%0 Journal Article %1 Yun01 %A Yeun, Yun Seog %A Lee, Kyung Ho %A Han, Sang Min %A Yang, Young Soon %D 2001 %J Information Sciences %K Author Genetic Keywords: Regularization Smooth algorithms, fitting, genetic parameter programming, programming; %N 3-4 %P 175--194 %R doi:10.1016/S0020-0255(01)00084-6 %T Smooth Fitting with a Method for Determining the Regularization Parameter under the Genetic Programming Algorithm %V 133 %X This paper deals with the smooth fitting problem under the genetic programming(GP) algorithm. To reduce the computational cost required for evaluating the fitness value of GP trees, numerical weights of GP trees are estimated by adopting both linear associative memories and the Hook & Jeeves method. The quality of smooth fitting is critically dependent on the choice of the regularization parameter. So, we present a novel method for choosing the regularization parameter. Two numerical examples are given with the comparison of generalized cross-validation B-splines

@article{Yun01, abstract = {This paper deals with the smooth fitting problem under the genetic programming(GP) algorithm. To reduce the computational cost required for evaluating the fitness value of GP trees, numerical weights of GP trees are estimated by adopting both linear associative memories and the Hook & Jeeves method. The quality of smooth fitting is critically dependent on the choice of the regularization parameter. So, we present a novel method for choosing the regularization parameter. Two numerical examples are given with the comparison of generalized cross-validation B-splines}, added-at = {2008-06-19T17:35:00.000+0200}, author = {Yeun, Yun Seog and Lee, Kyung Ho and Han, Sang Min and Yang, Young Soon}, biburl = {https://www.bibsonomy.org/bibtex/2e8819cb40078bd87fdcd2f84143545d6/brazovayeye}, doi = {doi:10.1016/S0020-0255(01)00084-6}, email = {yeonyun@road.daejin.ac.kr}, interhash = {cb5b05f430fc7340cf166805e508d2ad}, intrahash = {e8819cb40078bd87fdcd2f84143545d6}, journal = {Information Sciences}, keywords = {Author Genetic Keywords: Regularization Smooth algorithms, fitting, genetic parameter programming, programming;}, month = {April}, notes = {Euclidean norm = zero-order Tikhonov regularisation, is not sufficient p178 uses(?) weighting based on first derivative of evolved function but too CPU expensive(?). LAM HJ discrepancy principle DP cross-validation CV composite residual and smoothing operator CRESO L-curve zero crossing ZC considered in text but use heuristic two test functions 2*(sin(t))**4 1.5*(exp(-30*(t-0.25)**2)+sin(pi(t-0.2))**2) {"}..sometimes the GP tree that is discarded by the criterion proposed in this paper is far better than the tree selected as the best one.{"} p192 Information Sciences http://www.elsevier.com/inca/publications/store/5/0/5/7/3/0/505730.pub.htt}, number = {3-4}, pages = {175--194}, timestamp = {2008-06-19T17:54:53.000+0200}, title = {Smooth Fitting with a Method for Determining the Regularization Parameter under the Genetic Programming Algorithm}, volume = 133, year = 2001 }