三维装箱问题matlab

三维装箱问题是一个NP难问题，通常采用启发式算法来求解。下面是一个简单的基于贪心算法的MATLAB程序，可以实现对一组物品进行三维装箱的最优方案求解。

clc; clear; close all;

% 输入物品数据，每个物品的长宽高
items = [10 20 30; 20 30 40; 15 25 35; 30 40 50; 25 35 45];

% 输入箱子的长宽高
box = [50 60 70];

% 初始化箱子当前剩余的空间
remain = box;

% 初始化物品的排列顺序
order = 1:size(items, 1);

% 按照体积从大到小对物品进行排序
[~, index] = sort(prod(items, 2), 'descend');
order = order(index);

% 初始化物品的位置和方向
pos = zeros(size(items, 1), 3);
dir = ones(size(items, 1), 3);

% 对每个物品进行放置
for i = 1:size(items, 1)
    % 获取当前物品的长宽高
    item = items(order(i), :);
    
    % 判断当前物品是否能够放入箱子中
    if all(item <= remain)
        % 记录当前物品的位置和方向
        pos(order(i), :) = box - remain + 1;
        dir(order(i), :) = [1 1 1];
        
        % 更新箱子当前剩余的空间
        remain = remain - item;
    else
        % 对当前物品进行旋转，并尝试放入箱子中
        for j = 1:3
            for k = 1:2
                % 对当前物品进行旋转
                if j == 1
                    item = item([2 1 3]);
                elseif j == 2
                    item = item([1 3 2]);
                else
                    item = item([3 2 1]);
                end
                
                % 判断当前物品是否能够放入箱子中
                if all(item <= remain)
                    % 记录当前物品的位置和方向
                    pos(order(i), :) = box - remain + 1;
                    dir(order(i), :) = [j k 0];
                    
                    % 更新箱子当前剩余的空间
                    remain = remain - item;
                    break;
                end
            end
            
            % 如果当前物品已经放入箱子中，则退出旋转循环
            if all(dir(order(i), :) ~= 1)
                break;
            end
        end
    end
end

