See 'genetic programming' for techniques that are sort of based on this idea. Typical approach is to have a problem representation (gene analogues) that can be used to create a population of different individual solutions. Test them all against a fitness function and retain those that are 'best' according to some metric. Then create (breed) some new individuals who have some of the characteristics of the winners, perhaps mutated somewhat, insert these into the population. Repeat until you have solved the problem or have a good enough solution.

Challenges (apart from the time taken) are coming up with a good enough gene representation that captures the essence of the problem, building an efficient fitness function, and avoiding local maxima - i.e. a solution that is almost but not quite good enough, but from where you can't breed a better solution.,