tsp.m

利用模拟退火法求解TSP问题 可以求得50个城市的精确解

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])
% 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 = [3.64,2.68   %beijing
    4.18,1.76   %shanghai
    3.71,2.60   %tianjin
    2.77,1.50   %chongqing
    1.33,3.30   %wulumuqi
    4.20,2.96   %shenyang
    4.39,3.43   %haerbing
    3.92,1.82   %nanjing
    4.26,1.07   %taibei
    2.55,1.64   %chengdu
    2.37,1.02   %kunming
    3.43,2.09   %zhengzhou
    3.54,0.70   %xianggang
    3.51,1.62   %wuhan
    3.44,0.80   %guangzhou
    3.24,2.77   %huhehaote
    2.38,2.32   %xiling
    2.56,2.24   %lanzhou
    3.01,2.03   %xian
    2.79,2.51   %yinchuan
    3.33,2.44   %taiyuan
    2.94,0.76   %nanling
    3.39,1.36   %changsha
    3.49,2.46   %shijiazhuang
    2.78,1.17   %guiyang
    3.14,0.45   %haikou
    4.31,3.21   %changcun
    3.72,2.32   %jinan
    4.06,1.63   %hangzhou
    3.78,1.79   %hefei
    3.68,1.42   %nancang
    4.03,1.16   %fuzhou
    3.47,0.70   %aomen
    1.30,1.69]; %lasha
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, :));
	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); %四舍五入
	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);

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;
	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

	% 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