三维装箱MATLAB程序.m_三维装箱算法资源-CSDN文库

共23个文件

m：21个

txt：2个

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三维装箱问题是一种经典的组合优化问题，主要涉及在有限的空间内如何最优地放置不同尺寸的物品，以最大化空间利用率或最小化容器的体积。在物流、仓储、包装设计等领域有广泛应用。MATLAB作为一款强大的数学计算软件，可以用来解决此类问题。在MATLAB程序中，"三维装箱"通常是指通过编写算法来模拟物品放入箱子的过程，考虑的因素包括物品的尺寸、旋转可能性以及排列方式。描述中提到"目前求解方法主要是近似算法"，这意味着该程序可能采用了非精确的解决方案，因为三维装箱问题属于NP难问题，难以找到全局最优解，尤其是在大规模数据下。近似算法是针对这类问题的一种实用策略，它能在较短的时间内找到接近最优解的方案，虽然不保证是最优，但通常能接受。常见的近似算法有贪心算法、遗传算法、模拟退火算法、粒子群优化等。这些算法会根据特定的启发式规则进行决策，如先放置大件物品、优先填充底部等。在"3D with rotation"这个子文件中，可能包含了支持物品旋转的代码实现。物品旋转是提升装箱效率的重要手段，因为它可能让原本无法放入的物品通过适当的角度调整得以容纳。例如，可以允许物品进行90度、180度或更复杂的旋转，使得物品的长宽高在三个维度上都能灵活适应。在编写这样的MATLAB程序时，通常会涉及以下步骤： 1. 定义物品和箱子的三维尺寸。 2. 初始化装箱状态，比如空箱子。 3. 设计并实现近似算法，包括物品的排序、尝试放置、回溯等过程。 4. 在每一步中检查是否违反约束（如物品尺寸超过箱子边界、无法放入等）。 5. 计算当前装箱方案的效率指标（如利用率、总体积等）。 6. 重复上述过程，直到所有物品被装入或无法继续装入。 7. 输出最终的装箱结果，可能包括每个物品的位置、旋转角度及剩余空间信息。在实际应用中，为了优化性能，可能还需要考虑并行计算、多目标优化等技术。同时，为了评估算法的性能，通常会用到不同的数据集，包括随机生成的数据和真实场景的数据。 "三维装箱MATLAB程序"是一个结合了组合优化、近似算法和空间几何的项目，它通过MATLAB强大的计算能力来解决实际问题，为物流、包装等行业提供高效的空间利用策略。

