CN115689240A - Space planning method applied to container loading - Google Patents
Space planning method applied to container loading Download PDFInfo
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- CN115689240A CN115689240A CN202211421228.9A CN202211421228A CN115689240A CN 115689240 A CN115689240 A CN 115689240A CN 202211421228 A CN202211421228 A CN 202211421228A CN 115689240 A CN115689240 A CN 115689240A
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Abstract
The invention relates to the technical field of cargo loading planning, and discloses a space planning method applied to box loading. The invention solves the problems of the prior art that the problem of large-scale carton loading is difficult to solve, the space utilization rate is difficult to further promote when the cartons are loaded, and the like.
Description
Technical Field
The invention relates to the technical field of cargo loading planning, in particular to a space planning method applied to container loading.
Background
With the development of logistics automation, intelligent three-dimensional storage and automatic sorting systems and equipment are widely applied, but the loading and unloading process of a logistics truck on a platform still highly depends on manual work, and at present, no mature automatic loading and unloading system exists in China.
In order to meet the requirements of automatic loading and unloading vehicles of tobacco enterprises, research and development of automatic finished product cigarette box loading systems are carried out in the market, urgent needs are provided for research of loading stack type algorithms in the systems, and the space utilization rate of trucks is maximized while loading efficiency is guaranteed.
Such a problem is called the Container Loading Problem (CLP) in theoretical studies. The container loading problem is a classical combinatorial optimization problem, given a number of three-dimensional boxes of different sizes, loading a subset of the boxes into the container, maximizing the space utilization of the container. The container loading problem is an NP-hard problem. It is an extension of the Knapsack Problem (Knapack Problem) in three-dimensional space: the container loading problem also does not have a polynomial time complexity algorithm, since the knapsack problem itself is an NP-complete problem. Due to the enormous search space of the problem itself, container loading algorithms that solve exact solutions can usually only solve small scale problems. In most of real-world boxing applications, the number of goods is large, so that it is difficult to solve an optimal solution of the problem, and in this case, how to solve an approximate solution (a better solution) in a short time is a key direction for researching the problem. The combination optimization method and the algorithm structure design in the prior art are difficult to solve a better solution of the problem of large-scale carton loading and further improve the space utilization rate of the carton loading.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a space planning method applied to part box loading, and solves the problems that in the prior art, a better solution of the problem of large-scale part box loading is difficult to solve, the space utilization rate during part box loading is difficult to further improve and the like.
The technical scheme adopted by the invention for solving the problems is as follows:
a space planning method applied to box loading aims at the problem of box loading, and solves the maximum space utilization rate by taking box loading sequencing and/or the space placing position of boxes in a truck as decision variables and taking the maximum volume ratio of the boxes as an objective function.
As a preferred technical solution, the constraint factor of the carton loading sequence includes: bottom area, weight, type, number, destination of the box.
As a preferred technical solution, the priority order of the constraint factors of the carton loading sequence is: destination > weight > floor area.
As a preferred technical solution, the objective function is:
wherein T represents the maximum volume ratio of the parts box, m represents the part box number, n represents the total number of the parts box, l m Length, w, of the display box m m Width, h, of the display case m m The height of the display box m, L the length of the loading space of the truck, W the width of the loading space of the truck, and H the height of the loading space of the truck;
the constraint conditions of the space arrangement position of the box in the truck comprise:
and (3) boundary constraint: the goods cannot exceed the boundary size of the loading space of the truck, and the formula is as follows:
wherein x is m Representing the coordinate, y, of the part box numbered m in the X-axis direction of a rectangular spatial coordinate system m Representing the coordinate of the part box numbered m in the Y-axis direction of a rectangular spatial coordinate system, z m And the coordinates of the part box with the number m in the Z-axis direction of the space rectangular coordinate system are shown.
