This vaguely reminds me (I said vaguely) a problem an former AI professor said he had to solve at a map company ... efficient layout of labels on maps. This problem basically kept trying various things using simulated annealing until a certain measurably "tolerable overlap" was computed... but to do that, you need to be able to programatically compute some sort of neatness scale...which is hard.

That's why I said 'vaguely'. It would be more closely relevant if you were trying to draw an organized network topology, or something like that. This is simpler by being fairly rectilinear.

Still, it's an interesting problem. And those are the good kind.