1、%多旅行商问题的 matlab 程序function varargout = mtspf_ga(xy,dmat,salesmen,min_tour,pop_size,num_iter,show_prog,show_res)% MTSPF_GA Fixed Multiple Traveling Salesmen Problem (M-TSP) Genetic Algorithm (GA)% Finds a (near) optimal solution to a variation of the M-TSP by setting% up a GA to search for the shorte
2、st route (least distance needed for% each salesman to travel from the start location to individual cities% and back to the original starting place)% Summary:% 1. Each salesman starts at the first point, and ends at the first% point, but travels to a unique set of cities in between% 2. Except for the
3、 first, each city is visited by exactly one salesman% Note: The Fixed Start/End location 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% SALESMEN (scalar inte
4、ger) is the number of salesmen to visit the cities% MIN_TOUR (scalar integer) is the minimum tour length for any of the% salesmen, NOT including the start/end point% POP_SIZE (scalar integer) is the size of the population (should be divisible by 8)% NUM_ITER (scalar integer) is the number of desired
5、 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
6、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 4 2 8 10 3 7, brks = 3 7% Ta
7、ken together, these represent the solution 1 5 6 9 11 4 2 8 11 10 3 7 1,% which designates the routes for the 3 salesmen as follows:% . Salesman 1 travels from city 1 to 5 to 6 to 9 and back to 1% . Salesman 2 travels from city 1 to 4 to 2 to 8 and back to 1% . Salesman 3 travels from city 1 to 10 t
8、o 3 to 7 and back to 1% 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 = mtspf_ga(xy,dmat,salesmen,min_tour, .% pop_size,num_iter,1,1);% 3D Examp
9、le:% 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 = mtspf_ga(xyz,dmat,salesmen,min_tour, .% pop_size,num_iter,1,1);% See also: mtsp_ga, mtspo_ga, mtspof_
10、ga, mtspofs_ga, mtspv_ga, distmat% Author: Joseph Kirk% Email: % Release: 1.3% Release Date: 6/2/09% Process Inputs and Initialize Defaultsnargs = 8;for k = nargin:nargs-1switch kcase 0xy = 10*rand(40,2);case 1N = size(xy,1);a = meshgrid(1:N);dmat = reshape(sqrt(sum(xy(a,:)-xy(a,:).2,2),N,N);case 2s
11、alesmen = 5;case 3min_tour = 2;case 4pop_size = 80;case 5num_iter = 5e3;case 6show_prog = 1;case 7show_res = 1;otherwiseendend% Verify InputsN,dims = size(xy);nr,nc = size(dmat);if N = nr | N = ncerror(Invalid XY or DMAT inputs!)endn = N - 1; % Separate Start/End City% Sanity Checkssalesmen = max(1,
12、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 Selectionnum_brks = salesm
13、en-1;dof = n - min_tour*salesmen; % degrees of freedomaddto = ones(1,dof+1);for k = 2:num_brksaddto = cumsum(addto);endcum_prob = cumsum(addto)/sum(addto);% Initialize the Populationspop_rte = zeros(pop_size,n); % population of routespop_brk = zeros(pop_size,num_brks); % population of breaksfor k =
14、1:pop_sizepop_rte(k,:) = randperm(n)+1;pop_brk(k,:) = randbreaks();end% Select the Colors for the Plotted Routesclr = 1 0 0; 0 0 1; 0.67 0 1; 0 1 0; 1 0.5 0;if salesmen 5clr = hsv(salesmen);end% Run the GAglobal_min = Inf;total_dist = zeros(1,pop_size);dist_history = zeros(1,num_iter);tmp_pop_rte =
