing genetic operation like crossover, mutation and genetic selection. Numerical results show that it is a feasible as well as an effective approach for selecting regularization parameter.