Tower drum factory linear programming method

Through the linear planning method of the tower factory, the tower processing technology is divided and optimized and the site layout is adapted to the high transportation cost of tower processing plants in remote mountainous areas, and the factory is optimized and cost savings are achieved.

CN120235307APending Publication Date: 2025-07-01SINOHYDRO BUREAU 11 CO LTD
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Patent Information

Application Number
CN202510371051.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-03-27
Publication Date
2025-07-01

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Abstract

The invention discloses a tower drum factory linear planning method, and belongs to the technical field of layout planning. Comprising the following steps: a tower drum processing technology segmentation method; a processing technology adaptation method; a processing technology site layout method and a processing technology optimization combination method. The system reduces the investment cost, shortens the construction period, improves the flexibility, and is convenient to move; and the system can be quickly reassembled at different places according to project requirements, so that the mobility and adaptability of a factory are improved.
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Description

Technical Field

[0001] The present invention relates to the technical field of layout planning, and particularly relates to a linear programming method for a tower barrel factory. Background Art

[0002] The tower barrel processing factory is an indispensable part of the wind power field. It undertakes the heavy responsibility of manufacturing the tower barrels of wind turbines and provides solid support for the wind power industry. Especially in this era when high technology and environmental protection concepts go hand in hand, the tower barrel processing factory is leading the development trend of the wind power industry with its unique charm and value.

[0003] The tower barrel processing factory is generally arranged near towns in plain areas, which is convenient for the procurement, transportation and processing of raw materials, as well as the use of human resources. As wind power gradually develops towards remote mountainous areas, many problems have emerged in the original layout plan; mainly manifested as the problem of excessively high transportation costs caused by being far from the installation site, and the one-time use problem of the tower barrel factory, all of which have caused huge costs.

[0004] In view of the above problems, the present invention patent proposes a tower barrel production layout method and a production process optimization method applicable to various plots in remote mountainous areas, which adapt the processing and manufacturing location of the tower barrel factory to the installation site in remote mountainous areas, can greatly reduce transportation costs and transportation risks, and realize the optimized layout and cost savings of the tower barrel factory. Summary of the Invention

[0005] The purpose of the present invention is to propose a linear programming method for a tower barrel factory to achieve the optimized layout and cost savings of the tower barrel factory, etc.

[0006] In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0007] A linear programming method for a tower barrel factory includes the following steps:

[0008] A tower barrel processing technology segmentation method;

[0009] A processing technology adaptation method;

[0010] A processing technology site layout method and a processing technology optimization combination method.

[0011] Preferably, in the tower barrel processing technology segmentation method:

[0012] According to the tower barrel manufacturing process flow, it is divided into 16 process modules: raw material stacking area, marking and cutting area, bevel grinding area, rolling area, longitudinal seam waiting for welding area, longitudinal seam welding area, roundness correction area, unit section storage area, tile assembly area, circumferential seam welding area, accessory welding and installation area, sandblasting area, paint spraying area, internal accessory assembly area of the cylinder, finished tower barrel storage area, and tower barrel protection cover installation area.

[0013] Preferably, in the processing technology adaptation method, the following steps are included:

[0014] Considerations for tower barrel processing technology;

[0015] Measure and collect the on-site equipment occupation data, material storage and transfer data, equipment action range data, and production capacity data according to the integrated tower barrel processing technological process;

[0016] Divide the production process of the tower barrel into units.

[0017] Preferably, the considerations for tower barrel processing technology are as follows:

[0018] The production area area mainly considers: types and floor areas of production equipment, equipment action areas, material stacking area areas, tower barrel tile types, production capacity, cycle, and equipment quantity;

[0019] The raw material stacking area mainly considers: raw material floor area, stacking layers, storage quantity, and stacking height;

[0020] The finished product stacking area mainly considers: tower barrel floor area, storage quantity;

[0021] The moving line area mainly considers: daily incoming and outgoing material vehicles, material hoisting, and personnel safety passages.

