Object placement

So I'm at a point where I need to code a system that places objects so they aren't overlaping each other. I'm looking for more of a algorithmic solution rather than a loop-test-loop solution. This is what Ive considered so far:


Maybe Im thinking too far into it, this doesnt seem like the most simple and efficient solution. So those of you with some good engine design, or related experience, please give me some advice here.

Thanks :)