写一个用自适应变异粒子群法求解关于四维变量X的函数的最小值 MATLAB

MATLAB 中可以使用自适应变异粒子群法求解 X 的函数的最小值，可以利用函数 pso 来实现，例如：[x, fval] = pso(@(x)myfun(x),nvars,[-5 15],[-5 15]），其中 myfun 是求解的目标函数，nvars 是 X 的维数，[-5 15] 是 X 的最小值和最大值。

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写一个用自适应变异粒子群法求解关于四维变量X的函数的最小值的代码 MATLAB

以下是使用 MATLAB 编写的自适应变异粒子群算法求解四维变量函数最小值的代码：

function [xmin, fmin] = AdaptiveMutationPSO()
% 优化函数
objFunc = @(x) (x(1)^2 + x(2)^2 + x(3)^2 + x(4)^2);

% 参数设置
maxIter = 100;           % 最大迭代次数
popSize = 30;            % 粒子群规模
wMax = 0.9;              % 惯性权重上界
wMin = 0.4;              % 惯性权重下界
c1 = 2;                  % 自我学习因子
c2 = 2;                  % 社会学习因子
mu = 0.05;               % 变异率
sigmaMax = 0.2;          % 变异范围上界
sigmaMin = 0.001;        % 变异范围下界
k = 10;                  % 突变邻域大小

% 初始化粒子群
pop = rand(popSize, 4);   % 初始位置随机生成
vel = zeros(popSize, 4);  % 初始速度为零

% 计算初始适应度
fit = zeros(popSize, 1);
for i = 1:popSize
    fit(i) = objFunc(pop(i,:));
end

% 初始化个体最优位置和适应度
pBest = pop;
pBestFit = fit;

% 初始化全局最优位置和适应度
[gBestFit, gBestIndex] = min(fit);
gBest = pop(gBestIndex,:);

% 迭代
for iter = 1:maxIter
    % 更新惯性权重
    w = wMax - (wMax - wMin) * iter / maxIter;
    
    % 粒子位置更新
    vel = w .* vel + c1 .* rand(popSize, 4) .* (pBest - pop) + ...
          c2 .* rand(popSize, 4) .* (repmat(gBest, popSize, 1) - pop);
    pop = pop + vel;
    
    % 限制粒子位置范围
    for i = 1:popSize
        for j = 1:4
            if pop(i,j) < -10
                pop(i,j) = -10;
                vel(i,j) = 0;
            elseif pop(i,j) > 10
                pop(i,j) = 10;
                vel(i,j) = 0;
            end
        end
    end
    
    % 计算适应度
    for i = 1:popSize
        fit(i) = objFunc(pop(i,:));
    end
    
    % 更新个体最优位置和适应度
    for i = 1:popSize
        if fit(i) < pBestFit(i)
            pBest(i,:) = pop(i,:);
            pBestFit(i) = fit(i);
        end
    end
    
    % 更新全局最优位置和适应度
    [tempFit, tempIndex] = min(fit);
    if tempFit < gBestFit
        gBestFit = tempFit;
        gBestIndex = temp

写一个用自适应变异粒子群法求解关于四维变量X的函数的最小值的代码 MATLAB...

好的，以下是一个简单的用自适应变异粒子群算法（AMPSO）求解关于四维变量 X 的函数的最小值的 MATLAB 代码：

function [best_value, best_position] = AMPSO(fitness_func, dim, lower_bound, upper_bound, max_iter)

% Set parameters
particle_size = 30;
w_min = 0.4;
w_max = 0.9;
c1 = 2;
c2 = 2;
r1 = rand();
r2 = rand();
max_no_improve = 10;
mutate_rate = 0.1;

% Initialize particles
particle_position = rand(particle_size, dim) .* (upper_bound - lower_bound) + lower_bound;
particle_velocity = rand(particle_size, dim) .* (upper_bound - lower_bound) * 0.05;
particle_fitness = zeros(particle_size, 1);
particle_best_position = particle_position;
particle_best_fitness = Inf(particle_size, 1);
global_best_fitness = Inf;
global_best_position = zeros(1, dim);
no_improve = 0;

% Evaluate fitness
for i = 1:particle_size
    particle_fitness(i) = fitness_func(particle_position(i, :));
    if particle_fitness(i) < particle_best_fitness(i)
        particle_best_fitness(i) = particle_fitness(i);
        particle_best_position(i, :) = particle_position(i, :);
    end
    if particle_fitness(i) < global_best_fitness
        global_best_fitness = particle_fitness(i);
        global_best_position = particle_position(i, :);
    end
end

% Main loop
for iter = 1:max_iter
    % Update velocity and position
    w = w_max - (w_max - w_min) * iter / max_iter;
    for i = 1:particle_size
        r1 = rand();
        r2 = rand();
        if rand() < mutate_rate
            particle_velocity(i, :) = rand(1, dim) .* (upper_bound - lower_bound) * 0.1;
        else
            particle_velocity(i, :) = w * particle_velocity(i, :) + c1 * r1 * (particle_best_position(i, :) - particle_position(i, :)) + c2 * r2 * (global_best_position - particle_position(i, :));
        end
        particle_position(i, :) = particle_position(i, :) + particle_velocity(i, :);
        particle_position(i, :) = max(particle_position(i, :), lower_bound);
        particle_position(i, :) = min(particle_position(i, :), upper_bound);
    end
    
    % Evaluate fitness
    for i = 1:particle_size
        particle_fitness(i) = fitness_func(particle_position(i, :));
        if particle_fitness(i) < particle_best_fitness(i)
            particle_best_fitness(i) = particle_fitness(i);
            particle_best_position(i, :) = particle_position(i, :);
        end
        if particle_fitness(i) < global_best_fitness
            global_best_fitness = particle_fitness(i);
            global_best_position = particle_position(i, :);
            no_improve = 0;
        else
            no_improve = no_improve + 1;
        end
    end
    
    % Check for stagnation
    if no_improve >= max_no_improve
        % Mutate particles
        for i = 1:particle_size
            particle_position(i, :) = rand(1, dim) .* (upper_bound - lower_bound) + lower_bound;
            particle_velocity(i, :) = rand(1, dim) .* (upper_bound - lower_bound) * 0.05;
            particle_fitness(i) = fitness_func(particle_position(i, :));
            if particle_fitness(i) < particle_best_fitness(i)
                particle_best_fitness(i) = particle_fitness(i);
                particle_best_position(i, :) = particle_position(i, :);
            end
            if particle_fitness(i) < global_best_fitness
                global_best_fitness = particle_fitness(i);
                global_best_position = particle_position(i, :);
            end
        end
        no_improve = 0;
    end
    
    % Display progress
    fprintf('Iteration %d: Best fitness value = %f\n', iter, global_best_fitness);
end

% Return best value and position
best_value = global_best_fitness;
best_position = global_best_position;
end

其中，参数 `fitness_func` 是要求解的函数，参数 `dim` 是变量 X 的维度，`lower_bound` 和 `upper_bound` 是 X 各维度的下界和上界，`max_iter` 是迭代次数。函数返回最小值和最小值对应的 X。

请注意，这只是一个简单的实现，可能需要根据具体问题进行调整。