CN114742326A - Three-dimensional boxing method for irregular articles - Google Patents
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Abstract
The invention discloses a three-dimensional boxing method for irregular articles, which is characterized by comprising the following steps of: approximating the three-dimensional irregular-shaped article to be loaded to a corresponding minimum enveloping cube, and setting the compression rate and the maximum compression ratio of the article; wherein the compression ratio represents a ratio of a variation in height of one article to a total weight of all articles placed above the article, and the maximum compression ratio represents a maximum ratio at which the height of the article can be compressed; the packing is performed with the compression rate and maximum compression ratio of the articles as constraints and with the goal of maximizing the space utilization of the box and the sum of the initial volumes of the articles packed in the box, based on the dynamic changes in volume of the articles due to the height changes resulting from the compression of the articles by the articles above during the packing process.
Description
Technical Field
The invention relates to the technical field of modern logistics transportation, in particular to a three-dimensional boxing method for irregular articles.
Background
With the rapid development of the logistics industry in recent years, a large number of orders bring great challenges to the packaging, distribution and other links of logistics enterprises. The packaging link is a preorder link of distribution, and the packaging cost and the labor cost generated in the link are important components in the operation cost of the logistics enterprises. If the space of the box can be more effectively utilized, certain commodities can be loaded by the fewest boxes or the total quantity of the commodities loaded by a single box is maximized under the condition of meeting actual conditions, so that the transportation cost can be reduced, the transportation time is saved, the logistics efficiency is improved, the profitability of enterprises is improved, and considerable economic and social benefits are obtained. Therefore, it is a critical need in the logistics industry to increase the loading level of boxes to the maximum and reduce the loading cost of boxes.
The three-dimensional boxing problem, which addresses the problem of how to load three-dimensional rectangular articles (e.g., boxes) in one or more boxes to maximize the use of box space, is of paramount importance to supply chain and logistics companies that are directly related to operating costs.
To date, a number of scholars have conducted extensive research into the three-dimensional boxing problem, and various methods for solving the problem have been published. Although published literature on three-dimensional boxing solutions is very extensive, most of them default to the articles to be loaded being regularly shaped (e.g., rectangular or cylindrical). However, irregularly shaped items are ubiquitous in enterprise logistics, particularly the packaging and shipping of fresh food. For the problem of three-dimensional boxing of irregularly-shaped articles, the original three-dimensional boxing method is not applicable, so that a new method needs to be designed to maximize the space utilization rate of boxes.
The three-dimensional packing problem of regular objects is a strong NP-hard problem that has been very challenging to solve, and becomes more difficult to deal with after combining the properties of irregular shapes. Documents directed to three-dimensional boxing of regular articles generally aim to load rectangular or cylindrical articles into containers, and in terms of precise algorithms, Elhedhli S et al propose a novel column generation solution, in which the pricing sub-problem is a two-dimensional layer generation problem; fekete S P et al propose a two-level tree search algorithm for solving the optimality of the high-dimensional packaging problem; hifi M et al introduced a mixed integer linear programming formula (MILP 1) and proposed some special effective inequalities to improve the lower bound of MILP 1. In the aspect of heuristic algorithm, Bischoff E E et al respectively provide corresponding methods for two new scenes, one method is used for producing stable and uniformly distributed packaging patterns, and the other method is used for multi-point loading of articles; eley M et al propose a heuristic to construct homogenous blocks of the same directional project in order to solve the heterogeneous single and multiple container loading problem. The above mentioned solutions assume that the object is a rigid object, i.e. the volume and shape of the object is constant throughout the loading process. In fact, however, the actual volume of the items will typically vary dynamically as the loading process progresses, and ignoring volume changes will result in some wastage of container space and packaging material.
Disclosure of Invention
The invention mainly aims to overcome the defects of the prior art, provides a three-dimensional boxing method for irregular articles, and solves the problem that the space utilization rate of a box is low due to the fact that the dynamic changes of the volume and the shape of the articles in the boxing process are ignored in the existing three-dimensional boxing scheme.
