My questions concern the use of crossovers in genetic algorithms. The three basic ingredients of genetic algorithms are:
If we think of genetic algorithm acting on binary strings…
Crossover is the process by which two parent strings get mixed to give born to offspring strings. For example: 11000 and 00010 can create the offspring 11010 by crossover only.
In some genetic algorithm people authorize double-crossover. For example the two parents: 110011 and 001100 can give birth to 111111.
I don't fully understand the advantageous of crossovers! It seems to me that one can obtain similar results with algorithms that do not contain crossover.
Under what conditions is the use of crossover in genetic algorithm beneficial? why?
Under what conditions is the use of double-crossover more beneficial than single crossover? why? What about triple crossover?
When I say "Under what conditions", I mean "for what fitness landscape" or "for what problem type".
By fitness landscape, I mean a mapping of each possibility to fitness (reproductive success) in a hyperspace of $n+1$ dimensions where $n$ is the length of the string (the additional dimension being the fitness).