遗传算法旅行商matlab程序

以下是一个简单的遗传算法旅行商问题的 Matlab 程序：

clc; clear all; close all;

% 遗传算法参数
npop = 100; % 种群大小
ngen = 500; % 迭代次数
pc = 0.8; % 交叉概率
pm = 0.05; % 变异概率
elitism = 0.05; % 精英比例

% 城市坐标
x = [0 3 6 2 5];
y = [0 1 5 2 6];
n = length(x); % 城市数量

% 距离矩阵
d = zeros(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

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

% 迭代
for t = 1:ngen
    % 计算适应度
    fit = zeros(npop,1);
    for i = 1:npop
        for j = 1:n
            fit(i) = fit(i) + d(pop(i,j),pop(i,j+1));
        end
    end
    
    % 选择
    [fit,idx] = sort(fit);
    pop = pop(idx,:);
    nelite = round(elitism*npop);
    newpop = pop(1:nelite,:);
    
    % 交叉
    ncross = round(pc*npop);
    for i = 1:ncross
        p1 = randi(nelite);
        p2 = randi(nelite);
        while p2 == p1
            p2 = randi(nelite);
        end
        child = zeros(1,n+1);
        idx1 = randi(n);
        idx2 = randi(n-idx1+1) + idx1;
        child(idx1:idx2) = pop(p1,idx1:idx2);
        j = 1;
        for k = 1:n
            if j < idx1 || j > idx2
                while ismember(pop(p2,j),child)
                    j = j+1;
                end
                child(j) = pop(p2,j);
                j = j+1;
            end
        end
        child(n+1) = child(1);
        newpop = [newpop; child];
    end
    
    % 变异
    nmutate = round(pm*npop);
    for i = 1:nmutate
        p = randi(nelite);
        child = pop(p,:);
        idx1 = randi(n);
        idx2 = randi(n);
        tmp = child(idx1);
        child(idx1) = child(idx2);
        child(idx2) = tmp;
        child(n+1) = child(1);
        newpop = [newpop; child];
    end
    
    % 更新种群
    pop = newpop;
    
    % 绘图
    clf;
    plot(x,y,'ro','MarkerSize',10,'LineWidth',2);
    hold on;
    plot([x(pop(1,:)) x(pop(1,1))],[y(pop(1,:)) y(pop(1,1))],'b.-','LineWidth',2,'MarkerSize',20);
    axis([-1 7 -1 7]);
    axis square;
    title(['Generation ' num2str(t)]);
    drawnow;
end

程序中使用了一个简单的遗传算法来解决旅行商问题。程序首先定义了遗传算法参数，然后根据城市坐标计算距离矩阵。接着，程序初始化种群，并在每一代中进行选择、交叉和变异操作，更新种群。最后，程序绘制当前最优解的路径。

运行程序后，您可以看到遗传算法逐渐找到更优的路径，直到迭代次数达到设定的值。