In order to solve the problems, the invention provides the following technical scheme:
a three-dimensional boxing method of irregular articles comprises the following steps: approximating the three-dimensional irregular-shaped article to be loaded to a corresponding minimum enveloping cube, and setting the compression rate and the maximum compression ratio of the article; wherein the compression ratio represents a ratio of a variation in height of one article to a total weight of all articles placed above the article, and the maximum compression ratio represents a maximum ratio at which the height of the article can be compressed; the packing is performed with the compression rate and maximum compression ratio of the articles as constraints and with the goal of maximizing the space utilization of the box and the sum of the initial volumes of the articles packed in the box, based on the dynamic changes in volume of the articles due to the height changes resulting from the compression of the articles by the articles above during the packing process.
Further, the packing is carried out by taking the compression rate and the maximum compression ratio of the articles as constraints and taking the maximization of the space utilization rate of the box and the sum of the initial volumes of the articles in the box as a target, and the method specifically comprises the following steps:
s1, enabling the box to be located in a three-dimensional coordinate system, wherein the origin of coordinates is the vertex of the lower left rear corner of the box; each article is represented by four attributes of vertex coordinates of the lower left rear corner, depth, width and height;
s2, sorting the articles according to the size of the bottom surface, then sorting the articles according to the compression rate, and considering the articles to be loaded into the box in sequence;
s3, initializing a pivot point list of the empty box, wherein the initialized pivot point list only has one pivot point of a coordinate origin; wherein the pivot points in the list of pivot points are used to determine where the item is loaded in the case;
s4, loading the articles according to the sequence of the step S2, traversing the pivot points contained in the pivot point list during loading, trying to place the articles on the pivot points, updating the actual height of each article in the box according to the compression rate and the maximum compression ratio of each article in the box and the total weight of all the articles placed above each article, and judging whether the articles can be placed on the traversed pivot points until the articles can be loaded on a certain pivot point;
s5, after an article is loaded, generating a new pivot point, and updating the pivot point list by using the new pivot point;
s6, sequencing the pivot points in the pivot point list, wherein the sequencing method comprises the following steps: sorting according to the coordinate value of the z axis of the pivot point from small to large firstly, then sorting according to the coordinate value of the y axis from small to large secondly, and finally sorting according to the coordinate value of the x axis from small to large finally;
and S7, returning to the step S4 for the next item to be loaded until all items to be loaded are traversed.
The present invention further provides a computer readable storage medium, on which a computer program is stored, which, when being executed by a processor, is capable of implementing the steps of the aforementioned three-dimensional boxing method.
The technical scheme of the invention has the beneficial effects that: compared with the traditional problem under the assumption of constant volume and shape, the space utilization rate of the container can be obviously improved by considering the problems of object shape and volume change, so that the packaging cost is further saved, and the operation efficiency is improved; the packing cost and the labor cost can be effectively reduced, the method has high practical value, and is a high-efficiency and practical three-dimensional packing algorithm.
Drawings
FIG. 1 is a flow chart of a method for three-dimensional boxing of irregular articles according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an embodiment of the present invention approximating an irregular three-dimensional shaped object as its corresponding minimal enveloping cube;
FIG. 3 is a representation of a case and article of an embodiment of the present invention in a three-dimensional coordinate system;
FIG. 4 is a schematic view of an embodiment of the present invention loading a first article into an empty box;
FIGS. 5-1 and 5-2 are schematic diagrams of two different scenarios for converting an invalid pivot point to a valid pivot point according to embodiments of the present invention;
FIG. 6 is a comparison of bin space utilization for a bin packing method of an embodiment of the present invention versus a bin packing method of the prior art;
FIG. 7 is a graph comparing the quantity of articles contained in a box for a method of boxing in accordance with an embodiment of the present invention and a prior art method of boxing;
fig. 8 is a packing visualization diagram of the packing method of the embodiment of the present invention for four types of boxes.
Detailed Description
The invention is further described with reference to the following figures and detailed description of embodiments.
