NEW MONITORING PARAMETER FOR THE TRAVELING SALESMAN PROBLEM

We introduce a new parameter, which is related to the well known trave ling salesman problem (TSP), by making an analogy with a classical par ticle traveling around a closed trajectory of the TSP. In order to exh ibit the broken symmetry associated with the rotation invariance of th e TSP set of cities around any space axis, the parameter behavior, as a function of the temperature, is found along a simulated annealing pr ocess. As expected, this behavior resembles the order parameter evolut ion, in temperature, of some physical systems. The discussion includes a set of a few cities up to a set of 500 cities.