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### Highlights from Fixed Start/End Point Multiple Traveling Salesmen Problem - Genetic Algorithm

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# Fixed Start/End Point Multiple Traveling Salesmen Problem - Genetic Algorithm

### Joseph Kirk (view profile)

02 Sep 2008 (Updated )

Finds a near-optimal solution to a variation of the M-TSP with fixed endpoints using a GA

File Information
Description

MTSPF_GA Fixed Multiple Traveling Salesmen Problem (M-TSP) Genetic Algorithm (GA)
Finds a (near) optimal solution to a variation of the M-TSP by setting
up a GA to search for the shortest route (least distance needed for
each salesman to travel from the start location to individual cities
and back to the original starting place)
Summary:
1. Each salesman starts at the first point, and ends at the first
point, but travels to a unique set of cities in between
2. Except for the first, each city is visited by exactly one salesman

Note: The Fixed Start/End location is taken to be the first XY point

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 city-to-city distances or costs
- NSALESMEN (scalar integer) is the number of salesmen to visit the cities
- MINTOUR (scalar integer) is the minimum tour length for any of the
salesmen, NOT including the start/end point
- POPSIZE (scalar integer) is the size of the population (should be divisible by 8)
- 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
- OPTBREAK (integer array) is the list of route break points (these specify the indices
into the route used to obtain the individual salesman routes)
- MINDIST (scalar float) is the total distance traveled by the salesmen

Route/Breakpoint Details:
If there are 10 cities and 3 salesmen, a possible route/break
combination might be: rte = [5 6 9 4 2 8 10 3 7], brks = [3 7]
Taken together, these represent the solution [1 5 6 9 1][1 4 2 8 10 1][1 3 7 1],
which designates the routes for the 3 salesmen as follows:
. Salesman 1 travels from city 1 to 5 to 6 to 9 and back to 1
. Salesman 2 travels from city 1 to 4 to 2 to 8 to 10 and back to 1
. Salesman 3 travels from city 1 to 3 to 7 and back to 1

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

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

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

Example:
% Pass a random set of user-defined XY points to the solver
userConfig = struct('xy',10*rand(35,2));
resultStruct = mtspf_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 = mtspf_ga(userConfig);

Example:
% Pass a random set of 3D (XYZ) points to the solver
xyz = 10*rand(35,3);
userConfig = struct('xy',xyz);
resultStruct = mtspf_ga(userConfig);

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

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

Acknowledgements
Required Products MATLAB
MATLAB release MATLAB 8.3 (R2014a)
05 Feb 2015 Aaron T. Becker

### Aaron T. Becker (view profile)

This worked well -- thanks! You can reduce the "mindist" about 80% by initializing each salesman to explore a non-overlapping sector of the cities. The following code replaces lines 180-185:

% popRoute(1,:) = (1:n) + 1;
% popBreak(1,:) = rand_breaks();
% for k = 2:popSize
% popRoute(k,:) = randperm(n) + 1;
% popBreak(k,:) = rand_breaks();
% end

%A Heuristic that reduces MINDIST in practice:
% initialize each salesman to a single sector, each sector has almost the same number of cities:
theta = atan2(xy(2:end,1),xy(2:end,2)); %angle from depot to each city
[~,thetaInd] = sort(theta); %sort the angles
breaks = round(linspace(0,n,nSalesmen+1)); %try to give each salesman the same number of cities
sectorLabels(thetaInd) = floor(linspace(0,nSalesmen-10*eps,n))'+1; %label each city with the assigned salesman

% generate populations where each salesman's sector is randomly permuted
for k = 1:popSize
for i =1:nSalesmen
indices = find(sectorLabels==i)+1;
r = randperm(numel(indices));
popRoute(k,breaks(i)+1:breaks(i+1)) = indices(r);
end
popBreak(k,:)= breaks(2:end-1)+1;
end

19 Feb 2014 Joseph Kirk

### Joseph Kirk (view profile)

@sukanya, why don't you just download the file? And a rating of 1 when you apparently haven't even used the code seems a little premature, no?

Comment only
19 Feb 2014 sukanya

### sukanya (view profile)

i need coding for
Fixed Start/End Point Multiple Traveling Salesmen Problem - Genetic Algorithm

03 Jan 2014 Joseph Kirk

### Joseph Kirk (view profile)

@Pedro, yes the notes are in error. They will be fixed shortly.

Comment only
30 Dec 2013 Pedro p

### Pedro p (view profile)

Thanks Joseph for this submission, It works great for me, from what i understand of how the algorithm works where it says:

"""Route/Breakpoint Details:
If there are 10 cities and 3 salesmen, a possible route/break
combination might be: rte = [5 6 9 4 2 8 10 3 7], brks = [3 7]
Taken together, these represent the solution [1 5 6 9 1][1 4 2 8 1][1 10 3 7 1]"""

Shouldn't it say brks = [3 6]?

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11 May 2013 Albert

### Albert (view profile)

Could you please tell me how i
can edit the number of points that a salesman visits at MOST ? ( Because each salesman has a limit)

I mean, I want to add this input:

MAX_TOUR (scalar integer) is the maximum tour length for any of the
salesmen, NOT including the start/end point

MINTOUR constraint will remain and MAX_TOUR constraint will be added.

01 Oct 2008 The Author

Update: The SINGLES parameter has been replaced with a more generalized MIN_TOUR.

Comment only
15 Sep 2008 barki yak

Thanks alot, it works superb! but could you please tell me how i can edit the number of points that a salesman visit at least? its "2" in your work but i couldnt manage to increase that number

03 Sep 2008

updated description

08 Sep 2008

updated title

02 Jun 2009 1.1

07 Nov 2011 1.2

03 Jan 2014 1.3

Corrected the route/break details in the comment section.

03 Jan 2014 1.4

Removed waitbar.

06 May 2014 1.5

Major overhaul of input/output interface.