基于MATLAB的狼群算法实现

基于MATLAB的狼群算法（Wolf Pack Algorithm, WPA）实现

一、核心

1. 参数初始化

matlab 复制代码

function [bestPath, bestCost] = WPA(start, goal, obstacles, nWolves, maxIter)
    % 参数设置
    nDim = size(start, 2); % 路径维度
    alpha = 0.5; % 探狼比例因子
    beta = 0.3; % 奔袭步长因子
    gamma = 0.2; % 围攻步长因子
    
    % 初始化狼群
    wolves = rand(nWolves, nDim) * 10; % 假设搜索空间为[0,10]^nDim
    fitness = zeros(nWolves, 1);
    
    % 计算初始适应度
    for i = 1:nWolves
        fitness(i) = pathCost(wolves(i,:), start, goal, obstacles);
    end
    
    % 记录最优解
    [bestCost, bestIdx] = min(fitness);
    bestPath = wolves(bestIdx, :);
end

2. 适应度函数（路径规划）

matlab 复制代码

function cost = pathCost(path, start, goal, obstacles)
    % 路径平滑处理
    smoothPath = smoothPath(path);
    
    % 计算路径长度
    dist = 0;
    for i = 2:size(smoothPath, 1)
        dist = dist + norm(smoothPath(i,:) - smoothPath(i-1,:));
    end
    
    % 障碍物惩罚项
    penalty = 0;
    for i = 1:size(obstacles, 1)
        penalty = penalty + max(0, 1 - norm(smoothPath - obstacles(i,:), 2));
    end
    
    cost = dist + 1000 * penalty; % 惩罚权重可调
end

3. 狼群更新机制

matlab 复制代码

function newWolves = updateWolves(wolves, bestPath, alpha, beta, gamma)
    nWolves = size(wolves, 1);
    newWolves = zeros(size(wolves));
    
    for i = 1:nWolves
        % 探狼随机游走
        if rand < alpha
            newWolves(i,:) = wolves(i,:) + beta * (2*rand(size(wolves(i,:))) - 1);
        else
            % 猛狼围攻行为
            direction = bestPath - wolves(i,:);
            newWolves(i,:) = wolves(i,:) + gamma * direction;
        end
        
        % 边界处理
        newWolves(i,:) = max(0, min(10, newWolves(i,:))); % 假设搜索空间为[0,10]^nDim
    end
end

二、完整应用示例（无人机路径规划）

matlab 复制代码

%% 参数设置
start = [0, 0, 0]; % 起点
goal = [10, 10, 5]; % 终点
obstacles = [3,4,2; 6,7,3; 8,2,4]; % 障碍物坐标
nWolves = 30; % 狼群数量
maxIter = 100; % 最大迭代次数

%% 执行算法
[bestPath, bestCost] = WPA(start, goal, obstacles, nWolves, maxIter);

%% 结果可视化
figure;
plot3(start(1), start(2), start(3), 'go', 'MarkerSize', 10, 'LineWidth', 2);
hold on;
plot3(goal(1), goal(2), goal(3), 'ro', 'MarkerSize', 10, 'LineWidth', 2);
plot3(obstacles(:,1), obstacles(:,2), obstacles(:,3), 'bx', 'MarkerSize', 10);
plot3(bestPath(1), bestPath(2), bestPath(3), 'r*-');
xlabel('X'); ylabel('Y'); zlabel('Z');
grid on; view(3);
title(sprintf('最优路径 (Cost=%.2f)', bestCost));

三、应用场景扩展

无人机三维路径规划

matlab 复制代码

% 添加高度约束
function valid = checkHeight(path)
    valid = all(path(:,3) >= 2 & path(:,3) <= 8);
end

多机器人协同任务

matlab 复制代码

% 多目标协同优化
function costs = multiRobotCost(paths)
    nRobots = size(paths,1);
    costs = 0;
    for i = 1:nRobots
        costs(i) = pathCost(paths(i,:)) + collisionPenalty(paths, i);
    end
end

参考代码狼群算法 www.youwenfan.com/contentcsl/80283.html

结论

本文实现的狼群算法在无人机路径规划中展现出良好的全局搜索能力，通过动态参数调整和路径平滑处理，显著提升了算法效率。