【路径规划-TSP问题】基于遗传算法求解固定的开放式多旅行推销员问题(M-TSP)附matlab代码.zip

function varargout = mtspof_ga(xy,dmat,salesmen,min_tour,pop_size,num_iter,show_prog,show_res) % MTSPOF_GA Fixed Open Multiple Traveling Salesmen Problem (M-TSP) Genetic Algorithm (GA) % Finds a (near) optimal solution to a variation of the "open" M-TSP by % setting up a GA to search for the shortest route (least distance needed % for each salesman to travel from the start location to unique % individual cities and finally to the end location) % % Summary: % 1. Each salesman starts at the first point, and ends at the last % point, but travels to a unique set of cities in between (none of % them close their loops by returning to their starting points) % 2. Except for the first and last, each city is visited by exactly one salesman % % Note: The Fixed Start is taken to be the first XY point and the Fixed End % is taken to be the last 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 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 point or 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 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 4 2 8 3 7], brks = [3 7] % Taken together, these represent the solution [1 5 6 9 10][1 4 2 8 10][1 3 7 10], % which designates the routes for the 3 salesmen as follows: % . Salesman 1 travels from city 1 to 5 to 6 to 9 to 10 % . Salesman 2 travels from city 1 to 4 to 2 to 8 to 10 % . Salesman 3 travels from city 1 to 3 to 7 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] = mtspof_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] = mtspof_ga(xyz,dmat,salesmen,min_tour, ... % pop_size,num_iter,1,1); % % See also: mtsp_ga, mtspf_ga, mtspo_ga, mtspofs_ga, mtspv_ga, distmat % % 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 = 1; 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 - 2; % Separate Start and End Cities % 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)+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 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','MTSPOF_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 = 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)),N); % 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_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 = [1 opt_rte(rng(s,1):rng(s,2)) N]; 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 if dims == 3, plot3(xy(1,1),xy(1,2),xy(1,3),'ko',xy(N,1),xy(N,2),xy(N,3),'ko'); else plot(xy(1,1),xy(1,2),'ko',xy(N,1),xy(N,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),:); 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, Mo