Multiple Traveling Salesman Problem (M-TSP) Genetic Algorithm (GA) 多旅行商问题

function [opt_rte,opt_brk,min_dist] = mtsp_ga(xy,dmat,salesmen,...
    pop_size,num_iter,singles,show_plots,show_waitbar)
% MTSP_GA Multiple Traveling Salesman 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)
%
% 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
%     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
%     SINGLES (scalar logical) is a flag that, if zero, forces the salesmen to
%         visit at least 2 cities
%     SHOW_PLOTS (scalar logical) is a flag that, if non-zero, generates a couple plots
%     SHOW_WAITBAR (scalar logical) is a flag that, if non-zero, displays a waitbar
%
% 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
%
% Example:
%     n = 35; dims = 2;
%     xy = 10*rand(n,dims);
%     salesmen = 5;
%     pop_size = 80;
%     num_iter = 5e3;
%     singles = 0;
%     show_plots = 1;
%     show_waitbar = 1;
%     a = reshape(xy,1,n,dims);
%     b = reshape(xy,n,1,dims);
%     dmat = sqrt(sum((a(ones(n,1),:,:)-b(:,ones(n,1),:)).^2,3));
%     [opt_rte,opt_brk,min_dist] = mtsp_ga(xy,dmat,salesmen,pop_size,...
%       num_iter,singles,show_plots,show_waitbar);
%
% Author: Joseph Kirk
% Email: jdkirk630 at gmail dot com
% Release: 1.0
% Release Date: 3/4/08

if ~nargin % Initialize Example Inputs
    n = 50; dims = 2;
    xy = 10*rand(n,dims);
    salesmen = 7;
    pop_size = 80;
    num_iter = 1e4;
    singles = 0;
    show_plots = 1;
    show_waitbar = 1;
    try % Compute the Distance Matrix
        dmat = distmat(xy); % File Exchange Contribution #15145
    catch
        a = reshape(xy,1,n,dims);
        b = reshape(xy,n,1,dims);
        dmat = sqrt(sum((a(ones(n,1),:,:)-b(:,ones(n,1),:)).^2,3));
    end
else % Process the Given Inputs
    n = size(xy,1);
    [nr,nc] = size(dmat);
    if nr ~= n || nc ~= n
        error('Invalid inputs XY and/or DMAT');
    end
end

% Verify Inputs
salesmen = max(1,min(n,round(real(salesmen(1)))));
if ~singles
    salesmen = min(floor(n/2),salesmen);
end
pop_size = max(8,8*ceil(pop_size(1)/8));
num_iter = max(2,round(real(num_iter(1))));
singles = logical(singles(1));
show_plots = logical(show_plots(1));
show_waitbar = logical(show_waitbar(1));

% Plot the Cities and the Distance Matrix
if show_plots
    hfig = figure('Name','MTSPGA','Numbertitle','off');
    subplot(2,2,1);
    plot(xy(:,1),xy(:,2),'.');
    for k = 1:n
        text(xy(k,1),xy(k,2),[' ' num2str(k)],'FontWeight','b');
    end
    title('City Locations')
    subplot(2,2,2);
    imagesc(dmat);
    colormap(flipud(gray));
    title('Distance Matrix');
end

% Initializations for Route Break Point Selection
num_brks = salesmen-1;
addto = ones(1,n-2*num_brks-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
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);

% 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);
if show_plots
    pfig = figure('Name','Current Best Solution','Numbertitle','off');
end
if show_waitbar
    wb = waitbar(0,'Searching ... Please Wait');
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 m = 1:salesmen
            d = d + dmat(p_rte(rng(m,2)),p_rte(rng(m,1)));
            for k = rng(m,1):rng(m,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]]';
        % Plot the Best Route
        if show_plots
            figure(pfig); hold off;
            for m = 1:salesmen
                rte = [opt_rte(rng(m,1):rng(m,2)) opt_rte(rng(m,1))];
                plot(xy(rte,1),xy(rte,2),'.-','Color',clr(m,:));
                title(sprintf('Total Distance = %1.4f',min_dist));
                hold on;
            end
        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_brks = 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_brks;
            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 = new_pop_brk;
    if show_waitbar, waitbar(iter/num_iter,wb); end
end
if show_waitbar, close(wb); end

% Plot the Results
if show_plots
    rng = [[1 opt_brk+1];[opt_brk n]]';
    figure(hfig); subplot(2,2,3); hold off;
    for m = 1:salesmen
        rte = [opt_rte(rng(m,1):rng(m,2)) opt_rte(rng(m,1))];
        plot(xy(rte,1),xy(rte,2),'.-','Color',clr(m,:));
        title(sprintf('Total Distance = %1.4f',min_dist));
        hold on;
    end
    subplot(2,2,4);
    plot(dist_history,'r','LineWidth',2);
    title('Best Solution History');
    set(gca,'XLim',[1 num_iter],'YLim',[0 1.1*max(dist_history)]);
end

    % Generate Random Set of Break Points
    function breaks = randbreaks()
        if singles % No Constraints on Breaks
            tmp_brks = randperm(n-1);
            breaks = sort(tmp_brks(1:num_brks));
        else % Force Breaks to be At Least Two Apart
            num_adjust = find(rand < cum_prob,1)-1;
            spaces = ceil(num_brks*rand(1,num_adjust));
            adjust = zeros(1,num_brks);
            for kk = 1:num_brks
                adjust(kk) = sum(spaces == kk);
            end
            breaks = 2*(1:num_brks) + cumsum(adjust);
        end
    end
end