Finding heuristic and Identifying Traveling Salesman like algorithm (With some changes)

Question

I need a heuristic for the Traveling Salesman Problem with the below changes:

• We need to visit only a subset of V (There is given a subset of V that we must visit). V=Cities.

• We does not need to end the travel at the start vertex(city).

Is there a known name for this problem? That I'll be able to find a good heuristic to solve it?

Thanks advanced :)