Lack of confidence in the optimization algorithm
I don't feel confident in the accuracy of our currently supported fitting algorithms. In my experience all gradient-based algorithms are unable to find the correct minimum, which excludes most of ROOTs minimizers. From the few remaining I have personally stuck with the Genetic algorithm, but based on this comparison, the genetic algorithm Galileo seems to fail miserably (it's not an entirely fair comparison - Galileo uses very few comparisons, while the ROOT implementation uses quite a lot).
I think we should generate an actual chi2 landscape for a fitting problem, and use it to track and verify the convergence of the Genetic algorithm. Alternatively we could either find or implement one of the algorithms from the earlier link and verify it reaches the same result as the Genetic algorithm.