If this question is out of scope for this forum, before closing it please advise me on a better platform to ask my question!
I'm very new to this field so apologies if my questions are not clear. I am fitting a known model to my data, and looking to obtain 3 parameters from 2 different functions simultaneously, which necessitates the use of multi-objective optimization algorithms.
I tried simply to minimize norm(error_fcn(1)) + norm(error_fcn(2))^2 using a simple scalar minimizer (from Python's scipy package) but often the output is so huge, that overflow occurs, crashing the programme. (where err_fnc is the difference between the real data and the model)
So after some research I decided to try a Python package (pymoo) offering evolutionary algorithms, specifically NSGA-II is the one I used. I optimized the parameters manually and the results seem promising (Close to what I expect the 3 parameters to be). Of course it outputs several solutions, depending on the population size, and in my case for my specific problem, I only need one solution for each parameter. Funnily enough running it with a population size of 1 and off-spring of about 10 (yeah, I am desperate) also gave a decent output on a quick test run, but my gut tells me this approach is wrong and should not be done, given the mechanism by which such algorithms work.
I tried the other algorithms in the package, but they seem to be for single-objective optimization or also producing a set of solutions (the other evolutionary algorithms I guess).
Can anyone point me in the right direction in terms of either what to read, or what kind of algorithms to search, where multiple objectives can be used to output a single best solution?