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三维装箱MATLAB程序.rar （23个子文件）

3D with rotation

test.m 2KB

main.m 1KB

genCollision.m 3KB

backup.txt 5KB

geneGpara.m 65B

maxStep.m 1KB

fval.m 77B

rt.m 1KB

fmin.m 233B

plotRec.txt 681B

zoutendijk1.m 3KB

maxStep5.m 587B

zoutendijk.m 6KB

zoutendijk2.m 6KB

diff_val.m 102B

plotResult.m 2KB

combsin.m 330B

zoutendijk7.m 3KB

zoutendijk6.m 4KB

genGi.m 2KB

numericSolve.m 740B

zoutendijk5.m 6KB

genFunction.m 583B

% f = (x1-dx1)^2+(y1-dy1)^2 + (x2-dx2)^2+(y2-dy2)^2 + Rcost * ((theta1-dtheta1)^2 + (theta2-dtheta2)^2); % x=[x1, y1, x2, y2, sinthe1, sinthe2]; % f = (x1-dx1)^2+(y1-dy1)^2 + (x2-dx2)^2+(y2-dy2)^2; % x=[x1, y1, x2, y2]; % f = (x1-dx1)^2+(y1-dy1)^2 + (x2-dx2)^2+(y2-dy2)^2 + Rcost * ((sinthe1-sin(dtheta1))^2 + (sinthe2-sin(dtheta2))^2); % x=[x1, y1, x2, y2, sinthe1, sinthe2]; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % rec1 % G(11,:) = -x1-a1*cos(theta1)-b1*sin(theta1); % G(12,:) = -x1+a1*cos(theta1)-b1*sin(theta1); % G(13,:) = -x1+a1*cos(theta1)+b1*sin(theta1); % G(14,:) = -x1-a1*cos(theta1)+b1*sin(theta1); % % G(15,:) = -y1-a1*sin(theta1)-b1*cos(theta1); % G(16,:) = -y1+a1*sin(theta1)-b1*cos(theta1); % G(17,:) = -y1+a1*sin(theta1)+b1*cos(theta1); % G(18,:) = -y1-a1*sin(theta1)+b1*cos(theta1); % % G(19,:) = -bbx+x1+a1*cos(theta1)+b1*sin(theta1); % G(20,:) = -bbx+x1+a1*cos(theta1)-b1*sin(theta1); % G(21,:) = -bbx+x1-a1*cos(theta1)-b1*sin(theta1); % G(22,:) = -bbx+x1-a1*cos(theta1)+b1*sin(theta1); % % G(23,:) = -bby+y1-a1*sin(theta1)-b1*cos(theta1); % G(24,:) = -bby+y1+a1*sin(theta1)+b1*cos(theta1); % G(25,:) = -bby+y1-a1*sin(theta1)+b1*cos(theta1); % G(26,:) = -bby+y1+a1*sin(theta1)-b1*cos(theta1); % % % rec2 % G(27,:) = -x2-a2*cos(theta2)-b2*sin(theta2); % G(28,:) = -x2+a2*cos(theta2)-b2*sin(theta2); % G(29,:) = -x2+a2*cos(theta2)+b2*sin(theta2); % G(30,:) = -x2-a2*cos(theta2)+b2*sin(theta2); % % G(31,:) = -y2-a2*sin(theta2)-b2*cos(theta2); % G(32,:) = -y2+a2*sin(theta2)-b2*cos(theta2); % G(33,:) = -y2+a2*sin(theta2)+b2*cos(theta2); % G(34,:) = -y2-a2*sin(theta2)+b2*cos(theta2); % % G(35,:) = -bbx+x2+a2*cos(theta2)+b2*sin(theta2); % G(36,:) = -bbx+x2+a2*cos(theta2)-b2*sin(theta2); % G(37,:) = -bbx+x2-a2*cos(theta2)-b2*sin(theta2); % G(38,:) = -bbx+x2-a2*cos(theta2)+b2*sin(theta2); % % G(39,:) = -bby+y2-a2*sin(theta2)-b2*cos(theta2); % G(40,:) = -bby+y2+a2*sin(theta2)+b2*cos(theta2); % G(41,:) = -bby+y2-a2*sin(theta2)+b2*cos(theta2); % G(42,:) = -bby+y2+a2*sin(theta2)-b2*cos(theta2); % G(43,:) = theta1-1.57; % G(44,:) = -theta1-1.57; % G(45,:) = theta2-1.57; % G(46,:) = -theta2-1.57; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % rec1 % G(11,:) = -x1-a1*sqrt(1-sinthe1^2)-b1*sinthe1; % G(12,:) = -x1+a1*sqrt(1-sinthe1^2)-b1*sinthe1; % G(13,:) = -x1+a1*sqrt(1-sinthe1^2)+b1*sinthe1; % G(14,:) = -x1-a1*sqrt(1-sinthe1^2)+b1*sinthe1; % % G(15,:) = -y1-a1*sinthe1-b1*sqrt(1-sinthe1^2); % G(16,:) = -y1+a1*sinthe1-b1*sqrt(1-sinthe1^2); % G(17,:) = -y1+a1*sinthe1+b1*sqrt(1-sinthe1^2); % G(18,:) = -y1-a1*sinthe1+b1*sqrt(1-sinthe1^2); % % G(19,:) = -bbx+x1+a1*sqrt(1-sinthe1^2)+b1*sinthe1; % G(20,:) = -bbx+x1+a1*sqrt(1-sinthe1^2)-b1*sinthe1; % G(21,:) = -bbx+x1-a1*sqrt(1-sinthe1^2)-b1*sinthe1; % G(22,:) = -bbx+x1-a1*sqrt(1-sinthe1^2)+b1*sinthe1; % % G(23,:) = -bby+y1-a1*sinthe1-b1*sqrt(1-sinthe1^2); % G(24,:) = -bby+y1+a1*sinthe1+b1*sqrt(1-sinthe1^2); % G(25,:) = -bby+y1-a1*sinthe1+b1*sqrt(1-sinthe1^2); % G(26,:) = -bby+y1+a1*sinthe1-b1*sqrt(1-sinthe1^2); % % % rec2 % G(27,:) = -x2-a2*sqrt(1-sinthe2^2)-b2*sinthe2; % G(28,:) = -x2+a2*sqrt(1-sinthe2^2)-b2*sinthe2; % G(29,:) = -x2+a2*sqrt(1-sinthe2^2)+b2*sinthe2; % G(30,:) = -x2-a2*sqrt(1-sinthe2^2)+b2*sinthe2; % % G(31,:) = -y2-a2*sinthe2-b2*sqrt(1-sinthe2^2); % G(32,:) = -y2+a2*sinthe2-b2*sqrt(1-sinthe2^2); % G(33,:) = -y2+a2*sinthe2+b2*sqrt(1-sinthe2^2); % G(34,:) = -y2-a2*sinthe2+b2*sqrt(1-sinthe2^2); % % G(35,:) = -bbx+x2+a2*sqrt(1-sinthe2^2)+b2*sinthe2; % G(36,:) = -bbx+x2+a2*sqrt(1-sinthe2^2)-b2*sinthe2; % G(37,:) = -bbx+x2-a2*sqrt(1-sinthe2^2)-b2*sinthe2; % G(38,:) = -bbx+x2-a2*sqrt(1-sinthe2^2)+b2*sinthe2; % % G(39,:) = -bby+y2-a2*sinthe2-b2*sqrt(1-sinthe2^2); % G(40,:) = -bby+y2+a2*sinthe2+b2*sqrt(1-sinthe2^2); % G(41,:) = -bby+y2-a2*sinthe2+b2*sqrt(1-sinthe2^2); % G(42,:) = -bby+y2+a2*sinthe2-b2*sqrt(1-sinthe2^2); % % G(43,:) = sinthe1-1; % G(44,:) = -sinthe1-1; % G(45,:) = sinthe2-1; % G(46,:) = -sinthe2-1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% % syms x1 x2; % f = 2*x1^2+2*x2^2-2*x1*x2-4*x1-6*x2; % x=[x1, x2]; %% % syms x1 y1 x2 y2; % f = (x1-1)^2+(y1+1)^2 + (11-x2)^2+(y2-8)^2; % x=[x1, y1, x2, y2]; %% % syms x1 x2 x3; % f = x1^2 + x1*x2 + 2*x2^2 - 6*x1 - 2*x2 - 12*x3; % x = [x1, x2, x3]; %% % syms x1 x2; % f = x1 + x2; % x = [x1, x2]; %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% % A=[1 1;1 5;-1 0;0 -1]; % b=[2 5 0 0]'; % G=[]; % x0=[0 0]; % Aeq=[]; % beq=[]; % label=1; %% % A=[-1 0 0 0; 0 -1 0 0; 1 0 0 0; 0 1 0 0; 0 0 -1 0; 0 0 0 -1; 0 0 1 0; 0 0 0 1]; % b=[-1 -1 9 9 -1 -1 9 9]'; % G=[]; % x0=[5 5 5 5]; % Aeq=[]; % beq=[]; % label=1; %% % A = []; % b = []; % G(1,:) = 2*x1^2 + x2^2 - 15; % G(2,:) = -x1 + 2*x2 + x3 - 3; % G(3,:) = -x1; % G(4,:) = -x2; % G(5,:) = -x3; % x0 = [0 0 0]; % Aeq = []; % beq = []; % label = 0; %% % A = []; % b = []; % G(1,:) = x1^2 + x2^2 - 1; % G(2,:) = x1^2 - x2; % x0 = [0 1]; % Aeq = []; % beq = []; % label = 0;

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