  In this pedagogical work we reviewed the mathematical formalism and the
physical interpretation, based on statistical mechanics, of the meta-heuristics
called simulated annealing. Moreover, we presented the mathematical formulation
of the algorithm and why it is capable to yield the optimal solution or a good
approximated solution of a given problem. Furthermore, we described the
travelling salesman problem, showing its interpretation as a Markov Chain and
how the simulated annealing can be used to optimize it and we did its
simulations for two scenarios. Firstly, for 50 cities distributed around a
circle and we found the best solution. Finally, we applied the meta-heuristic
in a another instance, with 100 nodes random uniformly distributed in a square,
and one shows that it allows finding a good solution.
