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# FindShortestTour

 FindShortestTour[{e1, e2, ...}] attempts to find an ordering of the ei that minimizes the total distance on a tour that visits all the ei once.
• The following options can be given:
 DistanceFunction the distance function to apply to pairs of objects Method the method to use
• The ei can be numbers or lists of numbers, in which case the default distance function used is EuclideanDistance.
• If the ei are strings, the default distance function used is EditDistance.
• For small numbers of points, FindShortestTour will usually find the shortest possible tour. For larger numbers of points it will normally find a tour whose length is at least close to the minimum.
Find the length and ordering of a shortest tour through six points in the plane:
Specify a list of points:
Order the points according to the tour found:
Plot the tour:
Find the length and ordering of a shortest tour through six points in the plane:
 Out[1]=

Specify a list of points:
 Out[2]=
Order the points according to the tour found:
 Out[3]=
Plot the tour:
 Out[4]=
 Scope   (2)
Find the shortest tour through points in 3D space:
Find the shortest tour through a list of strings:
Use a DistanceFunction based on a (symmetric) connectivity matrix:
 Options   (4)
This finds all points on a grid with coordinates that are coprime:
Find the shortest tour using "OrZweig" method, the default for 2D real inputs:
Finding shortest tour using "OrOpt" method, the default for non-2D or nonreal inputs:
The "TwoOpt" algorithm performs exchanges of edge endpoints for improvement:
"CCA" (Convex hull, Cheapest insertion and Angle selection) intended for points in n:
The "Greedy" algorithm moves from one point to the nearest unvisited neighbor:
"GreedyCycle" is a variant of the "Greedy" algorithm with a known upper bound:
"SimulatedAnnealing" uses simulated annealing to minimize the tour length:
By default EditDistance is used for strings:
This finds the shortest tour through 100 points, with a penalty added to cross a "river":
This plots the tour, and the "river" in red :
This defines a sparse distance matrix among six points and find the shortest tour:
This plot the shortest tour in red, as well as the distance on each edge:
 Applications   (6)
Find a shortest tour visiting 50 random points in the plane:
Find a shortest tour visiting 100 random points in 3D:
Find the shortest tour through 2D points whose coordinates are relatively prime:
Find a shortest tour for 3D points with relatively prime coordinates:
Find a "shortest tour" through the names of countries in Europe:
Find a traveling-salesman tour of Europe:
Plan a tour through every country of the world:
Visualize the tour:
New in 6
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