Fitting two related functions to two sets of data

Hi Everyone,

I need to fit the two functions below

and

These functions are related by the integral in line 2. They share common parameters and input values but produce different results. I have datasets for both F and F' related to x and need to fit these values simultaneously using the function:

Where Y1 corresponds the the y values in F' and Y2 those for F.

I would like to use a simulated annealing or genetic algorithm for minimization but have no experience with these functions or how to fit both datasets simultaneously.

Thanks for the help,

Will