MATLAB的蚁群算法代码

以下是一个基于MATLAB的蚁群算法的简单实现：

clc;
clear;
close all;

% 参数设定
alpha = 1; % 信息素重要程度因子
beta = 5; % 启发函数重要程度因子
rho = 0.5; % 信息素挥发因子
Q = 100; % 常数
num_ant = 50; % 蚂蚁数量
num_city = 20; % 城市数量
num_iter = 500; % 迭代次数

% 初始化信息素矩阵和距离矩阵
pheromone = ones(num_city, num_city);
distance = randi([1,10],num_city,num_city);
distance = triu(distance,1)+triu(distance,1)';

% 初始化最优路径
best_path = zeros(num_iter,num_city);
best_distance = inf;

% 主循环
for iter = 1:num_iter
    path = zeros(num_ant,num_city);
    distance_ant = zeros(num_ant,1);
    for ant = 1:num_ant
        current_city = randi(num_city);
        visited = zeros(1,num_city);
        visited(current_city) = 1;
        path(ant,1) = current_city;
        for city = 2:num_city
            prob = zeros(1,num_city);
            for next = 1:num_city
                if visited(next) == 0
                    prob(next) = pheromone(current_city,next)^alpha * (1/distance(current_city,next))^beta;
                end
            end
            prob = prob / sum(prob);
            cumprob = cumsum(prob);
            r = rand;
            next_city = find(cumprob>=r,1);
            visited(next_city) = 1;
            path(ant,city) = next_city;
            distance_ant(ant) = distance_ant(ant) + distance(current_city,next_city);
            current_city = next_city;
        end
        distance_ant(ant) = distance_ant(ant) + distance(path(ant,num_city),path(ant,1));
    end
    
    % 更新信息素矩阵
    delta_pheromone = zeros(num_city,num_city);
    for ant = 1:num_ant
        for city = 1:num_city-1
            delta_pheromone(path(ant,city),path(ant,city+1)) = delta_pheromone(path(ant,city),path(ant,city+1)) + Q/distance_ant(ant);
        end
        delta_pheromone(path(ant,num_city),path(ant,1)) = delta_pheromone(path(ant,num_city),path(ant,1)) + Q/distance_ant(ant);
    end
    pheromone = (1-rho)*pheromone + delta_pheromone;
    
    % 更新最优路径
    [min_distance,min_index] = min(distance_ant);
    if min_distance < best_distance
        best_distance = min_distance;
        best_path(iter,:) = path(min_index,:);
    else
        best_path(iter,:) = best_path(iter-1,:);
    end
    
    % 输出结果
    disp(['Iteration: ',num2str(iter),'  Distance: ',num2str(best_distance)]);
end

% 绘制最优路径
figure;
for i = 1:num_city-1
    plot([best_path(end,i),best_path(end,i+1)],[0,1],'r','LineWidth',2);
    hold on;
end
plot([best_path(end,num_city),best_path(end,1)],[0,1],'r','LineWidth',2);
axis off;
title(['Best Distance: ',num2str(best_distance)]);

该代码实现了基本的蚁群算法，其中包括初始化信息素和距离矩阵、初始化最优路径、主循环、更新信息素矩阵和最优路径等步骤。您可以根据需要进行修改和优化。