matlab代码实现蚁群算法

以下是一个简单的蚁群算法的 MATLAB 代码实现：

function [best_path, best_cost] = ant_colony_tsp(distance_matrix, num_ants, num_iterations, evaporation_rate, alpha, beta, initial_pheromone)

% distance_matrix: 距离矩阵，表示城市之间的距离
% num_ants: 蚂蚁数量
% num_iterations: 迭代次数
% evaporation_rate: 信息素挥发率
% alpha: 信息素重要程度系数
% beta: 启发式因子重要程度系数
% initial_pheromone: 初始信息素浓度

% 计算城市数量
num_cities = size(distance_matrix, 1);

% 初始化信息素矩阵
pheromone_matrix = initial_pheromone * ones(num_cities, num_cities);

% 初始化最佳路径和最佳成本
best_path = [];
best_cost = Inf;

% 迭代
for i = 1:num_iterations
    
    % 初始化蚂蚁位置和已访问城市
    ants = zeros(num_ants, num_cities);
    visited = zeros(num_ants, num_cities);
    
    % 随机初始化蚂蚁位置
    for j = 1:num_ants
        current_city = randi(num_cities);
        ants(j, 1) = current_city;
        visited(j, current_city) = 1;
    end
    
    % 计算每只蚂蚁的路径
    for j = 1:num_cities-1
        for k = 1:num_ants
            
            % 计算可选城市集合
            unvisited_cities = find(visited(k,:) == 0);
            
            % 计算每个城市的概率
            probabilities = zeros(1, length(unvisited_cities));
            for l = 1:length(unvisited_cities)
                city = unvisited_cities(l);
                pheromone = pheromone_matrix(ants(k,j), city);
                distance = distance_matrix(ants(k,j), city);
                probabilities(l) = (pheromone^alpha) * ((1/distance)^beta);
            end
            probabilities = probabilities / sum(probabilities);
            
            % 选择下一个城市
            next_city_index = roulette_wheel_selection(probabilities);
            next_city = unvisited_cities(next_city_index);
            ants(k, j+1) = next_city;
            visited(k, next_city) = 1;
        end
    end
    
    % 计算每只蚂蚁的成本和最佳路径
    costs = zeros(num_ants, 1);
    for j = 1:num_ants
        path = ants(j,:);
        cost = 0;
        for k = 1:num_cities-1
            cost = cost + distance_matrix(path(k), path(k+1));
        end
        cost = cost + distance_matrix(path(num_cities), path(1));
        costs(j) = cost;
        if cost < best_cost
            best_path = path;
            best_cost = cost;
        end
    end
    
    % 更新信息素
    pheromone_matrix = (1 - evaporation_rate) * pheromone_matrix;
    for j = 1:num_ants
        path = ants(j,:);
        for k = 1:num_cities-1
            pheromone_matrix(path(k), path(k+1)) = pheromone_matrix(path(k), path(k+1)) + (1/costs(j));
        end
        pheromone_matrix(path(num_cities), path(1)) = pheromone_matrix(path(num_cities), path(1)) + (1/costs(j));
    end
    
end

end

function selected_index = roulette_wheel_selection(probabilities)

% probabilities: 每个城市的概率

cumulative_probabilities = cumsum(probabilities);
random_number = rand;
for i = 1:length(cumulative_probabilities)
    if random_number <= cumulative_probabilities(i)
        selected_index = i;
        break;
    end
end

end

这是一个基本的蚁群算法实现，你可以根据自己的需求进行修改和扩展。