In the prior art, the scheme for boxing three-dimensional articles does not consider the volume change caused by the compression of the articles in the boxing process, namely, the shape and the volume of the articles are considered to be constant in the whole loading process. In fact, however, the actual volume of the articles typically changes dynamically (typically being compressed) as the loading process progresses, and ignoring the volume change results in some waste of container space and packaging material. In order to solve the problem, the embodiment of the invention provides a three-dimensional packing problem for irregular-shaped three-dimensional articles, firstly, the dynamic volume change of the irregular-shaped articles in the three-dimensional packing problem is considered, and a constructive heuristic algorithm (namely, a three-dimensional packing algorithm based on the dynamic change of the article volume) is provided to solve the problem. A series of numerical experiments were then conducted to investigate the benefits of taking into account the volume change factor. And finally, visually displaying the boxing result, and helping workers in enterprises to more easily realize the optimized loading effect.
Before mathematically defining the problem, we first understand the scheme for a particular application. At present, a fresh food wholesale distribution company is provided, which is used for loading a batch of fresh foods of different types into a plurality of fresh containers and delivering the containers to customers. Companies receive a large number of orders from different customers each day. To fulfill these orders, the company first purchases the food product, then arranges for workers to pick the food product and load it into fresh containers, and then sends out a delivery fleet to ship the loaded containers to customers. In order to improve the distribution efficiency, the following requirements need to be met in the article boxing process by enterprises:
1) fresh foods of different customers cannot be contained in the same box;
2) under the same customer, the same fresh food is preferentially put into the same box.
In addition, companies often try to reduce the number of boxes needed in order to save the rental cost of the boxes. In an embodiment of the present invention, the foregoing problems are solved by maximizing the space utilization of each case and maximizing the sum of the initial volumes of the articles contained within the case.
In the embodiment of the present invention, the three-dimensional irregular-shaped object is approximated to the minimum enveloping cube corresponding to the object, that is, the minimum cube capable of exactly and completely wrapping the irregular object is solved as follows: firstly, solving a contained convex polyhedron, namely a three-dimensional convex hull, of the outline of the article represented by the closed irregular article, then, assuming each plane of the convex hull to be coincident with one surface of the obtained enveloping cube, so that the enveloping cube at the moment can be obtained, wherein the article with the smallest volume is the optimal enveloping cube, namely the smallest enveloping cube, and the shape of the article pointed by the subsequent step is the approximate smallest enveloping cube. In the embodiment of the present invention, as shown in fig. 2, it is considered that the irregularly shaped objects are deformable, and the height of the objects is compressed by the extrusion of the objects above during the packing process, so that the actual occupied space of the objects in the box dynamically changes during the packing process. But the volume change of each article must be within a certain reasonable range, otherwise the articles (food and vegetables) are crushed and can not be used any more. To avoid this problem, the embodiment of the present invention needs to limit the height ratio at which each article is compressed to be less than or equal to the maximum compression ratio of the article. The maximum compression ratio refers to the maximum ratio of the height of the article that can be compressed (the compression beyond this value will not be allowed), and the maximum compression ratio of the article can be obtained by measurement or experience, and can be obtained in advance in the embodiment of the present invention, and belongs to known parameters. Based on the above explanation, the embodiment of the present invention first approximates the irregular article to a regular cube, and then converts the three-dimensional boxing problem of the irregular article into the three-dimensional boxing problem of the regular article considering the dynamic change of the volume. The three-dimensional irregularly-shaped object is approximated to a corresponding minimum enveloping cube, and the object has larger volume error under the approximation, so that a compression process is introduced, the object is squeezed to different degrees in the process of being put into a box, the volume of the object after being squeezed is reduced, and the compression characteristics (such as most of vegetables and fruits in fresh food) possibly existing in some special objects in real life are considered by the method, and the volume error after approximation is also reduced.
