遗传算法求解20个城市tsp问题 matlab代码

以下是使用遗传算法求解20个城市TSP问题的MATLAB代码：

% 遗传算法求解20个城市TSP问题
clc;
clear;

% 生成20个城市的坐标
n = 20;
city = rand(n, 2);

% 计算城市之间的距离
dist = zeros(n);
for i = 1:n
    for j = i+1:n
        dist(i,j) = norm(city(i,:) - city(j,:));
        dist(j,i) = dist(i,j);
    end
end

% 遗传算法参数设置
popSize = 100;
maxGen = 500;
pc = 0.8;
pm = 0.1;

% 初始化种群
pop = zeros(popSize, n);
for i = 1:popSize
    pop(i,:) = randperm(n);
end

% 迭代运行遗传算法
for gen = 1:maxGen
    % 计算适应度值
    fitness = zeros(popSize,1);
    for i = 1:popSize
        tour = pop(i,:);
        fitness(i) = 1/sum(dist(tour(1:n-1),tour(2:n))) + 1/dist(tour(n),tour(1));
    end
    
    % 选择操作
    prob = fitness/sum(fitness);
    cumProb = cumsum(prob);
    newPop = zeros(popSize, n);
    for i = 1:popSize
        r = rand;
        j = find(cumProb >= r, 1);
        newPop(i,:) = pop(j,:);
    end
    
    % 交叉操作
    for i = 1:2:popSize
        if rand < pc
            tour1 = newPop(i,:);
            tour2 = newPop(i+1,:);
            pos = randperm(n-1,2);
            pos = sort(pos);
            temp = tour1(pos(1):pos(2));
            tour1(pos(1):pos(2)) = tour2(pos(1):pos(2));
            tour2(pos(1):pos(2)) = temp;
            newPop(i,:) = tour1;
            newPop(i+1,:) = tour2;
        end
    end
    
    % 变异操作
    for i = 1:popSize
        if rand < pm
            tour = newPop(i,:);
            pos = randperm(n-1,2);
            pos = sort(pos);
            temp = tour(pos(1));
            tour(pos(1)) = tour(pos(2));
            tour(pos(2)) = temp;
            newPop(i,:) = tour;
        end
    end
    
    % 更新种群
    pop = newPop;
end

% 寻找最优解
bestTour = pop(1,:);
bestDist = sum(dist(bestTour(1:n-1),bestTour(2:n))) + dist(bestTour(n),bestTour(1));

% 绘制最优路径
figure(1);
plot(city(:,1), city(:,2), 'o');
hold on;
plot(city([bestTour,n]), city([bestTour([2:n,1]),bestTour(1)]), '-');
title(sprintf('最优路径长度为 %.2f', bestDist));
xlabel('x坐标');
ylabel('y坐标');

代码中使用了一些MATLAB内置函数，如`randperm`、`norm`和`cumsum`等，具体用法可以查阅MATLAB官方文档。运行该代码可以得到最优路径长度和最优路径的可视化结果。