车间布局优化的遗传算法 Matlab 代码，车间长10米，宽5米，设备16台，每台设备长1.2米，宽0.8，要求布局为两行，且不重叠，并绘图

以下是一个基本的遗传算法的 MATLAB 代码，用于优化车间布局：

% 定义问题参数
length = 10; % 车间长度
width = 5; % 车间宽度
num_equipments = 16; % 设备数
equip_length = 1.2; % 设备长度
equip_width = 0.8; % 设备宽度

% 定义遗传算法参数
pop_size = 50; % 种群大小
num_generations = 100; % 迭代次数
mutation_rate = 0.01; % 变异率
crossover_rate = 0.8; % 交叉率

% 初始化种群
pop = zeros(pop_size, num_equipments);
for i = 1:pop_size
    pop(i,:) = randperm(num_equipments);
end

% 迭代优化
for gen = 1:num_generations
    % 计算适应度
    fitness = zeros(pop_size, 1);
    for i = 1:pop_size
        % 将设备分成两行
        row1 = pop(i,1:num_equipments/2);
        row2 = pop(i,num_equipments/2+1:end);
        
        % 计算每行的长度和宽度
        row1_length = sum(equip_length.*ismember(row1,1:num_equipments/2));
        row1_width = max(equip_width.*ismember(row1,1:num_equipments/2));
        row2_length = sum(equip_length.*ismember(row2,num_equipments/2+1:num_equipments));
        row2_width = max(equip_width.*ismember(row2,num_equipments/2+1:num_equipments));
        
        % 计算适应度
        fitness(i) = -abs(row1_length-row2_length) - max(row1_width,row2_width);
    end
    
    % 选择优秀个体
    [~, idx] = sort(fitness,'descend');
    elite = pop(idx(1:2),:);
    
    % 交叉
    offspring = zeros(pop_size-2, num_equipments);
    for i = 1:(pop_size-2)/2
        % 随机选择两个个体进行交叉
        p1 = pop(randi([1,pop_size]),:);
        p2 = pop(randi([1,pop_size]),:);
        
        % 随机选择交叉点
        crossover_point = randi([1,num_equipments-1]);
        
        % 生成新个体
        offspring(2*i-1,:) = [p1(1:crossover_point), p2(crossover_point+1:end)];
        offspring(2*i,:) = [p2(1:crossover_point), p1(crossover_point+1:end)];
    end
    
    % 变异
    for i = 1:pop_size-2
        if rand() < mutation_rate
            % 随机选择两个位置进行变异
            pos1 = randi([1,num_equipments]);
            pos2 = randi([1,num_equipments]);
            
            % 交换位置
            temp = offspring(i,pos1);
            offspring(i,pos1) = offspring(i,pos2);
            offspring(i,pos2) = temp;
        end
    end
    
    % 更新种群
    pop = [elite; offspring];
    
    % 输出结果
    best_fitness = max(fitness);
    best_solution = pop(find(fitness == best_fitness, 1),:);
    disp(['Generation ', num2str(gen), ': Best Fitness = ', num2str(best_fitness)]);
end

% 绘制布局图
row1 = best_solution(1:num_equipments/2);
row2 = best_solution(num_equipments/2+1:end);
figure;
hold on;
for i = 1:num_equipments/2
    x = 0.1 + (i-1)*1.3;
    y = 0.1;
    rectangle('Position',[x,y,equip_length,equip_width],'FaceColor','r');
    if ismember(i,row1)
        text(x+0.5*equip_length,y+0.5*equip_width,num2str(i),'HorizontalAlignment','center','VerticalAlignment','middle','Color','w');
    else
        text(x+0.5*equip_length,y+0.5*equip_width,num2str(i),'HorizontalAlignment','center','VerticalAlignment','middle','Color','r');
    end
end
for i = 1:num_equipments/2
    x = 0.1 + (i-1)*1.3;
    y = 1.2;
    rectangle('Position',[x,y,equip_length,equip_width],'FaceColor','r');
    if ismember(i+num_equipments/2,row2)
        text(x+0.5*equip_length,y+0.5*equip_width,num2str(i+num_equipments/2),'HorizontalAlignment','center','VerticalAlignment','middle','Color','w');
    else
        text(x+0.5*equip_length,y+0.5*equip_width,num2str(i+num_equipments/2),'HorizontalAlignment','center','VerticalAlignment','middle','Color','r');
    end
end
xlim([0,length+0.2]);
ylim([0,width+0.2]);
axis equal;
axis off;

这段代码使用遗传算法优化车间布局，使得设备分布在两行中，不重叠，并且最大化两行长度的差异和最小化两行的最大宽度。最后，使用 `rectangle` 和 `text` 函数绘制布局图。