模拟退火算法tsp问题案例.zip_退火算法

clear clc a = 0.99; % 温度衰减函数的参数 t0 = 97; tf = 3; 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是当前解；sol_best是冷却中的最好解； E_current = inf;E_best = inf; % E_current是当前解对应的回路距离； % E_new是新解的回路距离； % E_best是最优解的 sol_current = sol_new; sol_best = sol_new; p = 1; while t>=tf for r=1:Markov_length % Markov链长度 % 产生随机扰动 if (rand < 0.5) % 随机决定是进行两交换还是三交换 % 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) ind2 = tmp3;ind3 = tmp2; elseif (ind2 < ind1) && (ind1 < ind3) ind1 = tmp2;ind2 = tmp1; 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+2):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 % 把冷却过程中最好的解保存下来 E_best = E_new; sol_best = sol_new; end else % 若新解的目标函数值小于当前解的， % 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)