蚁群算法matlab代码

蚁群算法是一种模拟蚂蚁觅食行为的优化算法，常用于解决组合优化问题。

matlab
function [bestTour, minDistance] = antColonyOptimization(distanceMatrix, numAnts, numIterations, alpha, beta, rho)

    numCities = size(distanceMatrix, 1);
    
    % 初始化信息素矩阵
    pheromoneMatrix = ones(numCities, numCities);
    
    % 迭代优化
    for iter = 1:numIterations
        % 生成蚂蚁路径
        antTours = generateAntTours(numAnts, pheromoneMatrix, distanceMatrix, alpha, beta);
        
        % 更新信息素
        pheromoneMatrix = updatePheromones(pheromoneMatrix, antTours, distanceMatrix, rho);
        
        % 找到最短路径
        [minDistance, bestTourIndex] = min(computeTourLength(antTours, distanceMatrix));
        bestTour = antTours{bestTourIndex};
        
        % 显示每次迭代的结果
        fprintf('Iteration %d: Best Tour Length = %f\n', iter, minDistance);
    end
end

function antTours = generateAntTours(numAnts, pheromoneMatrix, distanceMatrix, alpha, beta)
    numCities = size(distanceMatrix, 1);
    antTours = cell(1, numAnts);
    
    for ant = 1:numAnts
        % 初始化蚂蚁的位置
        currentCity = randi(numCities);
        antTour = zeros(1, numCities);
        antTour(1) = currentCity;
        
        % 生成蚂蚁路径
        for step = 2:numCities
            probabilities = computeProbabilities(currentCity, antTour, pheromoneMatrix, distanceMatrix, alpha, beta);
            nextCity = selectNextCity(probabilities);
            antTour(step) = nextCity;
            currentCity = nextCity;
        end
        
        antTours{ant} = antTour;
    end
end

function probabilities = computeProbabilities(currentCity, antTour, pheromoneMatrix, distanceMatrix, alpha, beta)
    numCities = length(antTour);
    probabilities = zeros(1, numCities);
    visitedCities = antTour(antTour > 0);
    
    % 计算转移概率
    for i = 1:numCities
        if ~ismember(i, visitedCities)
            pheromone = pheromoneMatrix(currentCity, i);
            distance = distanceMatrix(currentCity, i);
            probabilities(i) = pheromone^alpha * (1/distance)^beta;
        end
    end
    
    % 归一化概率
    probabilities = probabilities / sum(probabilities);
end

function nextCity = selectNextCity(probabilities)
    cumulativeProbabilities = cumsum(probabilities);
    randomValue = rand();
    nextCity = find(cumulativeProbabilities >= randomValue, 1);
end

function pheromoneMatrix = updatePheromones(pheromoneMatrix, antTours, distanceMatrix, rho)
    numAnts = length(antTours);
    pheromoneDelta = zeros(size(pheromoneMatrix));
    
    % 计算每只蚂蚁留下的信息素
    for ant = 1:numAnts
        tour = antTours{ant};
        tourLength = computeTourLength({tour}, distanceMatrix);
        for i = 1:length(tour)-1
            pheromoneDelta(tour(i), tour(i+1)) = pheromoneDelta(tour(i), tour(i+1)) + 1 / tourLength;
            pheromoneDelta(tour(i+1), tour(i)) = pheromoneDelta(tour(i+1), tour(i)) + 1 / tourLength;
        end
    end
    
    % 更新信息素矩阵
    pheromoneMatrix = (1 - rho) * pheromoneMatrix + pheromoneDelta;
end

function tourLength = computeTourLength(antTours, distanceMatrix)
    numAnts = length(antTours);
    tourLength = zeros(1, numAnts);
    
    for ant = 1:numAnts
        tour = antTours{ant};
        for i = 1:length(tour)-1
            tourLength(ant) = tourLength(ant) + distanceMatrix(tour(i), tour(i+1));
        end
    end
end

matlab
% 示例：解决旅行商问题

% 随机生成城市坐标
numCities = 10;
cities = rand(numCities, 2);

% 计算城市之间的距离矩阵
distanceMatrix = pdist2(cities, cities);

% 设置算法参数
numAnts = 5;
numIterations = 50;
alpha = 1;
beta = 2;
rho = 0.5;

% 调用蚁群算法
[bestTour, minDistance] = antColonyOptimization(distanceMatrix, numAnts, numIterations, alpha, beta, rho);

% 显示结果
fprintf('Best Tour: %s\n', num2str(bestTour));
fprintf('Minimum Distance: %f\n', minDistance);

% 绘制最佳路径
figure;
plot(cities(:, 1), cities(:, 2), 'o', 'MarkerSize', 10, 'MarkerFaceColor', 'b');
hold on;
plot(cities(bestTour, 1), cities(bestTour, 2), 'r', 'LineWidth', 2);
title('Best Tour');
xlabel('X-coordinate');
ylabel('Y-coordinate');
legend('Cities', 'Best Tour');
hold off;

这个示例假设存在一个包含城市坐标的cities矩阵，并且使用pdist2函数计算城市之间的距离矩阵。算法的参数在调用时进行了设置，您可以根据问题的需要进行调整。

这个代码示例是为了演示蚁群算法的基本原理，实际应用中可能需要根据具体问题进行更多的调整和优化。