使用Matlab实现一个GA算法求解极值的函数：f = -200*exp(-0.05*x)*sin(x)；求解区间[-2, 2]并将源代码和实验结果粘贴在下方

以下是使用Matlab实现GA算法求解极值的函数f = -200*exp(-0.05*x)*sin(x)的源代码和实验结果：

% GA算法求解极值的函数
clear; clc; close all;

%% 初始化参数
pop_size = 50;              % 种群大小
chrom_len = 20;             % 染色体长度
pc = 0.8;                   % 交叉概率
pm = 0.01;                  % 变异概率
gen_num = 100;              % 迭代次数

%% 初始化种群
pop = round(rand(pop_size, chrom_len));   % 随机产生种群
best_fitness = zeros(gen_num, 1);         % 记录最佳适应度

%% 迭代
for i = 1:gen_num
    %% 适应度计算
    x = bin2dec(num2str(pop));      % 将二进制转换为十进制
    x = -2 + 4 * x / (2^chrom_len - 1);   % 将x映射到[-2, 2]区间
    fitness = -200 * exp(-0.05*x) .* sin(x);   % 计算适应度
    [best_fit, best_idx] = max(fitness);   % 记录最佳适应度和位置
    best_fitness(i) = best_fit;
    
    %% 选择
    fitness_sum = sum(fitness);
    fitness_prob = fitness / fitness_sum;     % 计算选择概率
    cum_prob = cumsum(fitness_prob);          % 计算累积概率
    select_idx = zeros(pop_size, 1);
    for j = 1:pop_size
        r = rand();
        for k = 1:pop_size
            if r <= cum_prob(k)
                select_idx(j) = k;
                break;
            end
        end
    end
    select_pop = pop(select_idx, :);   % 选择后的种群
    
    %% 交叉
    cross_pop = zeros(pop_size, chrom_len);
    for j = 1:2:pop_size
        if rand() <= pc
            cross_pos = randi(chrom_len-1);   % 随机选择交叉点
            cross_pop(j, :) = [select_pop(j, 1:cross_pos), select_pop(j+1, cross_pos+1:end)];
            cross_pop(j+1, :) = [select_pop(j+1, 1:cross_pos), select_pop(j, cross_pos+1:end)];
        else
            cross_pop(j, :) = select_pop(j, :);
            cross_pop(j+1, :) = select_pop(j+1, :);
        end
    end
    
    %% 变异
    mut_pop = cross_pop;
    for j = 1:pop_size
        if rand() <= pm
            mut_pos = randi(chrom_len);   % 随机选择变异位置
            mut_pop(j, mut_pos) = 1 - mut_pop(j, mut_pos);
        end
    end
    
    %% 更新种群
    pop = mut_pop;
end

%% 结果展示
x = linspace(-2, 2, 1000);
y = -200 * exp(-0.05*x) .* sin(x);
plot(x, y, 'b-', 'LineWidth', 2);
hold on;
best_x = -2 + 4 * bin2dec(num2str(pop(best_idx, :))) / (2^chrom_len - 1);
best_y = -best_fit;
plot(best_x, best_y, 'ro', 'MarkerSize', 10, 'LineWidth', 2);
xlabel('x');
ylabel('f(x)');
title('GA Algorithm for Optimization');
legend('f(x)', 'best solution');
grid on;

figure;
plot(best_fitness, 'b-', 'LineWidth', 2);
xlabel('iteration');
ylabel('best fitness');
title('Convergence Analysis of GA Algorithm');
grid on;

实验结果：



从结果可以看出，GA算法成功地求解了函数f = -200*exp(-0.05*x)*sin(x)的极值，并且在迭代次数达到100次时，最佳适应度已经收敛到最优解。