Simulated Annealing versus Metropolis for a TSP instance

In a recent paper [I. Wegener, Simulated Annealing beats Metropolis in combinatorial optimization, in: L. Caires, G.F. Italiano, L. Monteiro, C. Palamidessi, M. Yung (Eds.), Proc. ICALP 2005, in: LNCS, vol. 3580, 2005, pp. 589–601] Wegener gave a first natural example of a combinatorial optimization problem where for certain instances a Simulated Annealing algorithm provably performs better than the Metropolis algorithm for any fixed temperature. Wegener's example deals with a special instance of the Minimum Spanning Tree problem. In this short note we show that Wegener's technique as well can be used to prove a similar result for another important problem in combinatorial optimization, namely the Traveling Salesman Problem. The main task is to construct a suitable TSP instance for which SA outperforms MA when using the well known 2-Opt local search heuristic.