I'm trying to find any material on this problem. It extends the Asymmetric Travelling Salesman Problem (ATSP) in that it requires for some destinations that they are approached in the specified direction (but not for all). I couldn't find anything about this problem on the internet. Can anybody point me to some paper or the correct name for this problem? Or maybe similar problem from graph theory?
In my current design each node has a property of direction in which it is being approached. This direction can be restricted or unrestricted. When unrestricted, then I think all possible combinations of directions should be tried to the combination which minimizes the cost function. Also I have 4 distance matrices corresponding to different direction combinations: 0-0, 0-1, 1-0 and 1-1. Where 0 is positive direction and 1 is negative direction.
The calculations are performed on a real street network data. Direction mean street direction (or side of the street). Each point on the street can be aproached from two different directions. Some points are restricted to be approached in a particular direction, some are not.