Based on the above approximate processing of the irregular object, a formal mathematical description of the three-dimensional binning problem of the irregular object is given. Consider a groupnGiven a regular and deformable set of three-dimensional objects, notedI={I 1, I 2 ,…,I n }. The characteristic of each article in the set (after being subjected to approximation, the articles referred to as follows are all regular three-dimensional articles obtained after the approximation, namely, the minimum enveloping cube corresponding to the article) is the depth of each articled i Width, widthw i Initial heighth i Weight, weightm i Compression ratioc i And maximum compression ratior i ，
. The compression ratio is expressed as the ratio of the height variation of an article to the total weight of all articles placed above the article, and the maximum compression ratio is expressed as the maximum ratio of the height of the article which can be compressed, and the two parameters can be obtained according to experience or a large amount of data observation, and are set to avoid damage caused by excessive extrusion of the article. During the packing process, some attributes of the currently loaded items need to be recorded, including the actual height of the items after packing
Actual compression ratio
And the total weight of all articles placed above the current articleu i . The relationship between the above characteristics and attributes satisfies the following equation:
these articles are packed into rectangular parallelepiped boxes of different sizes, including depthDWidth, widthWAnd heightH. Each box is located in a three-dimensional coordinate system, and the origin of coordinates is the lower left-rear corner of the box, i.e. the box is lifted off
. As shown in fig. 3, each article is represented by the position of the vertex coordinate of the lower left rear corner: (x i ,y i ,z i ) Depth, depth ofd i Width, widthw i Actual height
Four attributes.
Maximizing the space utilization of each box and the sum of the initial volumes of the items contained in the boxes can be expressed by the following formula:
wherein the content of the first and second substances,SUthe space utilization rate of the box is shown,IVrepresenting the sum of the initial volumes of the articles contained in the box,d i 、w i 、h i respectively representing articlesiThe depth, width, height of the panel,e i representing an articleiDecision variables of, as articlesiWhen put into a boxe i =1, otherwisee i =0；D、W、HRespectively represents the depth, width and height of the box,nindicating the quantity of the item.
In addition, the formula for maximizing the space utilization rate of the box and the formula for maximizing the initial volume sum of the articles in the box simultaneously meet the following constraint conditions (I) - (II):
weight limitation: the total weight of the articles loaded in the box cannot exceed the maximum bearing weight of the box;
space limitation: articles can be placed only in the box but not outside the box, namely the articles contained in the box cannot exceed the box in the three dimensions of width, depth and height;
(iii) orthogonality: each article is orthogonally arranged in the box, namely the surface of the article is parallel to the box wall;
fourthly, no overlapping: the space occupied by the articles in the box does not intersect;
stability: the loaded articles cannot be suspended in the air, and the bottom surfaces of the articles need to contact the upper surfaces of other articles or the bottom surface of the box;
direction: each article has 6 rectangular faces but only 3 different faces, since the opposite faces are identical, each of the three faces can be rotated orthogonally to obtain a new dimension of the article; thus, each article has 6 different types of rotation, i.e. 6 pendulum orientations, by winding aroundx、yAnd/orzAnd coordinate axis rotation is obtained. The rotation mode is referred to in table 1 below:
table 1 6 different rotation types can be obtained by rotating around different coordinate axes
The embodiment of the invention considers the influence caused by the dynamic change of the volume of the irregular article in the packing process, provides a three-dimensional packing method of the irregular article based on the dynamic change of the volume of the article, establishes a three-dimensional packing model of the dynamic change of the volume of the article, and finally applies an algorithm to the model for experimental analysis.
First, referring to fig. 1, the three-dimensional boxing method of irregular articles comprises the following steps of S1 to S7:
and S1, approximating the three-dimensional irregular-shaped article to be loaded to a corresponding minimum enveloping cube, and setting the compression rate and the maximum compression ratio of the article.
S2, enabling the box to be located in a three-dimensional coordinate system, wherein the origin of coordinates is the vertex of the lower left corner and the lower left corner of the box; each item is represented by its lower left-rear corner vertex coordinates, depth, width, and height attributes.