[0022] Preferably, the unit division includes: raw material stacking, blanking stacking area, marking and blanking, rolling into a circle, longitudinal seam welding, weld flaw detection inspection, single-section rounding, single-section storage, unit section assembly, groove grinding, circumferential seam welding, circumferential seam flaw detection, internal attachment group welding, grinding, calibration, anti-corrosion, assembly, final inspection, packaging;

[0023] Among them, the blanking stacking area, marking and blanking, unit section assembly, internal attachment group welding, anti-corrosion, and assembly can be parallel with several process lines.

[0024] Preferably, in the processing technology site layout method and the processing technology optimization combination:

[0025] Add constraint conditions and use the process for linear programming optimization.

[0026] Preferably, the constraint conditions include:

[0027] a. Process i objective function 1:

[0028] Q imax = ∑Q(C i , T i );

[0029] Among them, Q is the output; T i is the production cycle of a single process i; C i is the production capacity of a single process i;

[0030] C i = C(M i , P i , m i , A i );

[0031] M i The number of equipment supporting a single process i; P i The number of personnel supporting a single process i; m i The quantity of raw materials supporting a single process i; A i The floor area quantity of a single process i;

[0032] b. Objective function 2 of process i:

[0033] S imin = ∑S(K M M i , K A A i , k m m i , K P P i );

[0034] S constraint function; K M The equipment cost coefficient K of a single process i M = K B + K S ; Consisting of the price cost K B and the depreciation cost K S of the equipment; K A The rental cost coefficient of a single process i due to floor area; K P The personnel wage cost coefficient of a single process i; k m The amortization coefficient of the raw material purchase cost of a single process i;

[0035] c. Constraints of process i:

[0036] A i ≥ A i0 ;

[0037] P i ≥ P i0 ;

[0038] m i ≥ m i0 ;

[0039] M i ≥ M i0 ;

[0040] d. Objective function of the production process:

[0041] Q max = VQimax ;

[0042] S min = VS imin 。

[0043] Preferably, in the process site layout method and the process optimization combination:

[0044] According to the processing process adaptation method, on the premise of known output Q0, production cost C0, personnel allocation P0, and raw material allocation m0, optimize the allocation of the processing process site layout.

[0045] Preferably, the optimization configuration includes the following steps:

[0046] f1), The processing procedure objective function and the constraint calculation formula, substitute the known output Q0, production cost C0, personnel allocation P0, and raw material allocation m0, and use the linear programming method to calculate the minimum value A min and the maximum value A max ;

[0047] f2), Determine the connection relationship between process G i and process G i+1 , and whether process G i can connect multiple processes G i+1 ;

[0048] If process G i and process G i+1 can only correspond one by one, denoted as G i →G i+1 ; If process G i can be followed by multiple processes G i+1 , denoted as Finally, form a relationship set R of processes = ∪R(G i , G i+1 );

[0049] f3), Plot optimization;

[0050] fa1), Traverse the set R;

[0051] fa2), Obtain each process relationship R in the set R j ;

[0052] fa3), Obtain the land use shape of process G j in the process relationship R i and the land use shape of process G and the land use shape of process G i+1 ;

[0053] fa4), Without considering process G i and process Gi+1 The one-to-many relationship is used to connect the land use shapes Land use shape for connection;

[0054] fa5) Traverse all process relationships R j After that, obtain the single-chain long-strip land use shapes of all processes.

[0055] Preferably, the optimization configuration further includes the following steps:

[0056] fa6) Compress the single-chain long-strip land use shape into the actual plot shape;

[0057] Distribute the processes along the plot edge;

[0058] If process G i+1 exceeds the plot edge, place it below process G i ;

[0059] Search for relationships in set R. If there is G i →G i+1 , then process G i+2 is arranged in a Z shape;

[0060] If there is then retain the space below the land use shape for use. When necessary, it can be rotated to adapt to the site requirements; Rotate as needed to fit the site requirements;

[0061] Other spaces bypass the extra and are still arranged in a Z shape until all the sites are occupied;

[0062] fa7) Repeat step fa6 to compress the terrain multiple times until the actual land use area A and A min are closest.

[0063] Compared with the prior art, the present invention provides a linear programming method for a tower barrel factory, having the following beneficial effects.

[0064] 1. The present invention reduces the investment cost; the modular design of the nomadic tower barrel factory can greatly reduce the investment cost of factory construction; because each module can be reused as needed, the investment in fixed facilities is reduced.

