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Traveling Salesman Problem - Nearest Neighbor

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Traveling Salesman Problem - Nearest Neighbor

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02 Sep 2008 (Updated )

Finds a near-optimal solution to a TSP using Nearest Neighbor (NN)

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Description

TSP_NN Traveling Salesman Problem (TSP) Nearest Neighbor (NN) Algorithm
The Nearest Neighbor algorithm produces different results depending on which city is selected as the starting point. This function determines the Nearest Neighbor routes for multiple starting points and returns the best of those routes

Summary:
1. A single salesman travels to each of the cities and completes the route by returning to the city he started from
2. Each city is visited by the salesman exactly once

Input:
XY (float) is an Nx2 (or Nx3) matrix of cities
DMAT (float) is an NxN matrix of point to point distances/costs
POPSIZE (scalar integer) is the size of the population (should be <= N)
SHOWPROG (scalar logical) shows the GA progress if true
SHOWRESULT (scalar logical) shows the GA results if true

Output:
OPTRTE (integer array) is the best route found by the algorithm
MINDIST (scalar float) is the cost of the best route

Example:
n = 50;
xy = 10*rand(n,2);
popSize = n;
showProg = 1;
showResult = 1;
a = meshgrid(1:n);
dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),n,n);
[optRoute,minDist] = tsp_nn(xy,dmat,popSize,showProg,showResult);

Example:
n = 100;
phi = (sqrt(5)-1)/2;
theta = 2*pi*phi*(0:n-1);
rho = (1:n).^phi;
[x,y] = pol2cart(theta(:),rho(:));
xy = 10*([x y]-min([x;y]))/(max([x;y])-min([x;y]));
popSize = n;
showProg = 1;
showResult = 1;
a = meshgrid(1:n);
dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),n,n);
[optRoute,minDist] = tsp_nn(xy,dmat,popSize,showProg,showResult);

Example:
n = 50;
xyz = 10*rand(n,3);
popSize = n;
showProg = 1;
showResult = 1;
a = meshgrid(1:n);
dmat = reshape(sqrt(sum((xyz(a,:)-xyz(a',:)).^2,2)),n,n);
[optRoute,minDist] = tsp_nn(xyz,dmat,popSize,showProg,showResult);

Acknowledgements

Traveling Salesman Problem Genetic Algorithm inspired this file.

Required Products MATLAB
MATLAB release MATLAB 7.12 (R2011a)
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Comments and Ratings (6)
20 Jan 2014 Julien

@Joseph: OK it works fine. I was not sure wich coordinates to use in XY.

09 Dec 2013 Joseph Kirk

@Julien, it is already generalized (other than the figure displays, which you can turn off). Regardless of the dimensionality, the cost/distance matrix will be NxN, and it is this matrix that the algorithm operates on. So the algorithm really is agnostic to the number of dimensions.

06 Dec 2013 Julien

Thanks for the algorithm! It works very well.
Are you planning to implement it with higher dimensions ? N=4,5,6 ...

01 Aug 2010 Maroag

Pretty nice program. However, there is a small bug in line 103 when by any chance two points are at the same distance min_d. Easily solvable though by just adding a line to choose the first element of J in case length(J)>1. Otherwise, works flawlessly.

18 Jan 2009 Sandip Vijay  
16 Oct 2008 Kururunfa Goju

Very nice. It could benefit from the fact of working with TSPLIB files...

Updates
02 Jun 2009

Added 3D capability.

07 Nov 2011

Minor cosmetic updates.

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