Description |
MTSPF_GA Fixed Multiple Traveling Salesman 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:
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
Output:
OPTRTE (integer array) is the best route found by the algorithm
OPTBRK (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
Example:
n = 35;
xy = 10*rand(n,2);
nSalesmen = 5;
minTour = 3;
popSize = 80;
numIter = 5e3;
a = meshgrid(1:n);
dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),n,n);
[optRoute,optBreak,minDist] = mtspf_ga(xy,dmat,nSalesmen,minTour,popSize,numIter,1,1);
Example:
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]));
nSalesmen = 5;
minTour = 3;
popSize = 80;
numIter = 1e4;
a = meshgrid(1:n);
dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),n,n);
[optRoute,optBreak,minDist] = mtspf_ga(xy,dmat,nSalesmen,minTour,popSize,numIter,1,1);
Example:
n = 35;
xyz = 10*rand(n,3);
nSalesmen = 5;
minTour = 3;
popSize = 80;
numIter = 5e3;
a = meshgrid(1:n);
dmat = reshape(sqrt(sum((xyz(a,:)-xyz(a',:)).^2,2)),n,n);
[optRoute,optBreak,minDist] = mtspf_ga(xyz,dmat,nSalesmen,minTour,popSize,numIter,1,1); |