And S3, sequencing the articles according to the area of the bottom surface from large to small, then sequencing the articles according to the compression rate from large to small, and considering the articles to be loaded into the box in sequence. That is, in the order of the bottom surface area from large to small, the bottom surface areas are the same, and are again ordered in accordance with the compression rate from large to small.
S4, initializing a pivot point list of the empty box, wherein the initialized pivot point list only has one pivot point of a coordinate origin; wherein the pivot points in the list of pivot points are used to determine where the item is loaded in the case.
S5, loading the articles according to the sequence of the step S3, traversing the pivot points contained in the pivot point list when loading each article, trying to place the article on the pivot point, updating the actual height of each article in the box according to the compression rate and the maximum compression ratio of each article in the box and the total weight of all articles placed above each article, and judging whether the article can be placed on the traversed pivot point until the article can be loaded on a certain pivot point. As a constraint, the compression rate and the maximum compression ratio of the article should be considered during the packing process, and the actual compression ratio of the article after packing should not exceed the maximum compression ratio. If the width or depth of the article exceeds the width or depth of the box, the article cannot be placed in the box; if the traversed pivot point is a coordinate point located on the xy-plane of the coordinate system and the height of the item exceeds the height of the case or there is an area where the item overlaps with other items, the item cannot be put into the case; when the item is to be placed on top of other items in the box, calculating and checking whether the actual total height of the item with the other items in the box would exceed the height of the box; if the article is still unable to fit into the case after being compressed, the article cannot be placed into the case. An item that cannot be placed in a box may be added to a list of items that cannot be placed in the box. When each article is loaded, the rotation type that the bottom surface of the object (the surface with the largest area of the article is defined as the bottom surface which is helpful to a certain extent for ensuring the stability of the article when the article is loaded) faces downwards is preferably considered, the bottom surface of the object swings downwards to traverse each pivot point in the pivot point list until the article can be loaded at a certain pivot point in the swing direction that the bottom surface faces downwards, otherwise, the article is rotated to change the swing direction, and the pivot point list is traversed again after each change until the article can be loaded at a certain pivot point. For an article of some kind of rotation, we consider whether the article can be placed on the current pivot point, and the pivot point coordinates and the three-dimensional size of the article are considered to be the location where the article will be placed and the dimensions of the article, respectively, and when the article is to be placed on top of some other article in a box, we need to calculate and check whether the actual total height of the article in the box will exceed the height of the box. When it is determined that the article cannot be placed on the pivot point, the actual height of the article is calculated based on the compressed height ratio of the article and its maximum compressed ratio. Each article is compressed and updated with its actual compression ratio and actual height, as well as the position, total weight, actual compression ratio and actual height of all articles placed above the article. When the item cannot be loaded at any pivot point after all 6 rotation types have been tried, the item is added to the list of items that cannot be loaded into the case, and then step S5 is repeated for the next item to be loaded.
And S6, after an article is loaded, generating a new pivot point, and updating the pivot point list by using the new pivot point. After each item is loaded, new pivot points are created, as shown in FIG. 4, after the first item is loaded into an empty container, new pivot points are createdpX、pY、pZ. Some of the new pivot points created may be ineffective, for example, if an item is placed at that pivot point, the item may be left in the air, i.e., not connectedTouching the upper surface of an object in the box, the new pivot point is not valid and a conversion process is required to convert it to a valid pivot point and add it to the list of pivot points. Referring to FIG. 5-1, after loading the current item N1, point p is the new pivot point created0Is an invalid pivot point (if the top of the lower left and right corners of the subsequent article falls into the box, the article will hang in the air), and the invalid pivot point p needs to be set0Converting into an effective pivot point by the following method: taking an invalid pivot point p0Perpendicular projection point p of the upper surface of the object N2 therebelow1As a translated effective pivot point; if there is no article directly below the non-operative pivot point, as shown in fig. 5-2, then non-operative pivot point p is taken0Perpendicular projection point p of xy plane thereunder1' acts as an effective pivot point after conversion. After this treatment, the articles are loaded into the box without being suspended. All new valid pivot points will be added to the list of pivot points. It should be noted that the pivot point p to the left of the new effective pivot point during subsequent binning2、p2' is still prioritized (over p)1、p1') points under consideration.
