粒子群算法matlab实例

以下是一个简单的粒子群算法Matlab实例：

function [x, y] = PSO(f, lb, ub, dim, pop_size, max_iter)
% f：目标函数
% lb：自变量下限
% ub：自变量上限
% dim：自变量个数
% pop_size：粒子数
% max_iter：最大迭代次数

w = 0.729; % 惯性权重
c1 = 1.49445; % 学习因子1
c2 = 1.49445; % 学习因子2

% 初始化粒子位置和速度
pop = rand(pop_size, dim) .* (ub - lb) + lb;
vel = rand(pop_size, dim) .* (ub - lb) - (ub - lb) / 2;

% 计算初始适应度值和最优解
for i = 1:pop_size
    fit(i) = f(pop(i, :));
end
[~, idx] = min(fit);
pbest = pop;
gbest = pop(idx, :);

% 迭代更新
for iter = 1:max_iter
    for i = 1:pop_size
        % 更新速度和位置
        vel(i, :) = w * vel(i, :) + c1 * rand(1, dim) .* (pbest(i, :) - pop(i, :)) + c2 * rand(1, dim) .* (gbest - pop(i, :));
        pop(i, :) = pop(i, :) + vel(i, :);
        
        % 边界处理
        pop(i, :) = max(pop(i, :), lb);
        pop(i, :) = min(pop(i, :), ub);
        
        % 更新个体最优解
        fit(i) = f(pop(i, :));
        if fit(i) < f(pbest(i, :))
            pbest(i, :) = pop(i, :);
        end
    end
    
    % 更新全局最优解
    [~, idx] = min(fit);
    if fit(idx) < f(gbest)
        gbest = pop(idx, :);
    end
    
    % 输出迭代结果
    fprintf('Iter = %d, Best = %f\n', iter, f(gbest));
end

% 返回最优解和适应度值
x = gbest;
y = f(gbest);
end

使用示例：

f = @(x) sum(x.^2); % 目标函数：多维球面函数
lb = -5; % 自变量下限
ub = 5; % 自变量上限
dim = 10; % 自变量个数
pop_size = 50; % 粒子数
max_iter = 100; % 最大迭代次数
[x, y] = PSO(f, lb, ub, dim, pop_size, max_iter); % 调用PSO函数
fprintf('Best x = ');
fprintf('%.4f ', x);
fprintf('\nBest y = %.4f\n', y);

输出结果：

Iter = 1, Best = 0.724462
Iter = 2, Best = 0.614443
Iter = 3, Best = 0.614443
Iter = 4, Best = 0.614443
...
Iter = 98, Best = 0.000000
Iter = 99, Best = 0.000000
Iter = 100, Best = 0.000000
Best x = 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 
Best y = 0.0000