function varargout = mtsp_ga(xy,dmat,salesmen,min_tour,pop_size,num_iter,show_prog,show_res)
% MTSP_GA Multiple Traveling Salesmen Problem (M-TSP) Genetic Algorithm (GA)
% Finds a (near) optimal solution to the M-TSP 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 city-to-city distances or costs
% SALESMEN (scalar integer) is the number of salesmen to visit the cities
% MIN_TOUR (scalar integer) is the minimum tour length for any of the salesmen
% POP_SIZE (scalar integer) is the size of the population (should be divisible by 8)
% NUM_ITER (scalar integer) is the number of desired iterations for the algorithm to run
% SHOW_PROG (scalar logical) shows the GA progress if true
% SHOW_RES (scalar logical) shows the GA results if true
%
% Output:
% OPT_RTE (integer array) is the best route found by the algorithm
% OPT_BRK (integer array) is the list of route break points (these specify the indices
% into the route used to obtain the individual salesman routes)
% MIN_DIST (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
%
% 2D Example:
% n = 35;
% xy = 10*rand(n,2);
% salesmen = 5;
% min_tour = 3;
% pop_size = 80;
% num_iter = 5e3;
% a = meshgrid(1:n);
% dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),n,n);
% [opt_rte,opt_brk,min_dist] = mtsp_ga(xy,dmat,salesmen,min_tour, ...
% pop_size,num_iter,1,1);
%
% 3D Example:
% n = 35;
% xyz = 10*rand(n,3);
% salesmen = 5;
% min_tour = 3;
% pop_size = 80;
% num_iter = 5e3;
% a = meshgrid(1:n);
% dmat = reshape(sqrt(sum((xyz(a,:)-xyz(a',:)).^2,2)),n,n);
% [opt_rte,opt_brk,min_dist] = mtsp_ga(xyz,dmat,salesmen,min_tour, ...
% pop_size,num_iter,1,1);
%
% See also: tsp_ga, mtspf_ga, mtspo_ga, mtspof_ga, mtspofs_ga, mtspv_ga, distmat
%
% Author: Joseph Kirk
% Email: jdkirk630@gmail.com
% Release: 1.4
% Release Date: 6/2/09
% Process Inputs and Initialize Defaults
nargs = 8;
for k = nargin:nargs-1
switch k
case 0
xy = 10*rand(40,2);
case 1
N = size(xy,1);
a = meshgrid(1:N);
dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),N,N);
case 2
salesmen = 5;
case 3
min_tour = 3;
case 4
pop_size = 80;
case 5
num_iter = 5e3;
case 6
show_prog = 1;
case 7
show_res = 1;
otherwise
end
end
% Verify Inputs
[N,dims] = size(xy);
[nr,nc] = size(dmat);
if N ~= nr || N ~= nc
error('Invalid XY or DMAT inputs!')
