二元非线性函数的最大值点pso算法MATLAB

以下是一个使用PSO算法找到二元非线性函数最大值点的MATLAB代码示例：

% 二元非线性函数
f = @(x) -((x(1)^2 + x(2)^2)^0.25 * (sin(50*(x(1)^2 + x(2)^2)^0.1)^2 + 1));

% 定义PSO算法参数
nVar = 2; % 变量个数
nPop = 50; % 粒子个数
maxIter = 100; % 迭代次数
w = 1; % 惯性权重
wDamp = 0.99; % 惯性权重阻尼因子
c1 = 2; % 个体加速度系数
c2 = 2; % 全局加速度系数
vMax = 0.2*(10-(-10)); % 粒子速度最大值
vMin = -vMax; % 粒子速度最小值

% 初始化粒子位置和速度
emptyParticle.Position = [];
emptyParticle.Velocity = [];
emptyParticle.Cost = [];
emptyParticle.Best.Position = [];
emptyParticle.Best.Cost = [];

particles = repmat(emptyParticle, nPop, 1);
globalBest.Cost = -inf;

for i = 1:nPop
    particles(i).Position = unifrnd(-10, 10, [1, nVar]);
    particles(i).Velocity = zeros([1, nVar]);
    particles(i).Cost = f(particles(i).Position);
    particles(i).Best.Position = particles(i).Position;
    particles(i).Best.Cost = particles(i).Cost;
    
    if particles(i).Best.Cost > globalBest.Cost
        globalBest = particles(i).Best;
    end
end

% 开始迭代
for iter = 1:maxIter
    for i = 1:nPop
        % 更新粒子速度
        particles(i).Velocity = w*particles(i).Velocity + c1*rand([1, nVar]).*(particles(i).Best.Position - particles(i).Position) + c2*rand([1, nVar]).*(globalBest.Position - particles(i).Position);
        
        % 限制粒子速度范围
        particles(i).Velocity = max(particles(i).Velocity, vMin);
        particles(i).Velocity = min(particles(i).Velocity, vMax);
        
        % 更新粒子位置
        particles(i).Position = particles(i).Position + particles(i).Velocity;
        
        % 限制粒子位置范围
        particles(i).Position = max(particles(i).Position, -10);
        particles(i).Position = min(particles(i).Position, 10);
        
        % 计算粒子成本函数
        particles(i).Cost = f(particles(i).Position);
        
        % 更新个体最优解
        if particles(i).Cost > particles(i).Best.Cost
            particles(i).Best.Position = particles(i).Position;
            particles(i).Best.Cost = particles(i).Cost;
            
            % 更新全局最优解
            if particles(i).Best.Cost > globalBest.Cost
                globalBest = particles(i).Best;
            end
        end
    end
    
    % 输出当前迭代结果
    disp(['Iteration ' num2str(iter) ': Best Cost = ' num2str(-globalBest.Cost)]);
    
    % 更新惯性权重
    w = w*wDamp;
end

% 输出最终结果
disp('Final Result:');
disp(['Best Position = (' num2str(globalBest.Position) ')']);
disp(['Best Cost = ' num2str(-globalBest.Cost)]);