Let's imagine I have an unknown function that I want to approximate via Genetic Algorithms. For this case, I'll assume it is y = 2x.

I'd have a DNA composed of 5 elements, one y for each x, from x = 0 to x = 4, in which, after a lot of trials and computation and I'd arrive near something of the form:

best_adn = [ 0, 2, 4, 6, 8 ]

Keep in mind I don't know beforehand if it is a linear function, a polynomial or something way more ugly, Also, my goal is not to infer from the best_adn what is the type of function, I just want those points, so I can use them later.

This was just an example problem. In my case, instead of having only 5 points in the DNA, I have something like 50 or 100. What is the best approach with GA to find the best set of points?

1. Generating a population of 100, discard the worse 20%
2. Recombine the remaining 80%? How? Cutting them at a random point and then putting together the first part of ADN of the father with the second part of ADN of the mother?
3. Mutation, how should I define in this kind of problem mutation?
4. Is it worth using Elitism?
5. Any other simple idea worth using around?

Thanks