Considering all that, it is obvious that the real winner solution would be just look at the map and draw a path by hand, using human intuition and heuristics as an algorithm. Even if you would have to make a few corrections, this could be done in minutes instead of hours.
But of course I understand that the point was really to find an application as an excuse to practice working with optimisation algorithms. In that sense, it is a well done job !
Now for how "normal" humans would do it: they would try a few ways and settle on an approximate optimun depending on how much time each pass took and how easy it was to complete. The thing about those sort of task is that they are not really uniform (some places are bound to be dirtier than others and it is easier to approach some features in a certain way), so a naive optimisation like that is unlikely to be what's truly needed even if the solution is technically perfect.