The effect of asymmetry on traveling salesman problems

Distance or cost matrixes between groups of locations are of paramount importance when solving traveling salesman problems (TSP ) as well as other routing settings. Euclidean distances constitute a gross underestimation of reality. Furthermore, reality, especially in urban transportation, is highly asymmetric. This work studies the effect that asymmetry, geographical location and territory have over TSP methods. We conduct comprehensive experiments in order to assess the effects that these factors have over some of the best known algorithms for the TSP . We demonstrate that all these factors have a significant influence in solution time and quality. Furthermore, we show that the solutions obtained with Euclidean matrixes and those obtained with real distance matrixes differ significantly. Moreover, optimal solutions to TSP problems obtained with Euclidean matrixes, when calculated with real distances, are shown to be significantly worse than the optimal solutions initially obtained with real matrixes and vice-versa.