matlab 旅行商遗传算法

以下是使用Matlab实现旅行商遗传算法的示例代码：

% 城市坐标
city = [0.5, 0.5; 0.2, 0.8; 0.7, 0.9; 0.4, 0.3; 0.6, 0.1];

% 城市数量
n = size(city, 1);

% 种群大小
popsize = 100;

% 迭代次数
maxgen = 500;

% 交叉概率
pc = 0.8;

% 变异概率
pm = 0.1;

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

% 迭代
for gen = 1:maxgen
    % 计算适应度
    dist = zeros(popsize, 1);
    for i = 1:popsize
        for j = 1:n-1
            dist(i) = dist(i) + norm(city(pop(i,j),:) - city(pop(i,j+1),:));
        end
        dist(i) = dist(i) + norm(city(pop(i,n),:) - city(pop(i,1),:));
    end
    fitness = 1./dist;

    % 选择
    idx = randsample(popsize, popsize, true, fitness);

    % 交叉
    pop_new = zeros(popsize, n);
    for i = 1:2:popsize
        if rand < pc
            p1 = pop(idx(i), :);
            p2 = pop(idx(i+1), :);
            child = zeros(1, n);
            pos = randperm(n-1, 2);
            pos = sort(pos);
            child(pos(1):pos(2)) = p1(pos(1):pos(2));
            j = 1;
            for k = 1:n
                if ~ismember(p2(k), child)
                    while child(j) ~= 0
                        j = j + 1;
                    end
                    child(j) = p2(k);
                end
            end
            pop_new(i,:) = child;
            pop_new(i+1,:) = fliplr(child);
        else
            pop_new(i,:) = pop(idx(i), :);
            pop_new(i+1,:) = pop(idx(i+1), :);
        end
    end

    % 变异
    for i = 1:popsize
        if rand < pm
            pos = randperm(n, 2);
            pop_new(i, pos) = pop_new(i, pos(end:-1:1));
        end
    end

    % 更新种群
    pop = pop_new;
end

% 找到最优解
dist = zeros(popsize, 1);
for i = 1:popsize
    for j = 1:n-1
        dist(i) = dist(i) + norm(city(pop(i,j),:) - city(pop(i,j+1),:));
    end
    dist(i) = dist(i) + norm(city(pop(i,n),:) - city(pop(i,1),:));
end
[~, idx] = min(dist);
route = pop(idx, :);

% 输出结果
disp('最优路径：');
disp(route);
disp(['最短距离：', num2str(dist(idx))]);