Evolutionary programming seems to be a great way to solve many optimization problems. The idea is very easy and the implementation does not make problems.
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It can be done, but works very badly for most kinds of applications.
Genetic algorithms only work when the fitness function is continuous, i.e. you can determine which candidates in your current population are closer to the solution than others, because only then you'll get improvements from one generation to the next. I learned this the hard way when I had a genetic algorithm with one strongly-weighted non-continuous component in my fitness function. It dominated all others and because it was non-continuous, there was no gradual advancement towards greater fitness because candidates that were almost correct in that aspect were not considered more fit than ones that were completely incorrect.
Unfortunately, program correctness is utterly non-continuous. Is a program that stops with error X on line A better than one that stops with error Y on line B? Your program could be one character away from being correct, and still abort with an error, while one that returns a constant hardcoded result can at least pass one test.
And that's not even touching on the matter of the code itself being non-continuous under modifications...
Well this is very possible and @Jivlain correctly points out in his (nice) answer that genetic Programming is what you are looking for (and not simple Genetic Algorithms).
Genetic Programming is a field that has not reached a broad audience yet, partially because of some of the complications @MichaelBorgwardt indicates in his answer. But those are mere complications, it is far from true that this is impossible to do. Research on the topic has been going on for more than 20 years.
Andre Koza is one of the leading researchers on this (have a look at his 1992 work) and he demonstrated as early as 1996 how genetic programming can in some cases outperform naive GAs on some classic computational problems (such as evolving programs for Cellular Automata synchronization).
Here's a good Genetic Programming tutorial from Koza and Poli dated 2003.
For a recent reference you might wanna have a look at A field guide to genetic programming (2008).