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亲爱的您，这里是LearningYard学苑。今天小编为大家带来“学习知多少（14）：“快递打包算法”，欢迎您的访问。

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Dear you, this is The LearningYard Academy. Today Xiaobian brings you "How much to learn (14):”Express packaging algorithm ”, welcome your visit.

疫情突袭之下，在世界经济陷入深度衰退之际，中国快递业的表现分外亮眼。这是中国经济在全球率先复苏、国内消费回暖的直观体现，也折射出中国经济的蓬勃活力。2020年末，中国快递量高达800亿，那么800亿对于整个行业意味着什么？

Under the sudden impact of the epidemic, when the world economy fell into a deep recession, the performance of China's express delivery industry was particularly eye-catching. This is a direct embodiment of China's economy taking the lead in the world recovery and domestic consumption picking up, and it also reflects the vigorous vitality of China's economy. At the end of 2020, China's express delivery volume reached 80 billion, so what does 80 billion mean for the entire industry?

众所周知，一件快递，包含运单、封套、塑料袋、胶带等多种包装物，有的还要套上纸箱、编织袋、装填缓冲材料。这些材料不仅消耗了大量资源，而且属于一次性消耗品，被丢弃后对环境造成巨大影响。而这800亿件包裹背后，被大量丢弃的包裹想想就足够触目惊心。那我们是不是能够想到一个好的办法来优化包装，减少包装材料，进而减少对环境的危害呢？基于此，国内外不少科学家致力于研究新型包装材料，我们在参考众多文献之后，提出通过算法优化打包方式对快递包装进行利用最大化。

As we all know, a piece of express delivery, including waybills, envelopes, plastic bags, tapes and other packaging, and some also need to be covered with cartons, woven bags, and filling buffer materials. These materials not only consume a lot of resources, but are also disposable consumables that have a huge impact on the environment when discarded. And behind these 80 billion packages, the large number of discarded packages is shocking enough to think about. So can we think of a good way to optimize packaging, reduce packaging materials, and thus reduce the harm to the environment? Based on this, many scientists at home and abroad are committed to the research of new packaging materials, and after referring to many literatures, we propose to maximize the use of express packaging through algorithm optimization packaging.

Friesen 和 Langston 率先提出了一种多箱型的一维装箱策略，在他们的应用场景中，箱子的类型是有限的，个数是无限的，目的是在装入所有货物的前提下，使得所用的箱子体积总和最小。Correia 等人也针对一维装箱提出了几个公式化方法和有效不等式。Seiden 和 van Stee 建立了一种数学模型，能够给出n 维多箱型装箱问题所需容器数量的上界和下界。M Baazaoui 等人根据突尼斯某企业的实际情况，根据容器和货物的相似度，建立数学模型确定上下界。

Friesen and Langston pioneered a multi-box 1D packing strategy in which the types of boxes are limited and the number of boxes is infinite, with the goal of minimizing the sum of the boxes used while loading all the goods. Correia et al. also proposed several formulaic methods and valid inequalities for one-dimensional binning. Seiden and van Stee developed a mathematical model that gives the upper and lower bounds of the number of containers required for n-dimensional multi-box boxing problems. According to the actual situation of a Tunisian enterprise, M Baazaoui et al. established a mathematical model to determine the upper and lower bounds according to the similarity of containers and goods.

关于装箱算法的应用软件，市面上不是很多，较为成熟的为《装箱大师》，由北京达纬恒通信息技术有限公司开发，该软件有不同的版本，有的针对集装箱式的装载问题，有针对圆柱形货物的装载，最优秀的是自由设计版，可以用户手动调整装箱结果。另一个是提供装箱服务的网站，，该网站可以对规则物体，包括立方体、圆柱体，进行装箱，类似装箱大师，用户可以自定义货物的质量、尺寸、数量，自定义容器的承重、尺寸，系统最终会以 2D 图片的形式给出装配结果和装配步骤，该服务装载率比较高，用户体验也较好，但是不足的是该服务为第三类装箱问题：背包装载，即无法智能地调节容器以实现物品完全装箱。

Regarding the application software of the packing algorithm, there are not many on the market, the more mature is "Packing Master", developed by Beijing Dawei Hengtong Information Technology Co., Ltd., the software has different versions, some for container-type loading problems, some for cylindrical cargo loading, the best is the free design version, users can manually adjust the packing results. The other is to provide the website of the packing service, , the website can be the regular object, including cubes, cylinders, for boxing, similar to the packing master, users can customize the quality, size, quantity of the goods, customize the load-bearing and size of the container, the system will finally give the assembly results and assembly steps in the form of 2D pictures, the service loading rate is relatively high, the user experience is also better, but the shortcoming is that the service is the third type of boxing problem: backpack loading, That is, it is not possible to intelligently adjust the container to achieve complete boxing of items.

现今虽然有相关案例，但大家普遍技术不够成熟，关键在于算法优化不明显、实现性不高，所以我们应在这方面加强改进。

Although there are related cases today, the technology is generally not mature enough, the key is that the algorithm optimization is not obvious and the implementation is not high, so we should strengthen the improvement in this regard.

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翻译来源于谷歌翻译

部分来源于

百度文库

《基于遗传算法的多箱型 三维装箱问题的研究 》

编辑&排版|百味

审核|闫庆红