As a preferred technical solution, the constraint conditions of the spatial arrangement position of the container in the truck further include:
carrying and restraining: the total volume and total weight of the loaded goods can not exceed the volume and carrying capacity of the loading space of the truck, and the formula is as follows:
wherein t represents the number of the product gauge, q represents the total number of the product gauge, and f t Number of boxes, g, representing a master t t Weight of the container with the specification t, G total load of the truck, l t Case length, w, of the indicating gauge t t Width of box, h, of the indicating gauge t t Indicating the bin height of the master t.
As a preferable technical solution, the constraint condition of the spatial arrangement position of the container in the truck further includes:
and (3) overlapping constraint: there is no overlap between any two loads, and the formula is:
wherein m and k represent the numbers of any two boxes, and x m Representing the coordinate of the container m in the x-axis, y m Indicating the coordinate of the container m in the y-axis, z m Indicating the coordinate of the component case m in the z-axis, x k Coordinate of the presentation case k in the x-axis, y k Coordinate of the presentation case k in the y-axis, z k Coordinate of the presentation case k in the z-axis, l k Length, w, of the presentation case k k Width, h, of the presentation case k k Indicating the height of the part box k.
As a preferred technical solution, the constraint conditions of the spatial arrangement position of the container in the truck further include:
suspension restraint: the area of the cargo below the suspension can not exceed half of the bottom area of the cargo, wherein the cargo k is below the cargo m, and the formula is as follows:
wherein e represents a proportionality coefficient, and the value range of e is [0,1].
As a preferable technical solution, the constraint condition of the spatial arrangement position of the container in the truck further includes:
and (3) gravity center constraint: the stability of freight train needs to be guaranteed at the in-process that traveles of freight train, consequently needs plus the focus restraint, and the formula is:
wherein the content of the first and second substances,
is the barycentric coordinate of cargo m, (X) G min ，X G max ) For vehicles on the x-axisSafe range of center of gravity in direction (Y) G min ，Y G max ) For the safety range of the center of gravity of the vehicle in the y-axis direction, (Z) G min ，Z G max ) A safe range of the center of gravity of the vehicle in the z-axis direction.
As a preferred technical solution, the constraint conditions of the spatial arrangement position of the container in the truck further include:
the goods clearance constraint has the formula:
wherein dd is the value of the row of remaining gaps equally divided into each gap, dx m A designed goods space.
As a preferable technical solution, the constraint condition of the spatial arrangement position of the container in the truck further includes:
and (3) height difference constraint of a supporting surface:
H ii ≈H jj {H ii -H jj ≤D}
ii,jj∈{1,2,3,...}；
where jj denotes a certain loading plane number, ii denotes a loading plane number of a neighboring layer of the loading plane jj, and H jj Height, H, of the loading plane jj ii The height of the loading plane ii is shown, and D is the designed height difference of the supporting surface; and when the height difference of the loading surfaces of the adjacent layers is less than or equal to D, the adjacent layers are approximate to the same loading plane.
Compared with the prior art, the invention has the following beneficial effects:
(1) According to the warehouse-out order task, the spatial arrangement position of order materials in the truck is determined, and an automatic loading task is formed, so that the space utilization rate is maximized by taking the loading and sorting of the boxes as consideration automatically;
(2) According to the space planning of the container, the coordinate position of each piece of goods is sequentially determined according to a layer-surface-body mode, so that the position of the goods is reasonably planned, the placing direction of the goods, the placing posture of a special container and other factors are considered, the space planning of the container is realized, and the space is saved;
(3) The invention sets various constraints to further improve the space utilization rate of the container loading.
Drawings
FIG. 1 is a schematic view of an automatic loading process;
FIG. 2 is a loading simulation flowchart;
FIG. 3 is a flowchart for determining an order loading sequence;
FIG. 4 is a diagram of simulation results of order container loading;
FIG. 5 is a flowchart of the outbound order scheduling;
FIG. 6 is a basic algorithm flow chart;
FIG. 7 is one of the constraint diagrams;
FIG. 8 is a second schematic diagram of constraints.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited to these examples.
