OPTIMAL CALCULATION OF TIKHONOV REGULARIZATION PARAMETER BASED ON GENETIC ALGORITHM

Tikhonov regularization approach has been accepted as one of the most effective ways to solve ill-posed problems. In the approach, the key step is the calculation of a regularization parameter. Usually, iterative methods are used to obtain the parameter. However, the obtained iterative solutions are sensitive to the initial choice of the parameter, and different initial values may lead to quite different solutions. Presently, the optimal calculation of Tikhonov regularization parameter is discussed. A method based on the Genetic Algorithm (GA) is proposed, which uses the generalized cross-validation (GCV), L-curve and Engl’s error criterion as an optimal function, respectively. Numerical analysis is carried out for the load distribution model of a pin-jointed truss. It is shown that the method can achieve an optimal value of the parameter in the whole range, and therefore provides an efficient way for obtaining an optimal regularization solution.