[0065] 2. The present invention shortens the construction period: Since each module can be independently manufactured and transported, and can be quickly assembled and disassembled, the construction period of the factory can be greatly shortened.

[0066] 3. The present invention improves flexibility: The modular design of the nomadic tower barrel factory enables the factory to have higher flexibility and can quickly adjust the production scale and product type according to market demands.

[0067] 4. The present invention is convenient for movement: Since each module can be moved independently, the factory can be quickly reassembled at different locations according to project requirements, improving the mobility and adaptability of the factory.

[0068] Other advantages, objectives, and features of the present invention will, to some extent, be elaborated in the subsequent specification; and to some extent, will be obvious to those skilled in the art based on the study of the following text; or can be learned from the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a schematic diagram of the present invention.

[0070] Figure 2 It is a schematic diagram of the process module.

[0071] Figure 3 It is a schematic diagram of the unit division.

[0072] Figure 4 It is a schematic diagram of the shape of a single-chain long strip of land.

[0073] Figure 5 It is a schematic diagram of the Z-shaped arrangement.

[0074] Figure 6 It is a schematic diagram of the rotation.

[0075] Figure 7 It is a schematic diagram of the optimization of regular plots.

[0076] Figure 8 It is a schematic diagram of the optimization of irregular plots.

[0077] Figure 9 It is a schematic diagram of the original scheme 1.

[0078] Figure 10 It is a schematic diagram of the original scheme 1 (partial enlargement).

[0079] Figure 11 It is a schematic diagram of the optimized scheme 2.

[0080] Figure 12 It is a schematic diagram of the optimized scheme 2 (partial enlargement).

[0081] Figure 13 It is a schematic structural diagram of the optimized scheme 3.

[0082] Figure 14 It is a schematic diagram of the optimized scheme 3 (partial enlargement). Specific Embodiments

[0083] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0084] Referring to Figure 1-8 , a linear programming method for a tower barrel factory includes the following steps:

[0085] Tower barrel processing technology segmentation method;

[0086] Processing technology adaptation method;

[0087] Processing technology site layout method and processing technology optimization combination method.

[0088] In the tower barrel processing technology segmentation method:

[0089] Referring to Figure 2 ; It is divided into 16 process modules according to the tower barrel manufacturing process flow: raw material stacking area, marking and cutting area, bevel grinding area, rolling area, longitudinal seam waiting for welding area, longitudinal seam welding area, roundness correction area, unit section storage area, tile assembly area, circumferential seam welding area, accessory welding and installation area, sandblasting area, paint spraying area, in-barrel accessory assembly area, finished tower barrel storage area, and tower barrel protective cover installation area.

[0090] Each module has an independent function and structure and can be assembled and disassembled as needed.

[0091] In the processing technology adaptation method, it includes the following steps.

[0092] Consideration factors for tower barrel processing technology;

[0093] Measure and collect on-site equipment occupation data, material storage and transfer data, equipment action range data, production capacity data, etc. according to the integrated tower barrel processing process flow.

[0094] Table 1 Tower Barrel Processing Technology Unit Table

[0095]

[0096]

[0097] According to the above steps, divide the production process of the tower barrel into units.

[0098] Consideration factors for tower barrel processing technology are as follows:

[0099] The production area size mainly considers: the types and floor areas of production equipment, the areas where the equipment functions, the floor area of the material stacking area, the types of tower barrel tiles, production capacity, cycle, and the number of equipment.

[0100] The raw material stacking area mainly considers: the floor area of the raw materials, the number of stacking layers, the storage quantity, and the stacking height.

[0101] The finished product stacking area mainly considers: the floor area of the tower barrel and the storage quantity.

[0102] The moving line area mainly considers: the daily incoming and outgoing vehicles for materials, material hoisting, personnel safety passages, etc.

[0103] The unit division includes: raw material stacking, cutting stock stacking area, marking and cutting stock, rolling into a circle, longitudinal seam welding, weld flaw detection inspection, single-section rounding, single-section storage, unit section assembly, bevel grinding, circumferential seam welding, circumferential seam flaw detection, internal attachment group welding, grinding, calibration, anti-corrosion, assembly, final inspection, and packaging.

