遗传算法求函数极值matlab

以下是使用遗传算法求解函数极值的Matlab代码示例：

% 定义适应度函数
function f = fitness(x)
    f = -x^2 + 2*x + 1;
end

% 定义遗传法参数
popsize = 50; % 种群大小
maxgen = 100; % 最大迭代次数
Pcrossover = 0.8; % 交叉概率
Pmutation = 0.1; % 变异概率
x_min = -10; % 自变量x的最小值
x_max = 10; % 自变量x的最大值

% 初始化种群
pop = zeros(popsize, 2);
for i = 1:popsize
    pop(i, 1) = x_min + (x_max - x_min) * rand;
    pop(i, 2) = fitness(pop(i, 1));
end

% 迭代
for gen = 1:maxgen
    % 选择
    [parent1, parent2] = selection(pop);
    % 交叉
    [child1, child2] = crossover(parent1, parent2, Pcrossover, x_min, x_max);
    % 变异
    child1 = mutation(child1, Pmutation, x_min, x_max);
    child2 = mutation(child2, Pmutation, x_min, x_max);
    % 计算适应度
    child1(2) = fitness(child1(1));
    child2(2) = fitness(child2(1));
    % 替换
    pop = replacement(pop, child1, child2);
end

% 输出最优解
[~, idx] = max(pop(:, 2));
x_opt = pop(idx, 1);
f_opt = pop(idx, 2);
fprintf('最优解：x = %f, f(x) = %f\n', x_opt, f_opt);