mtsp_ga.zip_City Locations_MTSP_m.mtspw.com_多旅行商_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