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

version 1.5.0.0 (14.3 KB) by Joseph Kirk

Joseph Kirk (view profile)

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

Updated 06 May 2014

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);

xiao luo

xiao luo (view profile)

I want to implement the following features: When limiting the maximum path for each salesperson, after completing all the cities, I need several salespeople.

Soufian Mejdaoui

Soufian Mejdaoui (view profile)

i'm a bginner in matlab & i need powerfully this code for educational using, may someone explain me how the crossover & mutation have beeing implements in this code ??

Joseph Kirk

Joseph Kirk (view profile)

@noor, I used a genetic algorithm approach for this code, not simulated annealing.

noor kc

noor kc (view profile)

great work, is this simulated annealing or not?
if not can you please tell me whats the iteration criteria ?

and if its simulated annealing, whats the starting temperature ?

Joseph Kirk

Joseph Kirk (view profile)

@Jarev, a larger number of iterations will take longer to process, but will give the algorithm more chances to find a better solution. It is a trade-off inherent in GA approaches.

Jarev Divinagracia

Jarev Divinagracia (view profile)

Hi, what is the effect of increasing or decreasing the number of iterations in the code? and what does a very high iteration do to the results?

Joseph Kirk

Joseph Kirk (view profile)

@shang, if you have a DMAT input whose size is NxN, then you could provide a "dummy" XY matrix that is Nx2, and the algorithm will work as you would expect (in the case where a distance/cost matrix is provided, the XY points are only used for plots)

shang ni

shang ni (view profile)

Hi,Sir!What could I do when I don't have a input if xy but dmat?

Tharun Joseph

Tharun Joseph (view profile)

I would like to use mTSP(fixed) for my following code:

xx1 = [-0.5 -0.5 31 31 -0.5];
yy2 = [2.5 -2.5 -2.5 2.5 2.5];
spc = 2;
x = [-1,1];
y = x*spc;
hold on;
xx = 15;
yy = 0;
plot(xx1,yy2,'b'); % draw square
plot(xx,yy,'bo'); % Draw centre circle
f = 0:10:30 ;
F = repmat(f,[4 1]) ;
f = F' ;
Z = [x,y] ;
z = repmat(Z,[4 1]) ;
% draw pluses
plot(f,z,'+r')
% finding distance between ohvs and turbines by creating a distance matrix
for i = 1:size(z,1)
for j = 1:size(z,2)
dist = sqrt((15-f(i,j))^2+(0-z(i,j))^2);
distanceMatrix(i,j) = dist;
end
end
cost = distanceMatrix .* 2; %price of cable per metre
s1 = sum(cost(1,:));
s2 = sum(cost(2,:));
s3 = sum(cost(3,:));
s4 = sum(cost(4,:));
total = s1+s2+s3+s4
for i = 1:size(z,1)
for j = 1:size(z,2)
plot([f(i,j),xx],[z(i,j),yy],'k')
end
end

but finding quite difficult on how to implement it. Please help. thank you

learn

learn (view profile)

GOOD JOB!

Aaron T. Becker's Robot Swarm Lab

Aaron T. Becker's Robot Swarm Lab (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

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?

sukanya

sukanya (view profile)

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

Joseph Kirk

Joseph Kirk (view profile)

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

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]?

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.
Thanks a lot in advance.

The Author

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

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