蚁群算法求解多目标优化matlab代码

蚁群算法（Ant Colony Optimization，ACO）是一种基于群体智能的优化算法，用于求解多目标优化问题。下面是一个使用MATLAB实现蚁群算法求解多目标优化问题的示例代码：

% 初始化参数
numAnts = 50; % 蚂蚁数量
numIterations = 100; % 迭代次数
alpha = 1; % 信息素重要程度因子
beta = 2; % 启发式信息重要程度因子
rho = 0.5; % 信息素蒸发率
q0 = 0.9; % 选择下一个城市时的探索因子
cityNum = size(distance, 1); % 城市数量

% 初始化信息素矩阵
pheromone = ones(cityNum, cityNum);

for iter = 1:numIterations
    % 初始化蚂蚁位置和已访问城市标记
    ants = zeros(numAnts, cityNum);
    visited = zeros(numAnts, cityNum);
    
    for ant = 1:numAnts
        % 随机选择起始城市
        startCity = randi(cityNum);
        ants(ant, 1) = startCity;
        visited(ant, startCity) = 1;
        
        % 沿着路径选择下一个城市
        for i = 2:cityNum
            currentCity = ants(ant, i-1);
            
            % 计算选择下一个城市的概率
            probabilities = (pheromone(currentCity, :) .^ alpha) .* (1 ./ distance(currentCity, :)) .^ beta;
            probabilities(visited(ant, :) == 1) = 0; % 已访问城市概率置为0
            
            % 根据概率选择下一个城市
            if rand < q0
                [maxProb, nextCity] = max(probabilities);
            else
                probabilities = probabilities / sum(probabilities);
                nextCity = rouletteWheelSelection(probabilities);
            end
            
            ants(ant, i) = nextCity;
            visited(ant, nextCity) = 1;
        end
    end
    
    % 计算每只蚂蚁的路径长度和目标函数值
    pathLengths = zeros(numAnts, 1);
    objectives = zeros(numAnts, 2);
    
    for ant = 1:numAnts
        pathLength = 0;
        
        for i = 2:cityNum
            pathLength = pathLength +