  In this paper, we consider three similar optimization problems: the
fault-tolerant metric dimension problem, the local metric dimension problem and
the strong metric dimension problem. These problems have applications in many
diverse areas, including network discovery and verification, robot navigation
and chemistry, etc. We give integer linear programming formulations of the
fault-tolerant metric dimension problem and the local metric dimension problem.
Also, we study local metric dimension and strong metric dimension of two convex
polytopes $S_n$ and $U_n$.
