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<H1 class=ContentTitle><STRONG>SA解決TSP問題的程序</STRONG></H1>
<H2 class=ContentAuthor>作者:dinga 日期:2006-04-22</H2></DIV>
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<DIV class=Content-body id=logPanel>SA解決TSP問題的程序。<BR> <BR>
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class=UBBContent>function out = tsp(loc) <BR>% TSP Traveling salesman problem (TSP) using SA (simulated annealing). <BR>% TSP by itself will generate 20 cities within a unit cube and <BR>% then use SA to slove this problem. <BR>% <BR>% TSP(LOC) solve the traveling salesman problem with cities' <BR>% coordinates given by LOC, which is an M by 2 matrix and M is <BR>% the number of cities. <BR>% <BR>% For example: <BR>% <BR>% loc = rand(50, 2); <BR>% tsp(loc); <BR>if nargin == 0, <BR>% The following data is from the post by Jennifer Myers (jmyers@nwu. <BR>edu) <BR>edu) <BR>% to comp.ai.neural-nets. It's obtained from the figure in <BR>% Hopfield & Tank's 1985 paper in Biological Cybernetics <BR>% (Vol 52, pp. 141-152). <BR>loc = [0.3663, 0.9076; 0.7459, 0.8713; 0.4521, 0.8465; <BR>0.7624, 0.7459; 0.7096, 0.7228; 0.0710, 0.7426; <BR>0.4224, 0.7129; 0.5908, 0.6931; 0.3201, 0.6403; <BR>0.5974, 0.6436; 0.3630, 0.5908; 0.6700, 0.5908; <BR>0.6172, 0.5495; 0.6667, 0.5446; 0.1980, 0.4686; <BR>0.3498, 0.4488; 0.2673, 0.4274; 0.9439, 0.4208; <BR>0.8218, 0.3795; 0.3729, 0.2690; 0.6073, 0.2640; <BR>0.4158, 0.2475; 0.5990, 0.2261; 0.3927, 0.1947; <BR>0.5347, 0.1898; 0.3960, 0.1320; 0.6287, 0.0842; <BR>0.5000, 0.0396; 0.9802, 0.0182; 0.6832, 0.8515]; <BR>end <BR>NumCity = length(loc); % Number of cities <BR>distance = zeros(NumCity); % Initialize a distance matrix <BR>% Fill the distance matrix <BR>for i = 1:NumCity, <BR>for j = 1:NumCity, <BR>distance(i, j) = norm(loc(i, :) - loc(j, :)); <BR>distance(i, j) = norm(loc(i, :) - loc(j, :)); <BR>end <BR>end <BR>% To generate energy (objective function) from path <BR>%path = randperm(NumCity); <BR>%energy = sum(distance((path-1)*NumCity + [path(2:NumCity) path(1)])); <BR>% Find typical values of dE <BR>count = 20; <BR>all_dE = zeros(count, 1); <BR>for i = 1:count <BR>path = randperm(NumCity); <BR>energy = sum(distance((path-1)*NumCity + [path(2:NumCity) <BR>path(1)])); <BR>new_path = path; <BR>index = round(rand(2,1)*NumCity+.5); <BR>inversion_index = (min(index):max(index)); <BR>new_path(inversion_index) = fliplr(path(inversion_index)); <BR>all_dE(i) = abs(energy - ... <BR>sum(sum(diff(loc([new_path new_path(1)],:))'.^2))); <BR>end <BR>dE = max(all_dE); <BR>dE = max(all_dE); <BR>temp = 10*dE; % Choose the temperature to be large enough <BR>fprintf('Initial energy = %f\n\n',energy); <BR>% Initial plots <BR>out = [path path(1)]; <BR>plot(loc(out(:), 1), loc(out(:), 2),'r.', 'Markersize', 20); <BR>axis square; hold on <BR>h = plot(loc(out(:), 1), loc(out(:), 2)); hold off <BR>MaxTrialN = NumCity*100; % Max. # of trials at a <BR>temperature <BR>MaxAcceptN = NumCity*10; % Max. # of acceptances at a <BR>temperature <BR>StopTolerance = 0.005; % Stopping tolerance <BR>TempRatio = 0.5; % Temperature decrease ratio <BR>minE = inf; % Initial value for min. energy <BR>maxE = -1; % Initial value for max. energy <BR>% Major annealing loop <BR>while (maxE - minE)/maxE > StopTolerance, <BR>minE = inf; <BR>minE = inf; <BR>maxE = 0; <BR>TrialN = 0; % Number of trial moves <BR>AcceptN = 0; % Number of actual moves <BR>while TrialN < MaxTrialN & AcceptN < MaxAcceptN, <BR>new_path = path; <BR>index = round(rand(2,1)*NumCity+.5); <BR>inversion_index = (min(index):max(index)); <BR>new_path(inversion_index) = <BR>fliplr(path(inversion_index)); <BR>new_energy = sum(distance( ... <BR>(new_path-1)*NumCity+[new_path(2:NumCity) <BR>new_path(1)])); <BR>if rand < exp((energy - new_energy)/temp), % <BR>accept <BR>it! <BR>energy = new_energy; <BR>path = new_path; <BR>minE = min(minE, energy); <BR>maxE = max(maxE, energy); <BR>AcceptN = AcceptN + 1; <BR>end <BR>TrialN = TrialN + 1; <BR>end <BR>end <BR>% Update plot <BR>out = [path path(1)]; <BR>set(h, 'xdata', loc(out(:), 1), 'ydata', loc(out(:), 2)); <BR>drawnow; <BR>% Print information in command window <BR>fprintf('temp. = %f\n', temp); <BR>tmp = sprintf('%d ',path); <BR>fprintf('path = %s\n', tmp); <BR>fprintf('energy = %f\n', energy); <BR>fprintf('[minE maxE] = [%f %f]\n', minE, maxE); <BR>fprintf('[AcceptN TrialN] = [%d %d]\n\n', AcceptN, TrialN); <BR>% Lower the temperature <BR>temp = temp*TempRatio; <BR>end <BR>% Print sequential numbers in the graphic window <BR>for i = 1:NumCity, <BR>text(loc(path(i),1)+0.01, loc(path(i),2)+0.01, int2str(i), ... <BR>'fontsize', 8); <BR>end </DIV></DIV><BR><BR><BR>這個程序是.m文件，在matlab中運行。 <BR><BR><BR><BR><BR></DIV>
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