  Metaheuristics, as the simulated annealing used in the optimization of
disordered systems, goes beyond physics, and the traveling salesman is a
paradigmatic NP-complete problem that allows inferring important theoretical
properties of the algorithm in different random environments. Many versions of
the algorithm are explored in the literature, but so far the effects of the
statistical distribution of the coordinates of the cities on the performance of
the algorithm have been neglected. We propose a simple way to explore this
aspect by analyzing the performance of a standard version of the simulated
annealing (geometric cooling) in correlated systems with a simple and useful
method based on a linear combination of independent random variables. Our
results suggest that performance depends on the shape of the statistical
distribution of the coordinates but not necessarily on its variance
corroborated by the cases of uniform and normal distributions. On the other
hand, a study with different power laws (different decay exponents) for the
coordinates always produces different performances. We show that the
performance of the simulated annealing, even in its best version, is not
improved when the distribution of the coordinates does not have the first
moment. However, surprisingly, we still observe improvements in situations
where the second moment is not defined but not where the first one is not
defined. Finite-size scaling fits, and universal laws support all of our
results. In addition, our study show when the cost must be scaled.
