蚁群算法的matlab程序
时间: 2023-08-04 19:28:10 浏览: 40
以下是一个简单的蚁群算法的MATLAB程序:
```matlab
% 蚁群算法应用于TSP问题
% 声明城市坐标
Cities = [0.4000 0.4439;
0.2439 0.1463;
0.1707 0.2293;
0.2293 0.7610;
0.5171 0.9414;
0.8732 0.6536;
0.6878 0.5219;
0.8488 0.3609;
0.6683 0.2536;
0.6195 0.2634];
% 设置参数
nAnts = 10; % 蚂蚁数量
nCities = size(Cities, 1); % 城市数量
alpha = 1; % 启发式因子
beta = 5; % 期望因子
rho = 0.1; % 信息素挥发率
Q = 1; % 信息素常数
tau = ones(nCities, nCities); % 初始化信息素矩阵
% 执行搜索
for i = 1:1000
% 初始化路径和距离
Path = zeros(nAnts, nCities);
Distance = zeros(nAnts, 1);
% 每个蚂蚁选择路径
for j = 1:nAnts
% 选择起点
startCity = randi(nCities);
Path(j, 1) = startCity;
% 选择其余城市
for k = 2:nCities
currentCity = Path(j, k-1);
unvisitedCities = setdiff(1:nCities, Path(j, 1:k-1));
prob = zeros(1, length(unvisitedCities));
for l = 1:length(unvisitedCities)
nextCity = unvisitedCities(l);
prob(l) = tau(currentCity, nextCity)^alpha * (1/norm(Cities(currentCity,:) - Cities(nextCity,:)))^beta;
end
prob = prob / sum(prob);
nextCityIndex = randsrc(1, 1, [1:length(unvisitedCities); prob]);
nextCity = unvisitedCities(nextCityIndex);
Path(j, k) = nextCity;
end
% 计算距离
for k = 1:nCities-1
Distance(j) = Distance(j) + norm(Cities(Path(j,k),:) - Cities(Path(j,k+1),:));
end
Distance(j) = Distance(j) + norm(Cities(Path(j,nCities),:) - Cities(Path(j,1),:));
end
% 更新信息素
DeltaTau = zeros(nCities, nCities);
for j = 1:nAnts
for k = 1:nCities-1
DeltaTau(Path(j,k), Path(j,k+1)) = DeltaTau(Path(j,k), Path(j,k+1)) + Q/Distance(j);
end
DeltaTau(Path(j,nCities), Path(j,1)) = DeltaTau(Path(j,nCities), Path(j,1)) + Q/Distance(j);
end
tau = (1-rho)*tau + DeltaTau;
end
% 绘制结果
figure;
bestPath = Path(1,:);
bestDistance = Distance(1);
for i = 2:nAnts
if Distance(i) < bestDistance
bestPath = Path(i,:);
bestDistance = Distance(i);
end
end
bestPath = [bestPath bestPath(1)];
plot(Cities(:,1), Cities(:,2), 'ro', 'MarkerSize', 10, 'LineWidth', 2);
hold on;
plot(Cities(bestPath,1), Cities(bestPath,2), 'b-', 'LineWidth', 2);
title(sprintf('最佳路径长度:%.4f', bestDistance));
```
该程序使用蚁群算法解决TSP问题,其中包括城市坐标、参数设置、路径选择、距离计算和信息素更新等步骤。程序最终绘制了最佳路径和长度。