TSPLIB是一组各类TSP问题的实例集合。这里以TSPLIB中的berlin52为例进行求解。berlin52有52座城市。
% TSP模拟退火算法
clear
clc
a = 0.99; %温度衰减函数的参数
t0 = 97; %初始温度
tf = 3; %终止温度
t = t0;
Markov_length = 10000; %Markov链长度
coordinates = [
1 565.0 575.0; 2 25.0 185.0; 3 345.0 750.0;
4 945.0 685.0; 5 845.0 655.0; 6 880.0 660.0;
7 25.0 230.0; 8 525.0 1000.0; 9 580.0 1175.0;
10 650.0 1130.0; 11 1605.0 620.0; 12 1220.0 580.0;
13 1465.0 200.0; 14 1530.0 5.0; 15 845.0 680.0;
16 725.0 370.0; 17 145.0 665.0; 18 415.0 635.0;
19 510.0 875.0; 20 560.0 365.0; 21 300.0 465.0;
22 520.0 585.0; 23 480.0 415.0; 24 835.0 625.0;
25 975.0 580.0; 26 1215.0 245.0; 27 1320.0 315.0;
28 1250.0 400.0; 29 660.0 180.0; 30 410.0 250.0;
31 420.0 555.0; 32 575.0 665.0; 33 1150.0 1160.0;
34 700.0 580.0; 35 685.0 595.0; 36 685.0 610.0;
37 770.0 610.0; 38 795.0 645.0; 39 720.0 635.0;
40 760.0 650.0; 41 475.0 960.0; 42 95.0 260.0;
43 875.0 920.0; 44 700.0 500.0; 45 555.0 815.0;
46 830.0 485.0; 47 1170.0 65.0; 48 830.0 610.0;
49 605.0 625.0; 50 595.0 360.0; 51 1340.0 725.0;
52 1740.0 245.0;
];
coordinates(:,1) = [];
amount = size(coordinates,1); %城市的数目
%通过向量化的方法计算距离矩阵
dist_matrix = zeros(amount,amount);
coor_x_tmp1 = coordinates(:,1) * ones(1,amount);
coor_x_tmp2 = coor_x_tmp1';
coor_y_tmp1 = coordinates(:,2) * ones(1,amount);
coor_y_tmp2 = coor_y_tmp1';
dist_matrix = sqrt((coor_x_tmp1 - coor_x_tmp2).^2 + (coor_y_tmp1 - coor_y_tmp2).^2);
sol_new = 1:amount; %产生初始解，sol_new是每次产生的新解
sol_current = sol_new; %sol_current是当前解
sol_best = sol_new; %sol_best是冷却中的最好解
E_current = inf; %E_current是当前解对应的回路距离
E_best = inf; %E_best是最优解
p = 1;
while t >= tf
for r = 1:Markov_length %Markov链长度
%产生随机扰动
if(rand < 0.5)
%两交换
ind1 = 0;
ind2 = 0;
while(ind1 == ind2)
ind1 = ceil(rand * amount);
ind2 = ceil(rand * amount);
end
tmp1 = sol_new(ind1);
sol_new(ind1) = sol_new(ind2);
sol_new(ind2) = tmp1;
else
%三交换
ind1 = 0;
ind2 = 0;
ind3 = 0;
while( (ind1 == ind2) || (ind1 == ind3) || (ind2 == ind3) || (abs(ind1 -ind2) == 1) )
ind1 = ceil(rand * amount);
ind2 = ceil(rand * amount);
ind3 = ceil(rand * amount);
end
tmp1 = ind1;
tmp2 = ind2;
tmp3 = ind3;
%确保 ind1 < ind2 < ind3
if(ind1 < ind2) && (ind2 < ind3);
elseif(ind1 < ind3) && (ind3 < ind2)
ind1 = tmp1; ind2 = tmp3; ind3 = tmp2;
elseif(ind2 < ind1) && (ind1 < ind3)
ind1 = tmp2; ind2 = tmp1; ind3 = tmp3;
elseif(ind2 < ind3) && (ind3 < ind1)
ind1 = tmp2; ind2 = tmp3; ind3 = tmp1;
elseif(ind3 < ind1) && (ind1 < ind2)
ind1 = tmp3; ind2 = tmp1; ind3 = tmp2;
elseif(ind3 < ind2) && (ind2 < ind1)
ind1 = tmp3; ind2 = tmp2; ind3 = tmp1;
end
tmplist1 = sol_new((ind1 + 1):(ind2 - 1));
sol_new((ind1 + 1):(ind1 + (ind3 - ind2 + 1) )) = sol_new((ind2):(ind3));
sol_new((ind1 + (ind3 - ind2 + 1) + 1):(ind3)) = tmplist1;
end
%检查是否满足约束
%计算目标函数值（即内能）
E_new = 0;
for i = 1:(amount - 1)
E_new = E_new + dist_matrix(sol_new(i),sol_new(i + 1));
end
%再算上从最后一个城市到第一个城市的距离
E_new = E_new + dist_matrix(sol_new(amount),sol_new(1));
if E_new < E_current
E_current = E_new;
sol_current = sol_new;
if E_new < E_best
E_best = E_new;
sol_best = sol_new;
end
else
%若新解的目标函数值大于当前解，
%则仅以一定概率接受新解
if rand < exp(-(E_new - E_current) / t)
E_current = E_new;
sol_current = sol_new;
else
sol_new = sol_current;
end
end
end
t = t * a; %控制参数t（温度）减少为原来的a倍
end
disp('最优解为:');
disp(sol_best);
disp('最短距离:');
disp(E_best);对于berlin52,已用分支裁剪或分支定界法证明最优解为7542。