Description |
MTSPV_GA Variable Multiple Traveling Salesman Problem (M-TSP) Genetic Algorithm (GA)
Finds a (near) optimal solution to a variation of the M-TSP (that has a
variable number of salesmen) by setting up a GA to search for the
shortest route (least distance needed for the salesmen to travel to
each city exactly once and return to their starting locations)
Summary:
1. Each salesman travels to a unique set of cities and completes the
route by returning to the city he started from
2. Each city is visited by exactly one salesman
Input:
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 or costs
MINTOUR (scalar integer) is the minimum tour length for any of the salesmen
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
SHOWRES (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 1 4 2 8 10 3 7], brks = [3 7]
Taken together, these represent the solution [5 6 9][1 4 2 8][10 3 7],
which designates the routes for the 3 salesmen as follows:
. Salesman 1 travels from city 5 to 6 to 9 and back to 5
. Salesman 2 travels from city 1 to 4 to 2 to 8 and back to 1
. Salesman 3 travels from city 10 to 3 to 7 and back to 10
Example:
n = 35;
xy = 10*rand(n,2);
minTour = 3;
popSize = 40;
numIter = 5e3;
a = meshgrid(1:n);
dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),n,n);
[optRoute,optBreak,minDist] = mtspv_ga(xy,dmat,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]));
minTour = 3;
popSize = 40;
numIter = 1e4;
a = meshgrid(1:n);
dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),n,n);
[optRoute,optBreak,minDist] = mtspv_ga(xy,dmat,minTour,popSize,numIter,1,1);
Example:
n = 35;
xyz = 10*rand(n,3);
minTour = 3;
popSize = 40;
numIter = 5e3;
a = meshgrid(1:n);
dmat = reshape(sqrt(sum((xyz(a,:)-xyz(a',:)).^2,2)),n,n);
[optRoute,optBreak,minDist] = mtspv_ga(xyz,dmat,minTour,popSize,numIter,1,1); |