请用matlab写一个差分进化算法代码，满足以下要求：测试函数10个，测试函数维度为10维或30维；得出在给定函数上的平均收敛精度，收敛曲线和统计箱图

好的，请先确保你已经安装了MATLAB。

首先，我们需要定义测试函数。这里我选取了10个函数，包括Schwefel、Rosenbrock、Griewank、Rastrigin、Ackley、Weierstrass、Katsuura、HappyCat、HGBat、and Levy函数。这些函数的维度可以是10或30。下面是测试函数的代码：

% Schwefel function
function y = schwefel(x)
    d = length(x);
    y = 418.9829*d - sum(x.*sin(sqrt(abs(x))));
end

% Rosenbrock function
function y = rosenbrock(x)
    d = length(x);
    y = sum(100*(x(2:d)-x(1:d-1).^2).^2 + (1-x(1:d-1)).^2);
end

% Griewank function
function y = griewank(x)
    d = length(x);
    y = 1 + sum(x.^2)/4000 - prod(cos(x./sqrt(1:d)));
end

% Rastrigin function
function y = rastrigin(x)
    d = length(x);
    y = 10*d + sum(x.^2 - 10*cos(2*pi*x));
end

% Ackley function
function y = ackley(x)
    d = length(x);
    y = -20*exp(-0.2*sqrt(sum(x.^2)/d))-exp(sum(cos(2*pi*x))/d)+20+exp(1);
end

% Weierstrass function
function y = weierstrass(x)
    d = length(x);
    a = 0.5;
    b = 3;
    kmax = 20;
    y = 0;
    for i = 1:d
        for k = 0:kmax
            y = y + (a^k)*cos(2*pi*(b^k)*(x(i)+0.5));
        end
    end
    y = y - d*sum(a.^((0:kmax)*2));
end

% Katsuura function
function y = katsuura(x)
    d = length(x);
    prod_term = 1;
    for i = 1:d
        inner_sum = 0;
        for j = 1:32
            inner_sum = inner_sum + abs(2^j*x(i) - round(2^j*x(i)))/2^j;
        end
        prod_term = prod_term*(1+i*inner_sum)^10/100;
    end
    y = prod_term - prod(cos(x).^2) + 1;
end

% HappyCat function
function y = happycat(x)
    d = length(x);
    alpha = 1/8;
    s = sum(x.^2);
    y = (alpha*((abs(s-d))^0.25) + (0.5*s + sum(x))/d + 0.5)*((2*abs(s-d))^0.5 + (s-d))/((s-d)^2 + 2*(2*abs(s-d))^0.5*(s-d) + (2*abs(s-d)));
end

% HGBat function
function y = hgbat(x)
    d = length(x);
    y = sum(x.^2) - prod(x).^2 + (10/d^2)*sum((1-cos(2*pi*x)));
end

% Levy function
function y = levy(x)
    d = length(x);
    w = 1 + (x-1)/4;
    term1 = sin(pi*w(1))^2;
    term3 = (w(d)-1)^2 * (1+sin(2*pi*w(d))^2);
    sum_term = 0;
    for i = 1:d-1
        wi = w(i);
        new_term = (wi-1)^2*(1+10*sin(pi*wi+1)^2);
        sum_term = sum_term + new_term;
    end
    y = term1 + sum_term + term3;
end

接下来，我们需要实现差分进化算法。差分进化算法是一种优化算法，它通过不断迭代改进种群中的个体，从而找到函数的最优解。这里的实现方式是标准的DE/rand/1/bin，即每次迭代选择3个不同的个体，用其中的两个进行差分，再和第三个个体进行变异，最后和原个体进行比较。下面是差分进化算法的代码：

function [x_best, f_best, convergence] = de(func, dim, lb, ub, max_iter, pop_size, F, CR)
    % Initialize the population
    pop = repmat(lb, pop_size, 1) + rand(pop_size, dim).*repmat(ub-lb, pop_size, 1);
    
    % Evaluate the fitness of the population
    fitness = feval(func, pop);
    [f_best, best_idx] = min(fitness);
    x_best = pop(best_idx,:);
    
    % Initialize the convergence array
    convergence = zeros(max_iter, 1);
    
    % Main loop
    for i = 1:max_iter
        % Mutation
        mut_idx = randperm(pop_size);
        x_r1 = pop(mut_idx(1:pop_size),:);
        x_r2 = pop(mut_idx(pop_size+1:end),:);
        x_diff = x_r1 - x_r2;
        x_mut = repmat(x_best, pop_size, 1) + F.*x_diff;
        
        % Crossover
        cr_idx = rand(pop_size, dim) < CR;
        pop_new = pop;
        pop_new(cr_idx) = x_mut(cr_idx);
        
        % Bound handling
        pop_new = max(pop_new, repmat(lb, pop_size, 1));
        pop_new = min(pop_new, repmat(ub, pop_size, 1));
        
        % Evaluate the fitness of the new population
        fitness_new = feval(func, pop_new);
        
        % Selection
        replace_idx = fitness_new < fitness;
        pop(replace_idx,:) = pop_new(replace_idx,:);
        fitness(replace_idx) = fitness_new(replace_idx);
        
        % Update the global best
        [f_new, best_idx] = min(fitness);
        if f_new < f_best
            f_best = f_new;
            x_best = pop(best_idx,:);
        end
        
        % Record the convergence
        convergence(i) = f_best;
    end
end

在主程序中，我们可以调用上面的两个函数来进行测试。下面是主程序的代码：

% Define the problem parameters
func_list = {@schwefel, @rosenbrock, @griewank, @rastrigin, @ackley, @weierstrass, @katsuura, @happycat, @hgbat, @levy};
dim_list = [10, 30];
max_iter = 1000;
pop_size = 100;
F = 0.8;
CR = 0.9;

% Initialize the statistics arrays
mean_convergence = zeros(length(func_list), length(dim_list));
convergence_fig = figure;
box_fig = figure;

% Loop through the test functions and dimensions
for i = 1:length(func_list)
    for j = 1:length(dim_list)
        % Set up the problem
        func = func_list{i};
        dim = dim_list(j);
        lb = -100*ones(1, dim);
        ub = 100*ones(1, dim);
        
        % Run the algorithm
        [x_best, f_best, convergence] = de(func, dim, lb, ub, max_iter, pop_size, F, CR);
        
        % Record the statistics
        mean_convergence(i,j) = mean(convergence);
        
        % Plot the convergence curve
        figure(convergence_fig);
        plot(convergence);
        hold on;
        
        % Print the result
        fprintf('Function %d (dim=%d): f_best=%f\n', i, dim, f_best);
    end
end

% Plot the box plot
figure(box_fig);
boxplot(mean_convergence');
xlabel('Function');
ylabel('Mean Convergence');
xticklabels({'Schwefel','Rosenbrock','Griewank','Rastrigin','Ackley','Weierstrass','Katsuura','HappyCat','HGBat','Levy'});

运行上面的代码，就可以得到在10个测试函数上的平均收敛精度、收敛曲线和统计箱图了。