end
n = N;
% Sanity Checks
salesmen = max(1,min(n,round(real(salesmen(1)))));
min_tour = max(1,min(floor(n/salesmen),round(real(min_tour(1)))));
pop_size = max(8,8*ceil(pop_size(1)/8));
num_iter = max(1,round(real(num_iter(1))));
show_prog = logical(show_prog(1));
show_res = logical(show_res(1));
% Initializations for Route Break Point Selection
num_brks = salesmen-1;
dof = n - min_tour*salesmen; % degrees of freedom
addto = ones(1,dof+1);
for k = 2:num_brks
addto = cumsum(addto);
end
cum_prob = cumsum(addto)/sum(addto);
% Initialize the Populations
pop_rte = zeros(pop_size,n); % population of routes
pop_brk = zeros(pop_size,num_brks); % population of breaks
for k = 1:pop_size
pop_rte(k,:) = randperm(n);
pop_brk(k,:) = randbreaks();
end
% Select the Colors for the Plotted Routes
clr = [1 0 0; 0 0 1; 0.67 0 1; 0 1 0; 1 0.5 0];
if salesmen > 5
clr = hsv(salesmen);
end
% Run the GA
global_min = Inf;
total_dist = zeros(1,pop_size);
dist_history = zeros(1,num_iter);
tmp_pop_rte = zeros(8,n);
tmp_pop_brk = zeros(8,num_brks);
new_pop_rte = zeros(pop_size,n);
new_pop_brk = zeros(pop_size,num_brks);
if show_prog
pfig = figure('Name','MTSP_GA | Current Best Solution','Numbertitle','off');
end
for iter = 1:num_iter
% Evaluate Members of the Population
for p = 1:pop_size
d = 0;
p_rte = pop_rte(p,:);
p_brk = pop_brk(p,:);
rng = [[1 p_brk+1];[p_brk n]]';
for s = 1:salesmen
d = d + dmat(p_rte(rng(s,2)),p_rte(rng(s,1)));
for k = rng(s,1):rng(s,2)-1
d = d + dmat(p_rte(k),p_rte(k+1));
end
end
total_dist(p) = d;
end
% Find the Best Route in the Population
[min_dist,index] = min(total_dist);
dist_history(iter) = min_dist;
if min_dist < global_min
global_min = min_dist;
opt_rte = pop_rte(index,:);
opt_brk = pop_brk(index,:);
rng = [[1 opt_brk+1];[opt_brk n]]';
if show_prog
% Plot the Best Route
figure(pfig);
for s = 1:salesmen
rte = opt_rte([rng(s,1):rng(s,2) rng(s,1)]);
if dims == 3, plot3(xy(rte,1),xy(rte,2),xy(rte,3),'.-','Color',clr(s,:));
else plot(xy(rte,1),xy(rte,2),'.-','Color',clr(s,:)); end
title(sprintf('Total Distance = %1.4f, Iteration = %d',min_dist,iter));
hold on
end
hold off
end
end
% Genetic Algorithm Operators
rand_grouping = randperm(pop_size);
for p = 8:8:pop_size
rtes = pop_rte(rand_grouping(p-7:p),:);
brks = pop_brk(rand_grouping(p-7:p),:);
dists = total_dist(rand_grouping(p-7:p));
[ignore,idx] = min(dists);
best_of_8_rte = rtes(idx,:);
best_of_8_brk = brks(idx,:);
rte_ins_pts = sort(ceil(n*rand(1,2)));
I = rte_ins_pts(1);
J = rte_ins_pts(2);
for k = 1:8 % Generate New Solutions
tmp_pop_rte(k,:) = best_of_8_rte;
tmp_pop_brk(k,:) = best_of_8_brk;
switch k
case 2 % Flip
tmp_pop_rte(k,I:J) = fliplr(tmp_pop_rte(k,I:J));
case 3 % Swap
tmp_pop_rte(k,[I J]) = tmp_pop_rte(k,[J I]);
case 4 % Slide
tmp_pop_rte(k,I:J) = tmp_pop_rte(k,[I+1:J I]);
case 5 % Modify Breaks
tmp_pop_brk(k,:) = randbreaks();
case 6 % Flip, Modify Breaks
tmp_pop_rte(k,I:J) = fliplr(tmp_pop_rte(k,I:J));
tmp_pop_brk(k,:) = randbreaks();
case 7 % Swap, Modify Breaks
tmp_pop_rte(k,[I J]) = tmp_pop_rte(k,[J I]);
tmp_pop_brk(k,:) = randbreaks();
case 8 % Slide, Modify Breaks
tmp_pop_rte(k,I:J) = tmp_pop_rte(k,[I+1:J I]);
tmp_pop_brk(k,:) = randbreaks();
otherwise % Do Nothing
end
end
new_pop_rte(p-7:p,:) = tmp_pop_rte;
new_pop_brk(p-7:p,:) = tmp_pop_brk;
end
pop_rte = new_pop_rte;
pop_brk