The writeup for FindShortestTour does not give information about what method(s) are used. I am also wondering whether the function will always find the optimal (shortest) tour. Any information about the size of travelling salesman problem that can be reasonably attempted with FindShortestTour would be appreciated. Any further or related information would be appreciated. Dale Bent.
When possible, it uses the Concorde program under the hood. I believe that handles quite large problems. I do not recall offhand what are the restrictions that would cause another method to be used (maybe a nondefault DistanceFunction setting).
As for getting the names of nondefault methods, just ask it:
In[59]:= FindShortestTour[{{1, 2}, {2, 4}, {5, 6}},
Method -> nondefault]
During evaluation of In[59]:= FindShortestTour::illmet: Value of option Method → nondefault is not Automatic, “AllTours”, “CCA”, “Greedy”, “GreedyCycle”, “IntegerLinearProgramming”, “OrOpt”, “OrZweig”, “RemoveCrossings”, “SpaceFillingCurve”, “SimulatedAnnealing”, or “TwoOpt”. >>
Out[59]= FindShortestTour[{{1, 2}, {2, 4}, {5, 6}},
Method → nondefault]
Thank you Daniel.