三维装箱matlab代码

三维装箱问题是一个NP难问题，因此没有一种通用的最优解法。常见的解法包括启发式算法、贪心算法、遗传算法等。

以下是一个基于贪心算法的三维装箱Matlab代码示例，仅供参考。

clc; clear; close all;
%% 生成测试数据
N = 50; % 物品数量
W = 10; % 容器宽度
H = 10; % 容器高度
L = 10; % 容器长度
w = rand(1, N) * W; % 物品宽度
h = rand(1, N) * H; % 物品高度
l = rand(1, N) * L; % 物品长度

%% 贪心算法
% 初始化容器
box = [W, H, L];
% 初始化物品坐标和状态
pos = zeros(N, 3);
rot = zeros(N, 3);
used = zeros(1, N);
% 装箱
for i = 1:N
    % 找到最小空隙
    min_gap = inf;
    min_gap_pos = zeros(1, 3);
    min_gap_box = zeros(1, 3);
    min_gap_idx = -1;
    min_gap_rot = zeros(1, 3);
    for j = 1:N
        if ~used(j)
            for k = 1:6 % 6种旋转方式
                [pos_tmp, box_tmp] = rotate_box(pos(j,:), [w(j),h(j),l(j)], rot(j,:), box);
                gap = prod(box_tmp) - sum(used .* prod(box_tmp));
                if gap < min_gap
                    min_gap = gap;
                    min_gap_pos = pos_tmp;
                    min_gap_box = box_tmp;
                    min_gap_idx = j;
                    min_gap_rot = rot(j,:);
                end
                rot(j,:) = mod(rot(j,:) + [90,0,0], 360);
                if rot(j,1) == 0 % 旋转完毕
                    break;
                end
            end
        end
    end
    % 更新状态
    pos(min_gap_idx,:) = min_gap_pos;
    box = min_gap_box;
    used(min_gap_idx) = 1;
end

%% 可视化
figure;
hold on;
for i = 1:N
    pos_tmp = pos(i,:);
    box_tmp = [w(i),h(i),l(i)];
    rot_tmp = rot(i,:);
    [pos_tmp, box_tmp] = rotate_box(pos_tmp, box_tmp, rot_tmp, [W,H,L]);
    draw_box(pos_tmp, box_tmp);
end
axis equal;
axis([0,W,0,H,0,L]);
grid on;
xlabel('x');
ylabel('y');
zlabel('z');

%% 函数库
function draw_box(pos, box)
    x = box(1); y = box(2); z = box(3);
    X = [0, x, x, 0, 0, x, x, 0];
    Y = [0, 0, y, y, 0, 0, y, y];
    Z = [0, 0, 0, 0, z, z, z, z];
    for i = 1:8
        p = [X(i); Y(i); Z(i)];
        p = rotate_point(p, pos);
        X(i) = p(1); Y(i) = p(2); Z(i) = p(3);
    end
    patch(X, Y, Z, 'red');
end

function p = rotate_point(p, pos)
    theta = deg2rad(pos(4));
    Rx = [1, 0, 0; 0, cos(theta(1)), -sin(theta(1)); 0, sin(theta(1)), cos(theta(1))];
    Ry = [cos(theta(2)), 0, sin(theta(2)); 0, 1, 0; -sin(theta(2)), 0, cos(theta(2))];
    Rz = [cos(theta(3)), -sin(theta(3)), 0; sin(theta(3)), cos(theta(3)), 0; 0, 0, 1];
    R = Rz * Ry * Rx;
    p = R * p + pos(1:3)';
end

function [pos_tmp, box_tmp] = rotate_box(pos, box, rot, container)
    theta = deg2rad(rot);
    Rx = [1, 0, 0; 0, cos(theta(1)), -sin(theta(1)); 0, sin(theta(1)), cos(theta(1))];
    Ry = [cos(theta(2)), 0, sin(theta(2)); 0, 1, 0; -sin(theta(2)), 0, cos(theta(2))];
    Rz = [cos(theta(3)), -sin(theta(3)), 0; sin(theta(3)), cos(theta(3)), 0; 0, 0, 1];
    R = Rz * Ry * Rx;
    box_tmp = R * box';
    pos_tmp = pos;
    pos_tmp(4) = mod(pos_tmp(4) + rot(1), 360);
    if pos_tmp(4) == 90 || pos_tmp(4) == 270
        pos_tmp(1:2) = pos_tmp(1:2) + (box(1:2) - box_tmp(1:2)) / 2;
    else
        pos_tmp(1:2) = pos_tmp(1:2) + (box(2:-1:1) - box_tmp(2:-1:1)) / 2;
    end
    if any(pos_tmp(1:3) + box_tmp' > container) % 碰到边界
        pos_tmp(1:3) = pos_tmp(1:3) - (pos_tmp(1:3) + box_tmp' - container) .* (pos_tmp(1:3) + box_tmp' > container);
    end
end

该代码首先生成了50个随机物品，接着使用贪心算法将它们装入一个10x10x10的容器中，并可视化结果。该算法先遍历每个物品，然后在容器中找到最小空隙，并将物品放入其中，直到所有物品都被放置。在遍历每个物品时，算法会尝试6种旋转方式，并选择能够获得最小空隙的方式。在每次放置物品时，算法会更新容器大小、物品坐标和状态，并继续寻找下一个最小空隙。最终结果如下：


需要注意的是，该算法可能不能得到最优解，并且在物品数量较大时可能耗时较长。因此，在实际应用中，可以考虑使用其他算法，并根据具体情况做出优化。