粒子群优化极大似然估计matlab代码

粒子群优化算法（Particle Swarm Optimization，PSO）是一种常用的优化算法，而极大似然估计（Maximum Likelihood Estimation，MLE）则是一种常用的参数估计方法。将这两种方法结合起来，可以用粒子群优化算法来解决MLE问题。

以下是一份基于Matlab的粒子群优化极大似然估计代码，供参考：

% 极大似然估计

% 构造目标函数
fun = @(x) -sum(log(normpdf(x, 0, 1)));

% 粒子群参数设置
nVar = 1; % 变量个数
VarSize = [1 nVar]; % 变量维度
VarMin = -10; % 变量最小值
VarMax = 10; % 变量最大值

% 粒子群算法参数设置
MaxIt = 100; % 最大迭代次数
nPop = 50; % 种群大小
w = 1; % 惯性权重
wdamp = 0.99; % 惯性权重衰减系数
c1 = 2; % 个体学习因子
c2 = 2; % 社会学习因子

% 初始化粒子群
empty_particle.Position = [];
empty_particle.Velocity = [];
empty_particle.Cost = [];
empty_particle.Best.Position = [];
empty_particle.Best.Cost = [];
particle = repmat(empty_particle, nPop, 1);
global_best.Cost = inf;

for i = 1:nPop
    particle(i).Position = unifrnd(VarMin, VarMax, VarSize);
    particle(i).Velocity = zeros(VarSize);
    particle(i).Cost = fun(particle(i).Position);
    
    particle(i).Best.Position = particle(i).Position;
    particle(i).Best.Cost = particle(i).Cost;
    
    if particle(i).Best.Cost < global_best.Cost
        global_best = particle(i).Best;
    end
end

BestCosts = zeros(MaxIt, 1);

% 粒子群优化迭代
for it = 1:MaxIt
    for i = 1:nPop
        particle(i).Velocity = w*particle(i).Velocity ...
            + c1*rand(VarSize).*(particle(i).Best.Position - particle(i).Position) ...
            + c2*rand(VarSize).*(global_best.Position - particle(i).Position);
        particle(i).Position = particle(i).Position + particle(i).Velocity;
        particle(i).Cost = fun(particle(i).Position);
        
        if particle(i).Cost < particle(i).Best.Cost
            particle(i).Best.Position = particle(i).Position;
            particle(i).Best.Cost = particle(i).Cost;
            
            if particle(i).Best.Cost < global_best.Cost
                global_best = particle(i).Best;
            end
        end
    end
    
    BestCosts(it) = global_best.Cost;
    
    w = w*wdamp;
end

% 结果输出
disp(['最优解为： ' num2str(global_best.Position)]);
disp(['最优解对应的目标函数值为： ' num2str(global_best.Cost)]);

% 结果可视化
figure;
plot(BestCosts, 'LineWidth', 2);
xlabel('迭代次数');
ylabel('最优解对应的目标函数值');
grid on;