[R] Splitting dataset for Tuning Parameter with Cross Validation

[Tim]

Hi,
My question might be a little general.

I have a number of values to select for the complexity parameters in some classifier, e.g. the C and gamma in SVM with RBF kernel. The selection is based on which values give the smallest cross validation error.

I wonder if the randomized splitting of the available dataset into folds is done only once for all those choices for the parameter values, or once for each choice? And why?

Thanks and regards!