I'm looking for some information on what I would assume to be a variant of the traveling salesman problem. The trouble is I either don't see exactly how to effectively apply the variation this problem/ and or don't know the name of the variant so as to effectively research it myself. The informal concepts is simple enough, I'll explain:
The salesman has to visit a group of cities exactly once and has to find the shortest path to take, however every few stops he has to return to the hub-spot.
For instance, lets say he has to visit 16 spots plus he starts at the hub, we'll call this spot 0, and the the others are 1 through 16. He must find an optimized sequence of spots to visit, but must return to spot 0 every 4 spots he visits. Or perhaps more generally he can visit a certain amount of non-hub-spots before returning to the hub each trip, for instance he could visit 3, then 5, then 2, then 6. The problem is to find the shortest total path.
Is there a straight forward way to address such a problem, or perhaps a common name of a method that pertains to such?