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Even with a traveling salesman problem you can get "near-optimal" results with an algorithm that has a reasonable run time. It's still important to note that you have such a problem though, as the fact that you're settling for "near optimal" needs to be understood.


You can actually find the global optimal solution for surprisingly large real world instances. They do tens of thousands of cities.

Lots of interesting stuff here. The Concorde solver is probably the state of the art. http://www.tsp.gatech.edu/concorde/index.html




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