Example 1
As shown in fig. 1 to 8, the automatic loading system mainly completes the automation of delivery of the containers, interacts with the vehicle dispatching system upwards, acquires basic information of the containers and the vehicles, receives orders of delivery of customers, designs an order loading scheme, and executes loading tasks issued by the vehicle dispatching system. And interacting with the automatic loading robot downwards, issuing a loading task and receiving task execution feedback. The automatic loading system mainly comprises:
an interface module: and finishing information interfacing with a vehicle dispatching system.
The vehicle body position measuring and calculating module comprises: and calculating the space size inside the carriage by utilizing technologies such as laser detection, 3D vision and the like, and calculating the relative size between the vehicle body and the loading robot.
The automatic loading calculation module: and planning the space position of the material in the boxcar according to the optimization rule.
A task allocation module: the automatic loading line is a system consisting of a plurality of automatic loading robots, and the automatic loading system manages the automatic loading line in a unified way and issues loading tasks to the loading robots.
A monitoring module: the system and the method have the advantages that the monitoring on the whole automatic loading line is provided, a user can check the running state of each loading robot through the monitoring picture, and the operation on related equipment can be carried out according to the situation.
The automatic loading process is shown in fig. 1, and the following scheme is adopted during specific use:
1. ex-warehouse order simulation:
according to the input order, the loading and sorting of the order and the spatial arrangement position of the order materials in the truck are realized, and the result is visually displayed.
Firstly, analyzing a loading order, extracting information such as size, weight, type, quantity, destination and the like of goods, and determining an initial loading sequence for the goods with the same destination according to the size and weight of the bottom area of the goods, wherein the priority weight is greater than the bottom area. Then the 'box space planning algorithm' is called. And obtaining the ex-warehouse order simulation result. In fig. 1, the outbound order simulation scenario in the confirmed outbound order simulation scenario includes information such as a loading sequence and a loading platform.
The loading simulation process is shown in fig. 2, the process of determining the order loading sequence is shown in fig. 3, and the simulation result of loading the order container is shown in fig. 4.
2. Ex-warehouse order scheduling:
and according to the ex-warehouse order task, determining the spatial arrangement position of the order materials in the truck, and forming an automatic loading task, wherein the automatic loading task can be issued to the automatic loading robot. The outbound order scheduling process is shown in FIG. 5.
3. A box space planning algorithm:
and (4) planning the container space and sequentially determining the coordinate position of each cargo according to a layer-surface-body mode. In order to reasonably plan the position of the goods, the placing direction of the goods and the placing posture of the special container are considered, after each layer of goods is loaded, the loading plane of the next layer of goods is determined, and the stacking range and height are provided for the next layer of goods. The basic algorithm flow is shown in fig. 6. The algorithm input constraint design is shown in fig. 7 and 8.
The constrained mathematical expression is as follows:
a set of Box { } is used to record the coordinates of the loaded goods and the attributes of the length, width, height and kind of the goods. The position coordinate of the cargo m is the lower left corner coordinate (x) of the cargo in the truck m ，y m ，z m ) The coordinates of each point can be obtained according to the length, the width and the height of the box, so that the coordinates of each point of the goods can be known.
1) And (3) boundary constraint: the goods cannot exceed the boundary dimensions of the cargo space of the truck.
x m Representing the coordinate, y, of the part box numbered m in the X-axis direction of a rectangular spatial coordinate system m Representing the coordinate of the part box numbered m in the Y-axis direction of a rectangular spatial coordinate system, z m The coordinate of the container with the number m in the Z-axis direction of the space rectangular coordinate system takes a certain top point on the inner side of the loading space ground of the truck as an original point, the length direction of the loading space of the truck as the X-axis direction, the width direction of the loading space of the truck as the Y-axis direction, and the height direction of the loading space of the truck as the Z-axis direction.