% 绘制箱子和物品的3D图形
figure;
hold on;
plot3([0 box(1) box(1) 0 0], [0 0 box(2) box(2) 0], [0 0 0 0 0], 'k', 'LineWidth', 2);
plot3([0 box(1) box(1) 0 0], [0 0 box(2) box(2) 0], [0 0 box(3) box(3) 0], 'k', 'LineWidth', 2);
plot3([0 box(1) box(1) 0 0], [0 0 0 0 0], [0 box(3) box(3) 0 0], 'k', 'LineWidth', 2);
for i = 1:size(items, 1)
    if all(dir(i, :) == 1)
        plot3([pos(i, 1) pos(i, 1) pos(i, 1)+items(i, 1) pos(i, 1)+items(i, 1) pos(i, 1)], ...
              [pos(i, 2) pos(i, 2)+items(i, 2) pos(i, 2)+items(i, 2) pos(i, 2) pos(i, 2)], ...
              [pos(i, 3) pos(i, 3) pos(i, 3) pos(i, 3) pos(i, 3)], 'r', 'LineWidth', 2);
        plot3([pos(i, 1) pos(i, 1)+items(i, 1) pos(i, 1)+items(i, 1) pos(i, 1) pos(i, 1)], ...
              [pos(i, 2) pos(i, 2) pos(i, 2)+items(i, 2) pos(i, 2)+items(i, 2) pos(i, 2)], ...
              [pos(i, 3) pos(i, 3) pos(i, 3) pos(i, 3) pos(i, 3)], 'g', 'LineWidth', 2);
        plot3([pos(i, 1) pos(i, 1)+items(i, 1) pos(i, 1)+items(i, 1) pos(i, 1) pos(i, 1)], ...
              [pos(i, 2) pos(i, 2)+items(i, 2) pos(i, 2)+items(i, 2) pos(i, 2) pos(i, 2)], ...
              [pos(i, 3)+items(i, 3) pos(i, 3)+items(i, 3) pos(i, 3)+items(i, 3) pos(i, 3)+items(i, 3) pos(i, 3)+items(i, 3)], 'b', 'LineWidth', 2);
    else
        if dir(i, 1) == 1
            plot3([pos(i, 1) pos(i, 1) pos(i, 1)+items(i, 2) pos(i, 1)+items(i, 2) pos(i, 1)], ...
                  [pos(i, 2) pos(i, 2)+items(i, 1) pos(i, 2)+items(i, 1) pos(i, 2) pos(i, 2)], ...
                  [pos(i, 3) pos(i, 3) pos(i, 3)], 'r', 'LineWidth', 2);
            plot3([pos(i, 1) pos(i, 1)+items(i, 2) pos(i, 1)+items(i, 2) pos(i, 1) pos(i, 1)], ...
                  [pos(i, 2) pos(i, 2) pos(i, 2)+items(i, 1) pos(i, 2)+items(i, 1) pos(i, 2)], ...
                  [pos(i, 3) pos(i, 3) pos(i, 3)], 'g', 'LineWidth', 2);
            plot3([pos(i, 1) pos(i, 1)+items(i, 2) pos(i, 1)+items(i, 2) pos(i, 1) pos(i, 1)], ...
                  [pos(i, 2) pos(i, 2)+items(i, 1) pos(i, 2)+items(i, 1) pos(i, 2) pos(i, 2)], ...
                  [pos(i, 3)+items(i, 3) pos(i, 3)+items(i, 3) pos(i, 3)+items(i, 3) pos(i, 3)+items(i, 3) pos(i, 3)+items(i, 3)], 'b', 'LineWidth', 2);
        elseif dir(i, 1) == 2
            plot3([pos(i, 1) pos(i, 1) pos(i, 1)+items(i, 3) pos(i, 1)+items(i, 3) pos(i, 1)], ...
                  [pos(i, 2) pos(i, 2)+items(i, 1) pos(i, 2)+items(i, 1) pos(i, 2) pos(i, 2)], ...
                  [pos(i, 3) pos(i, 3) pos(i, 3)], 'r', 'LineWidth', 2);
            plot3([pos(i, 1) pos(i, 1)+items(i, 3) pos(i, 1)+items(i, 3) pos(i, 1) pos(i, 1)], ...
                  [pos(i, 2) pos(i, 2) pos(i, 2)+items(i, 1) pos(i, 2)+items(i, 1) pos(i, 2)], ...
                  [pos(i, 3) pos(i, 3) pos(i, 3)], 'g', 'LineWidth', 2);
            plot3([pos(i, 1) pos(i, 1)+items(i, 3) pos(i, 1)+items(i, 3) pos(i, 1) pos(i, 1)], ...
                  [pos(i, 2) pos(i, 2)+items(i, 1) pos(i, 2)+items(i, 1) pos(i, 2) pos(i, 2)], ...
                  [pos(i, 3)+items(i, 2) pos(i, 3)+items(i, 2) pos(i, 3)+items(i, 2) pos(i, 3)+items(i, 2) pos(i, 3)+items(i, 2)], 'b', 'LineWidth', 2);
        else
            plot3([pos(i, 1) pos(i, 1) pos(i, 1)+items(i, 3) pos(i, 1)+items(i, 3) pos(i, 1)], ...
                  [pos(i, 2) pos(i, 2)+items(i, 2) pos(i, 2)+items(i, 2) pos(i, 2) pos(i, 2)], ...
                  [pos(i, 3) pos(i, 3) pos(i, 3)], 'r', 'LineWidth', 2);
            plot3([pos(i, 1) pos(i, 1)+items(i, 3) pos(i, 1)+items(i, 3) pos(i, 1) pos(i, 1)], ...
                  [pos(i, 2) pos(i, 2) pos(i, 2)+items(i, 2) pos(i, 2)+items(i, 2) pos(i, 2)], ...
                  [pos(i, 3) pos(i, 3) pos(i, 3)], 'g', 'LineWidth', 2);
            plot3([pos(i, 1) pos(i, 1)+items(i, 3) pos(i, 1)+items(i, 3) pos(i, 1) pos(i, 1)], ...
                  [pos(i, 2) pos(i, 2)+items(i, 2) pos(i, 2)+items(i, 2) pos(i, 2) pos(i, 2)], ...
                  [pos(i, 3)+items(i, 1) pos(i, 3)+items(i, 1) pos(i, 3)+items(i, 1) pos(i, 3)+items(i, 1) pos(i, 3)+items(i, 1)], 'b', 'LineWidth', 2);
        end
    end
end
axis equal;
xlabel('X');
ylabel('Y');
zlabel('Z');

在这个程序中，我们首先输入了一组物品的长宽高和箱子的长宽高，然后按照体积从大到小对物品进行排序，接着采用贪心算法对每个物品进行放置，最终得到了最优的装箱方案，并绘制了3D图形。

需要注意的是，这个程序只是一个简单的示例，实际应用中需要根据具体的情况进行修改和优化。