Well, this is, in contrast to neural networks, a relatively new technique... and I know it very well. I don't use it, but a few colleagues of mine at the physics institute work with GAs. They're very interesting, but they are very far from creating true AI. Generally, you use them to solve <i>one</i> specific problem. The results are usually very impressive; however, it is still the case that the computer only does a preprogrammed learning sequence.
Genetic algorithms are very simple, actually, but very inventive and useful. From a pool of possible solutions, you must evaluate the "fitness" of each solution to your particular problem with a preprogrammed fitness funtion - which is, of course, a vital part of the algorithm. Then, you select the fittest and recombine them into a new pool. You can then repeat the process until your pool looks as good as you'd like, in theory.
However, the two most important aspects are hand-coded: the fitness function and the recombination algorithm. In that sense, the computer will be capable of a lot of calculations and will basically optimize your pool of solutions; however, there is absolutely not a hint of creativity there. The only thing that was "creative" was the programmer's thinking...

Nothing like a good programmer...
Anyway, in order to make computers really creative, they'd have to be able to write fitness functions and recombine possible solutions by themselves. Now <i>that</i> would require an ingenious programmer!...
😱
<font color=red><b>M</b></font color=red>ephistopheles