2) Carrying and restraining: the total volume and weight of the load must not exceed the volume and load carrying capacity of the cargo space of the truck.
Wherein t represents the number of the product gauge, q represents the total number of the product gauge, and f t Number of boxes, g, representing the gauge t t Weight of the container with the specification t, G total load of the truck, l t Case length, w, of the indicating gauge t t Width of box, h, of the indicating gauge t t Indicating the bin height of the master t.
3) And (3) overlapping constraint: there is no overlap between any two loads (m, k).
4) Suspension restraint: the area suspended under the cargo cannot exceed half of its own base area, with cargo k under cargo m.
Wherein e is a proportionality coefficient and has a value range of [0,1]Length (x) of goods k above k +l k ) Except for the length (x) of the following cargo m m +l m ) Value of 1 to 2]Width (y) of the upper cargo k k +w k ) Divided by the width (y) of the goods k below m +w m ) Value of 1 to 2]In between.
5) And (3) gravity center constraint: the stability of the truck needs to be ensured in the driving process of the truck, so that the additional gravity center constraint is needed.
Wherein:
is the barycentric coordinate of cargo m, (X) G min ，X G max )，(Y G min ，Y G max )，(Z G min ，Z G max ) The safe range of the center of gravity of the vehicle in the directions of the x axis, the y axis and the z axis is respectively.
6) Similarity of different kinds of goods:
wherein F is a similarity value, is an empirical value and can be designed to be between 0 and 3]In between. F ij F ≦ indicates that the two bins are very similar, approximately equal. F ij Smaller means a higher degree of similarity between the two boxes, F ij The larger the box the greater the degree of difference.
7) And (3) designing goods gaps:
dd is the value of the row of remaining gaps divided equally into each gap, dx m A designed goods space.
8) Height difference of support surface D:
the upper surface of each box is a loading surface, the boxes with the same height can be regarded as the same loading surface, and the height difference of the adjacent loading surfaces is within the design range and can be approximate to the same loading plane.
H ii ≈H jj {H ii -H jj ≤D}
ii,jj∈{1,2,3,...}；
Where jj denotes a certain loading plane number, ii denotes a loading plane number of a neighboring layer of the loading plane jj, and H jj Height, H, of the loading plane jj ii The height of the loading plane ii is shown, and D is the designed height difference of the supporting surface; when the height difference of the loading surfaces of the adjacent layers is less than or equal to D, the adjacent layers can be similar to the same loading plane.
Definition of the objective function:
with the maximum volume fraction of the cargo as the target, the maximum space utilization objective function can be expressed as:
as described above, the present invention can be preferably realized.
All features disclosed in all embodiments in this specification, or all methods or process steps implicitly disclosed, may be combined and/or expanded, or substituted, in any way, except for mutually exclusive features and/or steps.
The foregoing is only a preferred embodiment of the present invention, and the present invention is not limited thereto in any way, and any simple modification, equivalent replacement and improvement made to the above embodiment within the spirit and principle of the present invention still fall within the protection scope of the present invention.
Claims (10)
1. A space planning method applied to a piece box loading truck is characterized in that aiming at the problem of piece box loading, the piece box loading truck sequencing and/or the space placing position of a piece box in a truck are/is used as decision variables, the maximum volume ratio of the piece box is used as an objective function, and the maximum space utilization rate is solved.
2. The space planning method applied to the container loading vehicle according to claim 1, wherein the constraint factor of the container loading sequence comprises: bottom area, weight, type, number, destination of the box.
3. The space planning method applied to the container loading vehicle according to claim 2, wherein the priority order of the constraint factors of the container loading sequencing is as follows: destination > weight > floor area.