15、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_progpfig = figure(Name,MTSPF_GA | Current Best Solution,Numbertitle,off);endfor iter = 1:num_iter% Evaluate Members of the Populationfor p = 1:pop_sized = 0;p_rte = pop_rte(p,:);
16、p_brk = pop_brk(p,:);rng = 1 p_brk+1;p_brk n;for s = 1:salesmend = d + dmat(1,p_rte(rng(s,1); % Add Start Distancefor k = rng(s,1):rng(s,2)-1d = d + dmat(p_rte(k),p_rte(k+1);endd = d + dmat(p_rte(rng(s,2),1); % Add End Distanceendtotal_dist(p) = d;end% Find the Best Route in the Populationmin_dist,i
17、ndex = min(total_dist);dist_history(iter) = min_dist;if min_dist global_minglobal_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 Routefigure(pfig);for s = 1:salesmenrte = 1 opt_rte(rng(s,1):rng(s,2) 1;if dims = 3, plot3(xy
18、(rte,1),xy(rte,2),xy(rte,3),.-,Color,clr(s,:);else plot(xy(rte,1),xy(rte,2),.-,Color,clr(s,:); endtitle(sprintf(Total Distance = %1.4f, Iteration = %d,min_dist,iter);hold onendif dims = 3, plot3(xy(1,1),xy(1,2),xy(1,3),ko);else plot(xy(1,1),xy(1,2),ko); endhold offendend% Genetic Algorithm Operators
19、rand_grouping = randperm(pop_size);for p = 8:8:pop_sizertes = 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
20、_pts(1);J = rte_ins_pts(2);for k = 1:8 % Generate New Solutionstmp_pop_rte(k,:) = best_of_8_rte;tmp_pop_brk(k,:) = best_of_8_brk;switch kcase 2 % Fliptmp_pop_rte(k,I:J) = fliplr(tmp_pop_rte(k,I:J);case 3 % Swaptmp_pop_rte(k,I J) = tmp_pop_rte(k,J I);case 4 % Slidetmp_pop_rte(k,I:J) = tmp_pop_rte(k,I
21、+1:J I);case 5 % Modify Breakstmp_pop_brk(k,:) = randbreaks();case 6 % Flip, Modify Breakstmp_pop_rte(k,I:J) = fliplr(tmp_pop_rte(k,I:J);tmp_pop_brk(k,:) = randbreaks();case 7 % Swap, Modify Breakstmp_pop_rte(k,I J) = tmp_pop_rte(k,J I);tmp_pop_brk(k,:) = randbreaks();case 8 % Slide, Modify Breakstm
22、p_pop_rte(k,I:J) = tmp_pop_rte(k,I+1:J I);tmp_pop_brk(k,:) = randbreaks();otherwise % Do Nothingendendnew_pop_rte(p-7:p,:) = tmp_pop_rte;new_pop_brk(p-7:p,:) = tmp_pop_brk;endpop_rte = new_pop_rte;pop_brk = new_pop_brk;endif show_res% Plotsfigure(Name,MTSPF_GA | Results,Numbertitle,off);subplot(2,2,
23、1);if dims = 3, plot3(xy(:,1),xy(:,2),xy(:,3),k.);else plot(xy(:,1),xy(:,2),k.); endtitle(City Locations);subplot(2,2,2);imagesc(dmat(1 opt_rte,1 opt_rte);title(Distance Matrix);subplot(2,2,3);rng = 1 opt_brk+1;opt_brk n;for s = 1:salesmenrte = 1 opt_rte(rng(s,1):rng(s,2) 1;if dims = 3, plot3(xy(rte
24、,1),xy(rte,2),xy(rte,3),.-,Color,clr(s,:);else plot(xy(rte,1),xy(rte,2),.-,Color,clr(s,:); endtitle(sprintf(Total Distance = %1.4f,min_dist);hold on;endif dims = 3, plot3(xy(1,1),xy(1,2),xy(1,3),ko);else plot(xy(1,1),xy(1,2),ko); endsubplot(2,2,4);plot(dist_history,b,LineWidth,2);title(Best Solution
25、 History);set(gca,XLim,0 num_iter+1,YLim,0 1.1*max(1 dist_history);end% Return Outputsif nargoutvarargout1 = opt_rte;varargout2 = opt_brk;varargout3 = min_dist;end% Generate Random Set of Break Pointsfunction breaks = randbreaks()if min_tour = 1 % No Constraints on Breakstmp_brks = randperm(n-1);bre
26、aks = sort(tmp_brks(1:num_brks);else % Force Breaks to be at Least the Minimum Tour Lengthnum_adjust = find(rand cum_prob,1)-1;spaces = ceil(num_brks*rand(1,num_adjust);adjust = zeros(1,num_brks);for kk = 1:num_brksadjust(kk) = sum(spaces = kk);endbreaks = min_tour*(1:num_brks) + cumsum(adjust);endendend
