We study a parameter (σ) dependent relaxation of the Travelling Salesman Problem on ${ℝ}^2$. The relaxed problem is reduced to the Travelling Salesman Problem as $\sigma \to$ 0. For increasing σ it is also an ordered clustering algorithm for a set of points in ${ℝ}^2$. A dual formulation is introduced, which reduces the problem to a convex optimization, provided the minimizer is in the domain of convexity of the relaxed functional. It is shown that this last condition is generically satisfied, provided σ is large enough. ...