I don't understand how the simulated annealing is helping.
I quote the explanation of step 4:
If the candidate tour is worse than the existing tour, still maybe accept it, according to some probability.
The probability of accepting an inferior tour is a function of how much longer the candidate is compared to the current tour, and the temperature of the annealing process.
A higher temperature makes you more likely to accept an inferior tour
Why would you need a simulated annealing for a seemingly so simple function?