  In this paper we investigate instances with high integrality ratio of the
subtour LP. We develop a procedure to generate families of Euclidean TSP
instances whose integrality ratios converge to $\frac{4}{3}$ and may have a
different structure than the instances currently known from the literature.
Moreover, we compute the instances maximizing the integrality ratio for
Rectilinear TSP with up to 10 vertices. Based on these instances we give
families of instances whose integrality ratio converge to $\frac{4}{3}$ for
Rectilinear, Multidimensional Rectilinear and Euclidean TSP that have similar
structures. We show that our instances for Multidimensional Rectilinear TSP and
the known instances for Metric TSP maximize the integrality ratio under certain
assumptions. We also investigate the concept of local optimality with respect
to integrality ratio and develop several algorithms to find instances with high
integrality ratio. Furthermore, we describe a family of instances that are hard
to solve in practice. The currently fastest TSP solver Concorde needs more than
two days to solve an instance from the family with 52 vertices.
