基于MATLAB的狼群算法实现

最新推荐文章于 2025-11-30 19:11:04 发布

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#matlab #算法 #开发语言

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

一、核心

1. 参数初始化

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）

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

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）

%% 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

% 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

% 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