S7, sequencing the pivot points in the pivot point list, wherein the sequencing method comprises the following steps: the pivot points are sorted from small to large according to the coordinate value of the z axis of the pivot point, then sorted from small to large according to the coordinate value of the y axis, and finally sorted from small to large according to the coordinate value of the x axis. If the last article is the last article, finishing boxing; otherwise, the step S5 is returned to the next item to be loaded until all items to be loaded are traversed.
Pseudo code for a bin packing algorithm based on dynamic variation of the volume of an item is given below:
where a series of tuples are stored in the list of pivot points, each tuple being used to store one pivot point and an item directly touching below the pivot point, e.g. the tuple with the origin of coordinates as pivot point is stored as ((0,0,0), None), where None represents an item without direct contact below the pivot point.
The three-dimensional irregular article packing method and the three-dimensional irregular article packing model provided by the embodiment of the invention are subjected to numerical experiments and the experimental results are analyzed, and all the experiments are realized by using a Python3 language.
Experimental data
The effectiveness of the method of the present invention was tested in this experiment using randomly generated data, including four different size bins (as shown in table 2) and 4 types of articles (as shown in table 3). The articles are classified into four categories: vegetables (type 0), rice and flour (type 1), melons and fruits (type 2) and other types (type 3), each corresponding to different compression ratios and maximum compression ratios. Table 4 shows an example of candidate items used in the experiment, where we only consider placing items in one box at a time.
TABLE 2 four different types of boxes
TABLE 3 four different types of articles
TABLE 4 candidate items
Results of the experiment
In order to verify the performance of the boxing method proposed by the embodiment of the present invention, an algorithm and a model are tested on an experimental data set in an experiment, and the space utilization rate and the number of loaded articles of each box are compared in consideration of the compression characteristic (with compression) and the non-compression characteristic (with compression) of the articles, as shown in fig. 6 and fig. 7, respectively. As shown in fig. 6, the space utilization factor for boxes of different sizes, taking into account the compression characteristics of the article, is higher to a different degree than the space utilization factor for boxes without taking into account the compression characteristics of the article. Figure 7 shows that the case can accommodate a greater number of articles, taking into account the compression of the articles. The test result shows that compared with the traditional problem under the assumption of constant volume and shape, the problem of object shape change and volume change is considered, so that the space utilization rate of the container can be obviously improved, the packaging cost is further saved, and the operation efficiency is improved.
Table 5 shows the results of the initial volume and actual volume (after compression) of all articles in four boxes with different sizes, the total number of articles loaded and the box space utilization rate of the method proposed by the embodiment of the invention, and the results show that the method proposed by the embodiment of the invention can show better effect in increasing the initial volume of all articles in the boxes.
TABLE 5 comparison of results for compression and non-compression under boxes of different sizes
The third column of table 5, "actual volume of total articles in the box" refers to the sum of the actual volumes of the articles loaded into the box after compression, and the second column, "initial volume of total articles in the box" refers to the sum of the initial volumes (i.e., the original volume sizes) of the articles in the box when not compressed. For the same bin, the larger the "initial volume of total articles in the bin" the better the algorithm performs.
Visualization of packing
In order to more intuitively demonstrate the experimental results, the embodiment of the present invention also visualizes the results using python. Fig. 8 shows a visualization of the results for boxes of different sizes. It can be seen that the visualization scheme of the embodiment of the invention can conveniently provide a proper solution for workers in real time in practice.
Another embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, is capable of implementing the steps of the aforementioned boxing method. A computer readable storage medium may include, among other things, a propagated data signal with readable program code embodied therein, either in baseband or as part of a carrier wave. Such a propagated data signal may take many forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable storage medium may transmit, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer readable storage medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several equivalent substitutions or obvious modifications can be made without departing from the spirit of the invention, and all the properties or uses are considered to be within the scope of the invention.