4. A space planning method for container loading vehicles according to any one of claims 1 to 3, wherein the objective function is:
wherein T represents the maximum volume ratio of the parts box, m represents the part box number, n represents the total number of the parts box, l m Length, w, of the display box m m Width, h, of the display case m m The height of the display box m, L the length of the loading space of the truck, W the width of the loading space of the truck, and H the height of the loading space of the truck;
the constraint conditions of the space arrangement position of the box in the truck comprise:
and (3) boundary constraint: the goods cannot exceed the boundary size of the loading space of the truck, and the formula is as follows:
wherein x is m Denotes the coordinate, y, of the part case numbered m in the X-axis direction of the rectangular spatial coordinate system m Denotes the coordinate of the part case with the number m in the Y-axis direction of the rectangular space coordinate system, z m And the coordinates of the part box with the number m in the Z-axis direction of the space rectangular coordinate system are shown.
5. The space planning method applied to the container loading vehicle as claimed in claim 4, wherein the constraint condition of the space arrangement position of the container in the truck further comprises:
carrying and restraining: the total volume and total weight of the loaded goods can not exceed the volume and carrying capacity of the loading space of the truck, and the formula is as follows:
wherein t represents the number of the product gauge, q represents the total number of the product gauge, and f t Number of boxes, g, representing the gauge t t Weight of the container with the specification t, G total load of the truck, l t Case length, w, of the indicating gauge t t Width of box, h, of the indicating gauge t t Indicating the bin height of the master t.
6. The space planning method applied to the container loading vehicle according to claim 4, wherein the constraint condition of the space arrangement position of the containers in the truck further comprises:
and (3) overlapping constraint: there is no overlap between any two loads, and the formula is:
wherein m and k represent the numbers of any two boxes, and x m Representing the coordinate of the container m in the x-axis, y m Indicating the coordinate of the container m in the y-axis, z m Indicating the coordinate of the container m in the z-axis, x k Coordinate of the presentation Box k in the x-axis, y k Coordinate of the presentation case k in the y-axis, z k Coordinate of the presentation case k in the z-axis, l k Length, w, of the display case k k Width, h, of the presentation case k k Indicating the height of the part box k.
7. The space planning method applied to the container loading vehicle as claimed in claim 4, wherein the constraint condition of the space arrangement position of the container in the truck further comprises:
suspension restraint: the suspended area below the cargo cannot exceed half of its own bottom area, where cargo k is below cargo m, and the formula is:
wherein e represents a proportionality coefficient, and the value range of e is [0,1].
8. The space planning method applied to the container loading vehicle as claimed in claim 4, wherein the constraint condition of the space arrangement position of the container in the truck further comprises:
and (3) gravity center constraint: the stability of freight train needs to be guaranteed at the in-process that traveles of freight train, consequently needs plus the focus restraint, and the formula is:
wherein the content of the first and second substances,
is the barycentric coordinate of cargo m, (X) Gmin ，X Gmax ) For the safe range of the center of gravity of the vehicle in the x-axis direction, (Y) Gmin ，Y Gmax ) For the safe range of the center of gravity of the vehicle in the y-axis direction, (Z) Gmin ，Z Gmax ) A safe range of the center of gravity of the vehicle in the z-axis direction.
9. The space planning method applied to the container loading vehicle as claimed in claim 4, wherein the constraint condition of the space arrangement position of the container in the truck further comprises:
the goods clearance constraint has the formula:
where dd is the number of the row of remaining gaps evenly divided into each gap, dx m A designed goods space.
10. The space planning method applied to the container loading vehicle according to claim 4, wherein the constraint condition of the space arrangement position of the containers in the truck further comprises:
and (3) height difference constraint of a supporting surface:
H ii ≈H jj {H ii -H jj ≤D} ii,jj∈{1,2,3,...}；
where jj denotes a certain loading plane number, ii denotes a loading plane number of a neighboring layer of the loading plane jj, and H jj Height, H, of the loading plane jj ii The height of the loading plane ii is shown, and D is the designed height difference of the supporting surface; when the height difference of the loading surfaces of the adjacent layers is less than or equal to D, the adjacent layers are approximately the same loading plane.
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