[0104] Among them, the cutting stock stacking area, marking and cutting stock, unit section assembly, internal attachment group welding, anti-corrosion, and assembly can have several process lines running in parallel.

[0105] Such as Figure 3 shown; the plus sign represents the positions where several process lines can run in parallel.

[0106] In the processing technology site layout method and the optimized combination of processing technologies: Add constraints such as floor area, labor, and unit cost, and use the following process for linear programming optimization.

[0107] The constraints include:

[0108] a. Objective function 1 for process i:

[0109] Q imax = VQ(C i , T i )

[0110] Among them, Q is the output; T i is the production cycle of a single process i; C i is the production capacity of a single process i.

[0111] C i = C(M i , P i , m i , A i )

[0112] M i is the number of equipment supporting a single process i; P i is the number of personnel supporting a single process i; m i is the number of raw materials supporting a single process i; A iFloor area quantity of a single process i.

[0113] b. Objective function 2 of process i:

[0114] S imin = VS(K M M i , K A A i , k m m i , K P P i );

[0115] S constraint function; K M Equipment cost coefficient K of a single process i M = K B + K S ; Composed of the price cost K of the equipment B and the depreciation cost K S ; K A Rental cost coefficient of a single process i due to floor area; K P Labor cost coefficient of a single process i; k m Amortization coefficient of raw material purchase cost of a single process i.

[0116] c. Constraints of process i:

[0117] A i ≥ A i0 ;

[0118] P i ≥ P i0 ;

[0119] m i ≥ m i0 ;

[0120] M i ≥ M i0 .

[0121] d. Objective function of the production process:

[0122] Q max = ∑Q imax ;

[0123] S min = ∑S imin .

[0124] In the process site layout method and process optimization combination:

[0125] According to the processing technology adaptation method, under the premise of known production quantity Q0, production cost C0, personnel configuration P0, and raw material configuration m0, optimize the configuration of the processing technology site layout.

[0126] The optimization configuration includes the following steps.

[0127] f1), Calculate the processing procedure objective function and constraint calculation formula, substitute the known output Q0, production cost C0, personnel allocation P0, and raw material allocation m0, and use the method of linear programming to calculate the minimum value A of the site area min and the maximum value A max .

[0128] f2), Determine the connection relationship between process G i and process G i+1 , and whether process G i can be connected to multiple processes G i+1 .

[0129] If process G i and process G i+1 can only correspond one by one, record it as G i →G i+1 ; if process G i can be connected to multiple processes G i+1 behind it, record it as Finally, form a relationship set R of processes = ∪R(G i , G i+1 ).

[0130] f3), Plot optimization:

[0131] fa1), Traverse the set R;

[0132] fa2), Obtain each process relationship R in the set R j ;

[0133] fa3), Obtain the land use shape of process G j in the process relationship R i land use shape of process G land use shape of process G i+1 land use shape of process G

[0134] fa4), Without considering the one-to-many relationship between process G i and process G i+1 , connect the land use shapes land use shape ;

[0135] fa5), After traversing all process relationships R j ends, obtain the single-chain long-strip land use shapes of all processes; as Figure 4 shown.

[0136] It also includes:

[0137] fa6) Compress the single-chain long-strip land shape into the actual plot shape.

[0138] Distribute the processes along the plot edge. If process G i+1 extends beyond the plot edge, place it below process G. i Below;

[0139] Search for relationships in set R. If there is G i →G i+1 , then arrange process G i+2 in a Z-shape; as Figure 5 shown;

[0140] If there is then retain the space below the land shape for use. Rotate it if necessary to adapt to the site requirements; as shown; Other spaces bypass the extra Figure 6 and still arrange in a Z-shape until all the sites are occupied.

[0141] fa7) Repeat step fa6 to compress the terrain multiple times until the actual land area A and A are closest.

[0142] fa7) Repeat step fa6 to compress the terrain multiple times until the actual land area A and A min are closest.

[0143] Utilize the optimization results of the EvolveLAB plug-in of Revit for the plot, as Figure 7 , 8 shown; among them, Figure 7 is the optimization result of the regular plot, Figure 8 is the optimization result of the irregular plot.

