Matlab实现tsp遗传算法

遗传算法是一种优化算法，它可以用于解决旅行商问题(TSP)。下面是使用Matlab实现tsp遗传算法的步骤：

1. 定义城市坐标：首先，需要定义每个城市的坐标。可以通过随机生成城市坐标或者手动定义坐标。

2. 计算距离矩阵：计算每两个城市之间的距离。可以使用欧几里得距离公式进行计算。

3. 初始化种群：随机生成初始种群。每个个体代表一条旅行路线，即一组城市的排列序列。

4. 评估适应度：根据每个个体的旅行路线，计算其总路程长度。路程长度越短，个体的适应度越高。

5. 选择操作：使用轮盘赌选择算法从种群中选择优秀个体。

6. 交叉操作：对选择出的个体进行交叉操作，生成新的个体。

7. 变异操作：对新生成的个体进行变异操作，增加种群的多样性。

8. 评估适应度：计算新个体的适应度。

9. 更新种群：将新个体加入到种群中，更新种群。

10. 判断终止条件：重复以上操作直至满足终止条件，例如达到最大迭代次数或者收敛。

下面是一份示例代码：

% 定义城市坐标
numCities = 20;
mapWidth = 100;
mapHeight = 100;
cityLocations = [randi(mapWidth,1,numCities);randi(mapHeight,1,numCities)];

% 计算距离矩阵
distMatrix = zeros(numCities);
for i = 1:numCities
    for j = i+1:numCities
        distance = sqrt((cityLocations(1,i)-cityLocations(1,j))^2 + (cityLocations(2,i)-cityLocations(2,j))^2);
        distMatrix(i,j) = distance;
        distMatrix(j,i) = distance;
    end
end

% 初始化种群
popSize = 50;
pop = zeros(popSize,numCities);
for i = 1:popSize
    pop(i,:) = randperm(numCities);
end

% 定义参数
numIterations = 1000;
mutationRate = 0.01;

% 迭代
for iter = 1:numIterations
    % 评估适应度
    fitness = zeros(popSize,1);
    for i = 1:popSize
        route = pop(i,:);
        routeDist = 0;
        for j = 1:numCities-1
            currentCity = route(j);
            nextCity = route(j+1);
            routeDist = routeDist + distMatrix(currentCity,nextCity);
        end
        fitness(i) = 1/routeDist;
    end
    
    % 选择操作
    selectProb = fitness./sum(fitness);
    selectIndex = roulletteWheelSelection(selectProb);
    selectPop = pop(selectIndex,:);
    
    % 交叉操作
    crossIndex = randperm(popSize,2);
    crossRoute1 = selectPop(crossIndex(1),:);
    crossRoute2 = selectPop(crossIndex(2),:);
    crossPoint1 = randi(numCities);
    crossPoint2 = randi(numCities);
    if crossPoint1 > crossPoint2
        temp = crossPoint1;
        crossPoint1 = crossPoint2;
        crossPoint2 = temp;
    end
    childRoute = crossRoute1;
    for j = crossPoint1:crossPoint2
        city = crossRoute2(j);
        if ~ismember(city,childRoute)
            index = find(childRoute==crossRoute1(j));
            childRoute(index) = city;
        end
    end
    
    % 变异操作
    mutIndex = randi(popSize);
    mutRoute = pop(mutIndex,:);
    for j = 1:numCities
        if rand() < mutationRate
            swapIndex = randi(numCities);
            temp = mutRoute(j);
            mutRoute(j) = mutRoute(swapIndex);
            mutRoute(swapIndex) = temp;
        end
    end
    
    % 更新种群
    pop = [pop;childRoute;mutRoute];
    fitness = zeros(popSize*3,1);
    for i = 1:popSize*3
        route = pop(i,:);
        routeDist = 0;
        for j = 1:numCities-1
            currentCity = route(j);
            nextCity = route(j+1);
            routeDist = routeDist + distMatrix(currentCity,nextCity);
        end
        fitness(i) = 1/routeDist;
    end
    [~,sortIndex] = sort(fitness,'descend');
    pop = pop(sortIndex(1:popSize),:);
end

% 显示最佳路线
bestRoute = pop(1,:);
figure;
plot(cityLocations(1,bestRoute),cityLocations(2,bestRoute),'-o','MarkerSize',10);
title(sprintf('Shortest path length: %f',1/fitness(1)));

在这个示例代码中，我们使用了轮盘赌选择算法、单点交叉和随机交换变异。你可以根据需要调整参数和算法操作以获得更好的结果。