Travelling Salesman which can repeat cities
This is directly equivalent to metric TSP. That is, TSP in which the distances obey the triangle inequality: for all cities $A$, $B$ and&nbsp;$C$, the distance from $A$ to&nbsp;$B$ is no greater than the distance from $A$ to $C$ to&nbsp;$B$.

As Raphael points oun in the comments, you can reduce an instance of your problem to metric TSP by setting the distance from $A$ to&nbsp;$B$ to be the length of the shortest $A$&ndash;$B$ path in the original graph. This shows that your problem is no harder than metric TSP. But, conversely, every instance of metric TSP is already an instance of your problem. This is because, in metric TSP, the triangle inequality guarantees that it's never necessary to revisit a vertex so allowing revisiting doesn't change the optimal solution.