Imagine that you want to construct an AI that will never self-halt (easier to define than friendliness, but the same idea applies). You could build the machine so that it doesn't have an off switch, and therefore can't halt simply out of inability. However, if the machine can self-modify, it could subsequently grant itself the ability to halt. So in your design, you'd have to figure out a way to prevent self-halting under all possible input conditions, under all possible self-modifications of the machine. This latter task cannot be solved in the general case because of Rice's Theorem, and engineering a solution leads to an infinite regress:

1. Machine can't halt directly
2. Machine can't self-modify to change #1 above
3. Machine can't self-modify to change #2 above and so on.

So in practice, how can one create a relatively non-suicidal AI? An evolutionary/ecological approach is proven to work: witness biological life. (however, humans, who have the most general computational power, suicide at a more or less constant rate).

In short: genetic programming, or some other such search, can possibly find quasi-solutions (meaning they work under conditions that have been tested) if they exist, but designing in all the required characteristics up front would require tremendous ability to prove outcomes for each specific case. In practice, this debate is probably moot because it'll be a combination of both.