Claims (10)
1. A three-dimensional boxing method of irregular articles is characterized by comprising the following steps:
approximating the three-dimensional irregular-shaped article to be loaded to a corresponding minimum enveloping cube, and setting the compression rate and the maximum compression ratio of the article; wherein the compression ratio represents a ratio of a variation in height of one article to a total weight of all articles placed above the article, and the maximum compression ratio represents a maximum ratio at which the height of the article can be compressed;
the packing is performed with the compression rate and maximum compression ratio of the articles as constraints and with the goal of maximizing the space utilization of the box and the sum of the initial volumes of the articles packed in the box, based on the dynamic changes in volume of the articles due to the height changes resulting from the compression of the articles by the articles above during the packing process.
2. The three-dimensional packing method of irregular articles according to claim 1, characterized in that the packing is performed with the compression rate and maximum compression ratio of the articles as constraints and with the aim of maximizing the space utilization rate of the box and the sum of the initial volumes of the articles packed in the box, and comprises the following steps:
s1, enabling the box to be located in a three-dimensional coordinate system, wherein the origin of coordinates is the vertex of the lower left corner and the lower left corner of the box; each article is represented by four attributes of vertex coordinates of the lower left rear corner, depth, width and height;
s2, sorting the articles according to the size of the bottom surface, then sorting the articles according to the compression rate, and considering the articles to be loaded into the box in sequence;
s3, initializing a pivot point list of the empty box, wherein the initialized pivot point list only has one pivot point of a coordinate origin; wherein the pivot points in the list of pivot points are used to determine where the item is loaded in the case;
s4, loading the articles according to the sequence of the step S2, traversing the pivot points contained in the pivot point list when loading each article, trying to place the article on the pivot point, updating the actual height of each article in the box according to the compression rate and the maximum compression ratio of each article in the box and the total weight of all articles placed above each article, and judging whether the article can be placed on the traversed pivot point until the article can be loaded on a certain pivot point;
s5, after an article is loaded, generating a new pivot point, and updating the pivot point list by using the new pivot point;
s6, sequencing the pivot points in the pivot point list, wherein the sequencing method comprises the following steps: sorting according to the coordinate value of the z axis of the pivot point from small to large firstly, then sorting according to the coordinate value of the y axis from small to large secondly, and finally sorting according to the coordinate value of the x axis from small to large finally;
and S7, returning to the step S4 for the next item to be loaded until all items to be loaded are traversed.
3. The method for three-dimensional boxing of irregular articles as claimed in claim 2, wherein the step of determining whether the article can be placed on the traversed pivot point in step S4 comprises:
if the width or depth of the article exceeds the width or depth of the box, the article cannot be placed in the box;
if the traversed pivot point is a coordinate point located on the xy-plane of the coordinate system and the height of the item exceeds the height of the case or there is an area where the item overlaps with other items, the item cannot be put into the case;
when the item is to be placed on top of other items in the box, calculating and checking whether the actual total height of the item with the other items in the box would exceed the height of the box; if the article is still unable to fit into the case after being compressed, the article cannot be placed into the case.
4. The method for three-dimensional packing of irregular objects according to claim 2, wherein in step S4, when loading each object, the rotation type of the object with the bottom surface facing downward is preferentially considered, and the object is swung with the bottom surface facing downward through each pivot point in the pivot point list until the object can be loaded with the bottom surface facing downward at a certain pivot point, otherwise, the object is rotated to change the swing direction, and the pivot point list is re-traversed each time the change is made until the object can be loaded at a certain pivot point; when the item cannot be loaded at any pivot point after all 6 rotation types have been tried, the item is added to the list of items that cannot be loaded into the case, and then step S4 is repeated for the next item to be loaded.
5. The method for three-dimensional boxing of irregular articles as set forth in claim 2, wherein the step S5 further comprises: after generating new pivot points, judging whether each new pivot point is effective or not; if the result is valid, directly adding a pivot point list; if not, the pivot point list is added after the invalid pivot point is converted to a valid pivot point.
