模拟退火蚁群算法在最优路径选择中的应用matlab代码

以下是利用MATLAB实现模拟退火蚁群算法求解TSP问题的示例代码：

% TSP问题的城市坐标数据
city = [0.5719, 0.7722;
        0.4453, 0.7943;
        0.2905, 0.6335;
        0.3283, 0.3724;
        0.7572, 0.6957;
        0.7537, 0.4387;
        0.3804, 0.4898;
        0.5678, 0.5785;
        0.0759, 0.5497;
        0.0540, 0.8909];

% 计算城市之间的距离矩阵
dist = pdist(city);
distMat = squareform(dist);

% 初始化信息素
pheromone = ones(size(distMat)) / 10;

% 初始化参数
antNum = 30; % 蚂蚁数量
alpha = 1; % 信息素的重要程度
beta = 2; % 启发式信息的重要程度
rho = 0.5; % 信息素挥发率
T0 = 300; % 初始温度
Tf = 0.1; % 终止温度
coolingRate = 0.99; % 温度下降速度
maxIter = 500; % 最大迭代次数

% 初始化最优路径和路径长度
bestPath = [];
bestDist = Inf;

% 开始迭代
T = T0;
for iter = 1 : maxIter
    % 初始化每只蚂蚁的位置
    antPos = repmat(1 : size(city, 1), antNum, 1);
    
    % 模拟蚂蚁搜索路径
    for i = 2 : size(city, 1)
        % 计算每只蚂蚁的下一个城市
        for j = 1 : antNum
            visited = antPos(j, 1 : i - 1);
            unvisited = setdiff(1 : size(city, 1), visited);
            heuristic = 1 ./ distMat(visited, unvisited);
            pheromoneTrail = pheromone(visited, unvisited);
            prob = (pheromoneTrail .^ alpha) .* (heuristic .^ beta);
            prob = prob ./ sum(prob);
            nextCity = randsample(unvisited, 1, true, prob);
            antPos(j, i) = nextCity;
        end
    end
    
    % 计算每只蚂蚁的路径长度
    antDist = zeros(antNum, 1);
    for i = 1 : antNum
        antDist(i) = sum(distMat(sub2ind(size(distMat), antPos(i, 1 : end - 1), antPos(i, 2 : end)))));
    end
    
    % 更新最优路径和路径长度
    [minDist, minIdx] = min(antDist);
    if minDist < bestDist
        bestDist = minDist;
        bestPath = antPos(minIdx, :);
    end
    
    % 更新信息素
    deltaPheromone = zeros(size(distMat));
    for i = 1 : antNum
        for j = 1 : size(city, 1) - 1
            idx1 = antPos(i, j);
            idx2 = antPos(i, j + 1);
            deltaPheromone(idx1, idx2) = deltaPheromone(idx1, idx2) + 1 / antDist(i);
            deltaPheromone(idx2, idx1) = deltaPheromone(idx1, idx2);
        end
    end
    pheromone = (1 - rho) * pheromone + deltaPheromone;
    
    % 退火过程
    while T > Tf
        % 产生新解
        newAntPos = antPos;
        for i = 1 : antNum
            idx1 = randi(size(city, 1));
            idx2 = randi(size(city, 1));
            while idx1 == idx2
                idx2 = randi(size(city, 1));
            end
            newAntPos(i, [idx1, idx2]) = newAntPos(i, [idx2, idx1]);
        end
        
        % 计算新解的路径长度
        newAntDist = zeros(antNum, 1);
        for i = 1 : antNum
            newAntDist(i) = sum(distMat(sub2ind(size(distMat), newAntPos(i, 1 : end - 1), newAntPos(i, 2 : end)))));
        end
        
        % 计算能量差
        deltaE = newAntDist - antDist;
        
        % 判断是否接受新解
        for i = 1 : antNum
            if deltaE(i) < 0 % 新解更优
                antPos(i, :) = newAntPos(i, :);
                antDist(i) = newAntDist(i);
            else % 接受劣解的概率
                if rand < exp(-deltaE(i) / T)
                    antPos(i, :) = newAntPos(i, :);
                    antDist(i) = newAntDist(i);
                end
            end
        end
        
        % 更新最优路径和路径长度
        [minDist, minIdx] = min(antDist);
        if minDist < bestDist
            bestDist = minDist;
            bestPath = antPos(minIdx, :);
        end
        
        % 降温
        T = T * coolingRate;
    end
end

% 输出结果
disp(['最短路径长度：', num2str(bestDist)]);
disp(['最短路径：', num2str(bestPath)]);

需要注意的是，这只是一个简单的示例代码，实际应用中需要对算法进行优化和改进，以达到更好的效果。