使用遗传算法求解最大化函数f(x)=x+10sin(5x)+7cos(4x)的x，其中x ∈ [ 0 , 10 ]，用matlab进行编写

以下是使用遗传算法求解最大化函数f(x)=x+10sin(5x)+7cos(4x)的x，其中x ∈ [ 0 , 10 ] 的 Matlab 代码实现：

% 定义问题
function y = f(x)
    y = x + 10*sin(5*x) + 7*cos(4*x);
end

% 定义遗传算法参数
pop_size = 50; % 种群大小
chrom_length = 22; % 染色体长度
pc = 0.6; % 交叉概率
pm = 0.01; % 变异概率
max_iter = 100; % 最大迭代次数

% 初始化种群
function pop = init_pop()
    pop = repmat('0', pop_size, chrom_length);
    for i = 1:pop_size
        for j = 1:chrom_length
            if rand < 0.5
                pop(i,j) = '0';
            else
                pop(i,j) = '1';
            end
        end
    end
end

% 适应度函数计算
function fit = fitness(chrom)
    x = bin2dec(chrom) / (2^chrom_length-1) * 10;
    fit = f(x);
end

% 轮盘赌选择算子
function chrom = select(pop, fitness_sum)
    rand_num = rand * fitness_sum;
    for i = 1:pop_size
        rand_num = rand_num - fitness(pop(i,:));
        if rand_num <= 0
            chrom = pop(i,:);
            break;
        end
    end
end

% 单点交叉算子
function [child1, child2] = crossover(parent1, parent2)
    pos = randi(chrom_length-1);
    child1 = [parent1(1:pos), parent2(pos+1:end)];
    child2 = [parent2(1:pos), parent1(pos+1:end)];
end

% 随机变异算子
function chrom = mutation(chrom)
    pos = randi(chrom_length);
    if chrom(pos) == '0'
        chrom(pos) = '1';
    else
        chrom(pos) = '0';
    end
end

% 遗传算法求解最大化函数f(x)
function [best_x, best_f] = GA()
    pop = init_pop();
    for i = 1:max_iter
        % 计算适应度函数值
        fitness_list = zeros(pop_size, 1);
        for j = 1:pop_size
            fitness_list(j) = fitness(pop(j,:));
        end
        fitness_sum = sum(fitness_list);
        % 选择操作
        new_pop = repmat('0', pop_size*2, chrom_length);
        for j = 1:pop_size
            parent1 = select(pop, fitness_sum);
            parent2 = select(pop, fitness_sum);
            % 交叉操作
            if rand < pc
                [child1, child2] = crossover(parent1, parent2);
            else
                child1 = parent1;
                child2 = parent2;
            end
            % 变异操作
            if rand < pm
                child1 = mutation(child1);
            end
            if rand < pm
                child2 = mutation(child2);
            end
            new_pop((j-1)*2+1,:) = child1;
            new_pop((j-1)*2+2,:) = child2;
        end
        pop = new_pop;
    end
    % 选择最优解
    best_f = -inf;
    for i = 1:pop_size*2
        x = bin2dec(pop(i,:)) / (2^chrom_length-1) * 10;
        f_val = f(x);
        if f_val > best_f
            best_x = x;
            best_f = f_val;
        end
    end
end

% 调用遗传算法求解
[best_x, best_f] = GA();
fprintf('最优解：x=%.5f，f(x)=%.5f\n', best_x, best_f);

在 Matlab 中运行上述代码，即可得到最优解 x 和对应的最大化函数值 f(x)。