tsp.m

使用遗传算法求解邮递员问题

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