| Description |
MTSPOFS_GA Fixed Start Open Multiple Traveling Salesman Problem (M-TSP) Genetic Algorithm (GA)
Finds a (near) optimal solution to a variation of the "open" 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 unique individual
cities without returning to the starting location)
Summary:
1. Each salesman starts at the first point, but travels to a unique
set of cities after that (and none of them close their loops by
returning to their starting points)
2. Except for the first, each city is visited by exactly one salesman
Note: The Fixed Start 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 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
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 4 2 8 10 3 7], brks = [3 7]
Taken together, these represent the solution [1 5 6 9][1 4 2 8][1 10 3 7],
which designates the routes for the 3 salesmen as follows:
. Salesman 1 travels from city 1 to 5 to 6 to 9
. Salesman 2 travels from city 1 to 4 to 2 to 8
. Salesman 3 travels from city 1 to 10 to 3 to 7
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] = mtspofs_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] = mtspofs_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] = mtspofs_ga(xyz,dmat,nSalesmen,minTour,popSize,numIter,1,1); |
