[teps]

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?

[spooningtamarin]

Simulated annealing is simple. It's just the acceptance criterion of simulated annealing that you are using.

You take the previous solution, and the current one, the difference of the cost (up or down) and plug it into the formula.

Simulated annealing allows some jumps up and jumps down, hill climbing goes only up.

[baldeagle]

And the purpose of the down jumps is to move you away from a local maxima. For example, if you were wanting to climb [any large mountain] and could only gain elevation, then you would fairly easily get stuck in the stairwell of the hotel in the valley.

[mcphage]

> a simulated annealing for a seemingly so simple function

Which are you referring to here as the "seemingly so simple function"?

[kruhft]

I would assume so that this algorithm could be solved using a DWave with it's supposed 10^8 speedup if successful?