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1、多旅行商问题的matlab程序%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
2、 for the shortest 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 betw
3、een % 2. Except for the 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 o
4、r 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, NOT including the start/end point % POP_SIZE (scalar integer) is the size of the population (should be divisible by 8) % NUM_ITER (scala
5、r 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
6、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 m
7、ight be: rte = 5 6 9 4 2 8 10 3 7, brks = 3 7 % Taken 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 an
8、d back to 1 % . Salesman 3 travels from city 1 to 10 to 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 = mtsp
9、f_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 = mtspf_ga(xyz,dmat,sa
10、lesmen,min_tour, . % pop_size,num_iter,1,1); % % See also: mtsp_ga, mtspo_ga, mtspof_ga, mtspofs_ga, mtspv_ga, distmat % % Author: Joseph Kirk % Email: jdkirk630 % Release: 1.3 % Release Date: 6/2/09 % Process Inputs and Initialize Defaults nargs = 8; for k = nargin:nargs-1 switch k case 0 xy = 10*r
11、and(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 = 2; 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(
12、dmat); if N = nr | N = nc error(Invalid XY or DMAT inputs!) end n = N - 1; % Separate Start/End City % 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_i
13、ter(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
14、); % 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)+1; 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
15、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 =
16、figure(Name,MTSPF_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(1,p_rte(rng(s,1); % Add Start Distance for k =
17、rng(s,1):rng(s,2)-1 d = d + dmat(p_rte(k),p_rte(k+1); end d = d + dmat(p_rte(rng(s,2),1); % Add End Distance 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_distglobal_min global_min = min_dist; opt_rte = pop_
18、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 = 1 opt_rte(rng(s,1):rng(s,2) 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 tit
19、le(sprintf(Total Distance = %1.4f, Iteration = %d,min_dist,iter); hold on end if dims = 3, plot3(xy(1,1),xy(1,2),xy(1,3),ko); else plot(xy(1,1),xy(1,2),ko); 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)
20、,:); 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,:)
21、= 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 %
22、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,:) = randbr
23、eaks; 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; end if show_res % Plots figure(Name,MTSPF_GA | Results,Numbertitle,off); subplot(2,2,1); if dims = 3, plot3(xy(:,1),xy(:,2),xy(:,3),k.); else
24、 plot(xy(:,1),xy(:,2),k.); end title(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:salesmen rte = 1 opt_rte(rng(s,1):rng(s,2) 1; if dims = 3, plot3(xy(rte,1),xy(rte,2),xy(rte,3),.-,Color,clr(s,:); el
25、se plot(xy(rte,1),xy(rte,2),.-,Color,clr(s,:); end title(sprintf(Total Distance = %1.4f,min_dist); hold on; end if dims = 3, plot3(xy(1,1),xy(1,2),xy(1,3),ko); else plot(xy(1,1),xy(1,2),ko); end subplot(2,2,4); plot(dist_history,b,LineWidth,2); title(Best Solution History); set(gca,XLim,0 num_iter+1
26、,YLim,0 1.1*max(1 dist_history); end % Return Outputs if nargout varargout1 = opt_rte; varargout2 = opt_brk; varargout3 = min_dist; end % Generate Random Set of Break Points function breaks = randbreaks if min_tour = 1 % No Constraints on Breaks tmp_brks = randperm(n-1); breaks = sort(tmp_brks(1:num_brks); else % Force Breaks to be at Least the Minimum Tour Length 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 = min_tour*(1:num_brks) + cumsum(adjust); end end end
