you can use any of the algorithms as you mentioned for the problem provided it should have clear objective function, constraints etc

I'm not particularly familiar with parameter optimizers personally, but after a quick search, it appears that those optimizing techniques could perform similarly to things like Metropolis Light Transport (Veach and Guibas). Also see the quasi-Monte Carlo summary (Keller et. al). Recently MLT has been shown to work somewhat better at optimizing the light transport when used in the gradient domain (see Lehtinen et. al.). Kensler and Shirley (also linked) used an automated search optimization to optimize the ray triangle intersection math.

Article Metropolis Light Transport

Article Optimizing Ray-Triangle Intersection via Automated Search

Article Gradient-Domain Metropolis Light Transport

Article Monte Carlo and quasi-Monte Carlo methods 2006. Selected pap...