In theory, NO, none of those functions can take the place of a parameter sweep for a generalized calculation.
There are calculations for which it can be proven that knowing the value of a function at any finite number of locations does not give you information about the value of the function at a given location.
There are functions that there is no known way to calculate, such as the list of locations at which the prime number estimate function swaps between being an overestimate and underestimate.
So, it cannot always be done.
Whether it is possible for your calculation depends upon what you are calculating.
There is a set of functions for which unconstrained Genetic Algorithm is guaranteed to converge. It has been rather some time since I last looked at the relevant theory; my vague memory is that it is not much better than Quadratic functions. Unless, that is, you go by definitions such as https://www.researchgate.net/publication/220616519_Convergence_Criteria_for_Genetic_Algorithms which says that provided that you mutate long enough that you will get convergence (they give upper bounds on number of iterations for some conditions, but I cannot read the paper myself.)
