Optimal search in genetic algorithms

Question

I am implementing my dissertation M.Scc and in the theoretical aspect of my thesis I have a big problem.

Suppose we want to use genetic algorithms.

we have 2 types of functions:

a) some functions that have the following relationships: || x1 - x2 || → || f (x1) - f (x2) || e.g. y = (1/10) x ^ 2

b) some functions that have the following relationships: || x1 - x2 || <|| f (x1) - f (x2) || for example: y = x ^ 2

my question is which of the listed functions has more difficulties than others when we want to use genetic algorithms to find the optimal one (it doesn't matter the MINIMUM or MAXIMUM).

Thank you so much Armin

Answer 1

I do not believe that you can answer this question at all without imposing additional restrictions.

It depends on the specific type of genetic algorithm you are dealing with. If you use fitness proportional (roulette) choices, then changing the range of fitness values ​​can make a big difference. When choosing a tournament or selecting a ranking, while relations between customers remain between people, there will be no effects.

Even if you can say that it matters, it will still be hard to say which version is harder for GA. The main effect will be on the pressure of choice, which leads to the convergence of the algorithm more or less quickly. Is it good or bad? It depends. For a function like f (x) = x ^ 2, the approximation is probably great, because there is only one optimal one, so find it as soon as possible. For a more complex function, slower convergence may be required to find good solutions. Thus, for any given function, scaling and / or translation of fitness values ​​may or may not matter, and if this happens, the difference may or may not be useful.

There is probably also the No Free Lunch argument, which does not have the only best choice for all problems and optimization algorithms.

I would be glad if they corrected me, but I do not believe that you can say one way or another without specifying exactly which class of algorithms and problems you are focusing on.