# The use of crossovers in Genetic Algorithm

My questions concern the use of crossovers in genetic algorithms. The three basic ingredients of genetic algorithms are:

• selection
• mutation
• crossover

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.

My questions

• 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).