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## Open Traveling Salesman Problem - Genetic Algorithm

version 1.3.0.0 (9.61 KB) by Joseph Kirk

### Joseph Kirk (view profile)

Finds a near-optimal solution to a "open" variation of the TSP using a GA

Updated 06 May 2014

TSPO_GA Open Traveling Salesman Problem (TSP) Genetic Algorithm (GA)
Finds a (near) optimal solution to a variation of the TSP by setting up
a GA to search for the shortest route (least distance for the salesman
to travel to each city exactly once without returning to the starting city)
Summary:
1. A single salesman travels to each of the cities but does not close
the loop by returning to the city he started from
2. Each city is visited by the salesman exactly once

Input:
USERCONFIG (structure) with zero or more of the following fields:
- XY (float) is an Nx2 matrix of city locations, where N is the number 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 divisible by 4)
- NUMITER (scalar integer) is the number of desired iterations for the algorithm to run
- SHOWPROG (scalar logical) shows the GA progress if true
- SHOWRESULT (scalar logical) shows the GA results if true
- SHOWWAITBAR (scalar logical) shows a waitbar if true

Input Notes:
1. Rather than passing in a structure containing these fields, any/all of
these inputs can be passed in as parameter/value pairs in any order instead.
2. Field/parameter names are case insensitive but must match exactly otherwise.

Output:
RESULTSTRUCT (structure) with the following fields:
(in addition to a record of the algorithm configuration)
- OPTROUTE (integer array) is the best route found by the algorithm
- MINDIST (scalar float) is the cost of the best route

Usage:
tspo_ga
-or-
tspo_ga(userConfig)
-or-
resultStruct = tspo_ga;
-or-
resultStruct = tspo_ga(userConfig);
-or-
[...] = tspo_ga('Param1',Value1,'Param2',Value2, ...);

Example:
% Let the function create an example problem to solve
tspo_ga;

Example:
% Request the output structure from the solver
resultStruct = tspo_ga;

Example:
% Pass a random set of user-defined XY points to the solver
userConfig = struct('xy',10*rand(50,2));
resultStruct = tspo_ga(userConfig);

Example:
% Pass a more interesting set of XY points to the solver
n = 50;
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]));
userConfig = struct('xy',xy);
resultStruct = tspo_ga(userConfig);

Example:
% Pass a random set of 3D (XYZ) points to the solver
xyz = 10*rand(50,3);
userConfig = struct('xy',xyz);
resultStruct = tspo_ga(userConfig);

Example:
% Change the defaults for GA population size and number of iterations
userConfig = struct('popSize',200,'numIter',1e4);
resultStruct = tspo_ga(userConfig);

Example:
% Turn off the plots but show a waitbar
userConfig = struct('showProg',false,'showResult',false,'showWaitbar',true);
resultStruct = tspo_ga(userConfig);

### Cite As

Joseph Kirk (2020). Open Traveling Salesman Problem - Genetic Algorithm (https://www.mathworks.com/matlabcentral/fileexchange/21196-open-traveling-salesman-problem-genetic-algorithm), MATLAB Central File Exchange. Retrieved .

Joseph Kirk

### Joseph Kirk (view profile)

@mackhina, yes, see "Fixed Endpoints Open Traveling Salesman Problem - Genetic Algorithm"
https://www.mathworks.com/matlabcentral/fileexchange/21197-fixed-endpoints-open-traveling-salesman-problem-genetic-algorithm

mackhina

mackhina

### mackhina (view profile)

Very cool! Is there a way to define or restrict the start and end points for this algorithm?

PMmotBG

Pablo Vicente

Nathan Parrish

Are Losnegård

Jack

very good thing

António

### António (view profile)

Hi Joseph Kirk, awesome job. I saw that this file was in the "File Exchange Pick of the Week" and i tried to do the same that was made there, i tried to use a map of Europe and change the code the right way and run the program, but i was not suceeded, can u help with that?

mei

### mei (view profile)

what if there 10 cities, the salesman only have to go for 6 cities and no repeating cities and open?

Newmat

### Newmat (view profile)

Thanks Joseph for your great work!

I didnt find out yet at which point the route starts and where it ends. It seems to be neither the first nor the last point in xy :)

reza