If there are several results for one function while fitting the same dataset, which result should I choose? The one with higher R^2 value? The one best explain the hypotheses of the function? Or the one with the smallest errors or dependencies? Is there any rule I should follow while selecting the value of parameters of the function from different fitting results?
The fact that you are getting several fitting results from one dataset using just one function indicates that something is wrong with the fitting process - such as bad match of model and data, over-parametrization, etc. So it is not possible to recommend which result to pick in this situation.
Please send your data/OPJ/fitting function to your local tech support office so that we can take a look and see what is wrong.