6. The method for three-dimensional packing of irregular objects according to claim 5, wherein in step S5, if a new pivot point is floating, i.e. not touching the top surface of an object in the box, the new pivot point is invalid.
7. The method for three-dimensional packing of irregular objects according to claim 5, wherein the step of converting the invalid pivot point into the valid pivot point in step S5 comprises:
taking a vertical projection point of the upper surface of an object below the invalid pivot point as a converted valid pivot point; if there is no item directly below the invalid pivot point, the perpendicular projection of the xy-plane with the invalid pivot point below it is taken as the converted valid pivot point.
8. A method for three-dimensional boxing of irregular objects as recited in claim 1, wherein the space utilization of the box and the sum of the initial volumes of the objects contained in the box are maximized, and are formulated as follows:
wherein, the first and the second end of the pipe are connected with each other,SUthe space utilization rate of the box is shown,IVrepresenting the sum of the initial volumes of the articles contained in the box,d i 、w i 、h i respectively representing articlesiThe depth, width, height of the panel,e i representing an articleiDecision variables of, as articlesiWhen put into a boxe i =1, otherwisee i =0；D、W、HRespectively represents the depth, width and height of the box,nindicating the quantity of the item.
9. The three-dimensional boxing method of irregular articles as claimed in claim 8, wherein the formula for maximizing the space utilization rate of the box and the formula for maximizing the total initial volume of the articles contained in the box simultaneously satisfy the following constraints (i) - (sixth):
weight limitation: the total weight of the articles loaded in the box cannot exceed the maximum bearing weight of the box;
space limitation: articles can be placed only in the box but not outside the box, namely the articles contained in the box cannot exceed the box in the three dimensions of width, depth and height;
(iii) orthogonality: each article is orthogonally arranged in the box, namely the surface of the article is parallel to the box wall;
fourthly, no overlapping: the space occupied by the articles within the box does not intersect;
stability: the loaded articles cannot be suspended in the air, and the bottom surfaces of the articles need to contact the upper surfaces of other articles or the bottom surface of the box;
direction: each article has 6 rectangular faces but only 3 different faces, since the opposite faces are identical, each of the three faces can be rotated orthogonally to obtain a new dimension of the article; thus, each article has 6 different types of rotation, i.e. 6 pendular directions, by winding aroundx、yAnd/orzAnd coordinate axis rotation is obtained.
10. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, is adapted to carry out the steps of the three-dimensional binning method according to any of claims 1 to 9.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109761066A (en) * | 2019-03-14 | 2019-05-17 | 宁波大学科学技术学院 | One kind is based on the didactic 3 D Container packing method of combination |
| CN110633930A (en) * | 2018-06-22 | 2019-12-31 | 北京京东振世信息技术有限公司 | Article size determination method and device, storage medium and electronic equipment |
| CN111311145A (en) * | 2020-01-22 | 2020-06-19 | 中国铁路上海局集团有限公司科学技术研究所 | Intelligent assembling method for railway freight |
| CN114581011A (en) * | 2022-03-08 | 2022-06-03 | 南京希音电子商务有限公司 | Packaging consumable recommendation method, device, equipment and storage medium |
-
2022
- 2022-06-09 CN CN202210648831.4A patent/CN114742326A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110633930A (en) * | 2018-06-22 | 2019-12-31 | 北京京东振世信息技术有限公司 | Article size determination method and device, storage medium and electronic equipment |
| CN109761066A (en) * | 2019-03-14 | 2019-05-17 | 宁波大学科学技术学院 | One kind is based on the didactic 3 D Container packing method of combination |
| CN111311145A (en) * | 2020-01-22 | 2020-06-19 | 中国铁路上海局集团有限公司科学技术研究所 | Intelligent assembling method for railway freight |
| CN114581011A (en) * | 2022-03-08 | 2022-06-03 | 南京希音电子商务有限公司 | Packaging consumable recommendation method, device, equipment and storage medium |
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