用Matlab写基于遗传算法的TSP问题的代码

以下是基于遗传算法的TSP问题的Matlab代码，代码中采用了简单的交叉和变异操作：

%% 遗传算法解决TSP问题

% 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];
y = [0.4439 0.1463 0.2293 0.7610 0.9414 0.6536 0.5219 0.3609 0.2536 0.2634];

% 参数设置
popSize = 50; % 种群大小
maxGen = 200; % 最大迭代次数
pc = 0.8; % 交叉概率
pm = 0.1; % 变异概率
numCity = length(x); % 城市数量

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

% 迭代寻优
for g = 1:maxGen
    % 计算适应度
    dist = zeros(popSize,1);
    for i = 1:popSize
        for j = 1:numCity-1
            dist(i) = dist(i) + sqrt((x(pop(i,j))-x(pop(i,j+1)))^2+(y(pop(i,j))-y(pop(i,j+1)))^2);
        end
        dist(i) = dist(i) + sqrt((x(pop(i,numCity))-x(pop(i,1)))^2+(y(pop(i,numCity))-y(pop(i,1)))^2);
    end
    fitness = 1./dist;
    [bestFit,idx] = max(fitness);
    bestRoute = pop(idx,:);
    
    % 选择
    p = fitness/sum(fitness);
    cumP = cumsum(p);
    newPop = zeros(popSize,numCity);
    for i = 1:popSize
        r = rand;
        for j = 1:popSize
            if r < cumP(j)
                newPop(i,:) = pop(j,:);
                break;
            end
        end
    end
    
    % 交叉
    for i = 1:2:popSize
        if rand < pc
            idx1 = randi(numCity);
            idx2 = randi(numCity);
            while idx2 == idx1
                idx2 = randi(numCity);
            end
            if idx1 > idx2
                temp = idx1;
                idx1 = idx2;
                idx2 = temp;
            end
            child1 = newPop(i,:);
            child2 = newPop(i+1,:);
            for j = idx1:idx2
                temp = child1(j);
                child1(j) = child2(j);
                child2(j) = temp;
            end
            newPop(i,:) = child1;
            newPop(i+1,:) = child2;
        end
    end
    
    % 变异
    for i = 1:popSize
        if rand < pm
            idx1 = randi(numCity);
            idx2 = randi(numCity);
            while idx2 == idx1
                idx2 = randi(numCity);
            end
            temp = newPop(i,idx1);
            newPop(i,idx1) = newPop(i,idx2);
            newPop(i,idx2) = temp;
        end
    end
    
    % 更新种群
    pop = newPop;
end

% 输出结果
disp(['最短路线：',num2str(bestRoute)]);
disp(['最短距离：',num2str(1/bestFit)]);

在运行代码之前，需要先定义城市坐标和一些参数，例如种群大小、最大迭代次数、交叉概率和变异概率等。然后，初始化种群并进行迭代，每次迭代计算种群的适应度，选择适应度高的个体进行交叉和变异操作，最后更新种群。最终输出最优解，即最短路线和最短距离。