Comparing Algorithms for the Traveling Salesman Problem

The traveling salesman problem (TSP) is an NP-complete problem. Different approximation algorithms have their advantages and disadvantages.
Mathematica's function FindShortestTour offers a choice of four methods ("OrZweig", "OrOpt", "TwoOpt", "CCA"), which may yield identical results.
This Demonstration provides another TSP algorithm called 3-Opt. Experiments show that the 3-Opt algorithm sometimes finds a better result than any of the four kinds of Mathematica FindShortestTour methods.


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Snapshot 1: with 30 points, FindShortestTour methods find a shorter result than the 3-Opt method
Snapshot 2: with 30 points, both 3-Opt and Mathematica's FindShortestTour methods find an optimal result
Snapshot 3: with 40 points, 3-Opt finds a shorter result than any of the FindShortestTour methods
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