[0144] This method case.

[0145] As Figure 9 , 10 shown; Original plan 1:

[0146] Areas A and B (raw material stacking area, marked cutting area, bevel grinding area), Area C (steel plate cutting and storage area, rolling area), Area D (longitudinal seam welding area, straightening area, single pipe section storage area), Area E (flange stacking area, tile assembly area, circumferential seam welding area), Area F (attachment assembly welding and installation area), Area G (sandblasting and painting area), Area H (finished tower barrel storage area).

[0147] Two steel plate cutting production lines are arranged in Areas A and B, and the bevel grinding area is located in the middle of the two steel plate cutting areas for easy bevel production. Two gantry cranes are arranged in this area; Two longitudinal seam welding lines in Area D, with improved production capacity to meet the requirements of front and back processes. The workshop (Areas ABCDE) is arranged compactly, with a floor area of 9324 m2 , but the blanking storage area and bevel preparation area are within the radiation ranges of two gantry cranes, making it somewhat difficult for hoisting and transfer.

[0148] Such as Figure 11 , 12 shown; Optimization Plan 2:

[0149] Area A (raw material stacking area, steel plate blanking storage area), Area B (raw material stacking area, marked blanking area, flange stacking area), Area C (bevel grinding area, rolling area), Area D (longitudinal seam welding area, straightening area), Area E (tile assembly area, circumferential seam welding area), Area F (attachment welding and installation area), Area G (sandblasting and painting area), Area H (finished tower barrel storage area). The overall layout of the site is in an "L" shape (as Figure 11 shown) and a "one" shape (as Figure 12 shown). The workshop (Areas ABCDE) is compactly arranged, covering an area of 5200 m 2 .

[0150] Such as Figure 13 , 14 shown; Optimization Plan 3:

[0151] One side of Area A is the steel plate blanking storage area. One gantry crane is arranged in each of Areas A and B; The bevel grinding and rolling in Area C are in the same area, facilitating rolling; Two longitudinal seam welding lines are arranged in Area D to meet the rolling progress; The single-section tile storage area in Area E is nearly 700 m 2 , meeting the pre-assembly requirements.

[0152] After planning each area according to the above plan, area modules can be formed, and each module has mobility and flexibility.

[0153] The present invention has at least the following advantages:

[0154] Reducing investment costs: The modular design of the nomadic tower barrel factory can significantly reduce the investment costs for factory construction; Because each module can be reused as needed, the investment in fixed facilities is reduced;

[0155] Shortening the construction period: Since each module can be independently manufactured and transported, and can be quickly assembled and disassembled, the construction period of the factory can be greatly shortened;

[0156] Improving flexibility: The modular design of the nomadic tower barrel factory can make the factory have higher flexibility and can quickly adjust the production scale and product type according to market demand;

[0157] Facilitating movement: Since each module can be independently moved, the factory can be quickly reassembled at different locations according to project requirements, improving the mobility and adaptability of the factory.

[0158] As described above, it is only the preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, making equivalent substitutions or changes should be covered within the protection scope of the present invention.

[0159] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A tower plant linear programming method, characterized in that: The following steps are involved: Tower processing technology segmentation method; Processing technology adaptation method; Processing technology site layout method and processing technology optimization combination method.

2. The tower plant linear programming method according to claim 1, characterized in that: In the tower processing technology segmentation method: According to the tower manufacturing process, it is divided into 16 process modules: raw material stacking area, marking and cutting area, bevel grinding area, rounding area, longitudinal seam waiting for welding area, longitudinal seam welding area, rounding correction area, unit section storage area, tile assembly area, circumferential seam welding area, accessory welding and installation area, sandblasting area, paint spraying area, inner tube accessory assembly area, finished tower storage area, tower protection cover installation area.

3. The tower plant linear programming method according to claim 1, characterized in that: The processing technology adaptation method includes the following steps: Tower machining process considerations; According to the integrated process flow of tower processing, the on-site equipment land occupation data, material storage and transportation data, equipment range data, and production capacity data are measured and collected; Divide the tower production process into units.

