tsp旅行商三十个城市matlab遗传算法
时间: 2023-11-22 13:04:53 浏览: 43
以下是使用MATLAB遗传算法解决TSP旅行商问题的代码,其中包含30个城市的情况:
```matlab
% 定义城市坐标
x = [0.4000 0.2439 0.1707 0.2293 0.5171 0.8732 0.6878 0.8488 0.6683 0.6195 0.3443 0.1966 0.0780 0.0000 0.1391 0.3061 0.5085 0.6878 0.5946 0.7415 0.9449 0.9195 0.8054 0.6667 0.5878 0.4966 0.3902 0.2134 0.1667 0.0000];
y = [0.4439 0.1463 0.2293 0.7610 0.9415 0.6537 0.5219 0.3609 0.2537 0.2634 0.2756 0.1992 0.1884 0.4278 0.4610 0.4695 0.4551 0.3085 0.2122 0.1366 0.1390 0.0817 0.0000 0.0585 0.1695 0.2707 0.3720 0.3902 0.5000 0.5244];
% 计算城市之间的距离
n = length(x);
d = zeros(n,n);
for i = 1:n
for j = 1:n
d(i,j) = sqrt((x(i)-x(j))^2 + (y(i)-y(j))^2);
end
end
% 遗传算法参数设置
popSize = 100; % 种群大小
numGen = 1000; % 迭代次数
pc = 0.8; % 交叉概率
pm = 0.01; % 变异概率
% 初始化种群
pop = zeros(popSize,n);
for i = 1:popSize
pop(i,:) = randperm(n);
end
% 迭代
bestDist = Inf;
for i = 1:numGen
% 计算适应度
dist = zeros(1,popSize);
for j = 1:popSize
for k = 1:n-1
dist(j) = dist(j) + d(pop(j,k),pop(j,k+1));
end
dist(j) = dist(j) + d(pop(j,n),pop(j,1));
end
[minDist,minIdx] = min(dist);
if minDist < bestDist
bestDist = minDist;
bestPath = pop(minIdx,:);
end
% 选择
fitness = 1./dist;
fitness = fitness./sum(fitness);
cumFitness = cumsum(fitness);
newPop = zeros(size(pop));
for j = 1:popSize
idx = find(cumFitness >= rand,1);
newPop(j,:) = pop(idx,:);
end
% 交叉
for j = 1:2:popSize
if rand < pc
k = randi(n-1);
temp = newPop(j,k+1:end);
newPop(j,k+1:end) = newPop(j+1,k+1:end);
newPop(j+1,k+1:end) = temp;
for k = k+1:n
if ~ismember(newPop(j,k),newPop(j,1:k-1))
continue;
end
idx = find(~ismember(newPop(j+1,:),newPop(j,1:k-1)),1);
temp = newPop(j+1,k);
newPop(j+1,k) = newPop(j+1,idx);
newPop(j+1,idx) = temp;
end
end
end
% 变异
for j = 1:popSize
if rand < pm
k = randi(n-1);
temp = newPop(j,k);
newPop(j,k) = newPop(j,k+1);
newPop(j,k+1) = temp;
end
end
% 更新种群
pop = newPop;
end
% 输出结果
disp(['最短路径长度为:',num2str(bestDist)]);
disp(['最短路径为:',num2str(bestPath)]);
% 绘制路径图
figure;
plot(x(bestPath),y(bestPath),'-o');
title(['最短路径长度为:',num2str(bestDist)]);
```