4. The tower plant linear programming method according to claim 3, characterized in that: The tower processing technology considerations are as follows: The production area mainly considers: the type of production equipment and floor space, equipment function area, material storage area, tower tile type, production capacity, cycle and equipment quantity; The main considerations for the raw material stacking area are: raw material floor space, number of stacking layers, storage volume and stacking height; The main considerations for the finished product storage area are: tower floor space and storage capacity; The main considerations for the traffic area are: daily material entry and exit vehicles, material lifting, and personnel safety passages.

5. The tower plant linear programming method according to claim 3, characterized in that: Unit division includes: raw material stacking, material stacking area, marking and cutting, rolling, longitudinal seam welding, weld flaw detection, single section rounding, single section storage, unit section assembly, groove grinding, girth welding, girth flaw detection, internal accessory assembly welding, grinding, calibration, anti-corrosion, assembly, final inspection, and packaging; Among them, the material stacking area, marking and unloading, unit section assembly, internal accessory welding, anti-corrosion and assembly can be carried out in parallel on several process lines.

6. The tower plant linear programming method according to claim 1, characterized in that: In the layout method of processing technology site and the optimization combination of processing technology: Add constraints and use the process for linear programming optimization.

7. The tower plant linear programming method according to claim 6, characterized in that: The constraints include: a. Objective function 1 of process i: Q imax =∑Q(C i ,T i ); Among them, Q is the output; T i Single process i production cycle; C i Production capacity of a single process i; C i =C(M i ,P i ,m i ,A i ); M i The number of equipment for a single process i; P i Number of personnel supporting a single process i; m i The number of raw materials for a single process i; A i The amount of floor space occupied by a single process i; b. Objective function 2 of process i: S imin =∑S(K M M i ,K A A i ,k m m i ,K P P i ); S constraint function; K M Equipment cost coefficient K for a single process i M =K B +K S ; The price cost of the equipment K B and depreciation cost K S Composition: K A K is the rental cost coefficient of a single process i due to the floor space occupied; P The salary cost coefficient of the personnel in a single process i; k m Amortization coefficient of raw material purchase cost for single process i; c. Process i constraints: A i ≥A i0 ; P i ≥P i0 ; m i ≥m i0 ; M i ≥M i0 ; d. Objective function of the production process: Q max =VQ imax ; S min =VS imin 。 8. The tower plant linear programming method according to claim 7, characterized in that: In the process site layout method and process optimization combination: According to the processing technology adaptation method, the processing technology site layout is optimized on the premise of known output Q0, production cost C0, personnel allocation P0, and raw material allocation m0.

9. The tower plant linear programming method according to claim 8, characterized in that: The optimization configuration includes the following steps: f1), the objective function and constraint calculation formula of the processing procedure, bring in the known output Q0, production cost C0, staff allocation P0, raw material allocation m0, and use the linear programming method to calculate the minimum value A of the site area min and the maximum value A max ; f2) Determine process G i and process G i+1 The connection relationship and process G i Can multiple processes be connected? i+1 ; If process G i and process G i+1 There can only be one-to-one correspondence, recorded as G i →G i+1 ; If process G i Multiple processes can be connected later G i+1 , denoted as Finally, a process relation set R = ∪R(G i ,G i+1 ); f3), plot optimization; fa1), traverse the set R; fa2) Get each process relationship R in the set R j ; fa3) Get process relationship R j Middle process G i The shape of the land Process G i+1 The shape of the land fa4) Ignore process G i and process G i+1 A one-to-many relationship between the land shape Land shape To connect; fa5) Traverse all process relationships R j After completion, a single-chain long strip of land shape is obtained for all processes.

10. The tower plant linear programming method according to claim 9, characterized in that: The optimization configuration also includes the following steps: fa6) Compress the single-chain long strip land shape into the actual land shape; Distribute the processes along the edges of the plot; If process G i+1 If it exceeds the edge of the plot, it will be placed in process G i below; Find a relation in set R, if there is a relation G i →G i+1 , then process G i+2 Arrange in a Z shape; If exists The shape of the land is retained The space below is Use, if necessary Rotate to suit venue needs; Other spaces bypass the extra Still arrange in Z shape until all the places are occupied; fa7) Repeat step fa6 to compress the terrain several times until the actual land area A and A min The closest so far.