Rectangular one-step layout optimization method and system considering template replication

Abstract

The invention belongs to the technical field of blanking layout of plate materials, and discloses a rectangular one-step layout optimization method and system considering template replication, and the method comprises the steps: (1) initializing a solution set; (2) grouping: dividing the parts with the same number into a set and combining the sets to form block parts; (3) calculating a to-be-layout part subset which can be subjected to template copying at present and the corresponding template copying times of the to-be-layout part subset; (4) calling a one-cut layout algorithm based on tree search to construct a layout result of the one-cut constraint on the current template, and performing iteration until the layout of the current plate is completed; (5) copying the current template and updating the part sequence after stock layout is completed; (6) the remaining parts which cannot be subjected to template copying are subjected to stock layout again; (7) optimizing a part sequence, a part combination mode and template copying times; and (8) producing a new solution set until an iteration termination condition is met. According to the invention, the parts to be subjected to stock layout are uniformly distributed on the plate, so that high efficiency of template copying is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of blanking layout of plate materials, and more specifically, relates to an optimization method and system for rectangular one-cut blanking layout considering template replication. Background Technique

[0002] It is found in the investigation that in the production of plate materials in industries such as furniture and containers, blanking layout is the first process in the manufacturing process. Enterprises hope to achieve a high material utilization rate while minimizing the number of blanking layout templates for the plates. First, changing the layout template requires changing the cutting program and the clamping method of the plates on the equipment, which will increase the cutting cost and labor cost and result in low production efficiency. Second, in some manufacturing industries, plates with the same layout template can also be cut simultaneously. When blanking, several plates can be stacked together and cut simultaneously by a single machine for plates with the same template to improve the cutting efficiency. Therefore, reducing the number of layout templates has important practical significance and application value, helping enterprises reduce the total production cost and improve the production efficiency during production.

[0003] Currently, the research on rectangular layout is relatively extensive and in-depth. The solution algorithms for rectangular layout mainly include exact algorithms, heuristic algorithms, and meta-heuristic algorithms (intelligent algorithms). Among them, intelligent algorithms are the current mainstream development direction. However, there is little research on considering template replication. Currently, there are studies starting to consider optimization algorithms for reducing the number of layout methods, but there are two deficiencies in the problems they consider: First, the research direction on considering template replication mainly focuses on the rectangular layout problem without the one-cut constraint; Second, the problems solved are mainly small-scale problems and are not suitable for solving the large-scale rectangular one-cut blanking layout problems in industries such as furniture and containers. Therefore, there is an urgent need to develop a layout optimization method to improve production efficiency. Summary of the Invention

[0004] In view of the above defects and improvement requirements of the prior art, the present invention provides an optimization method and system for rectangular one-cut blanking layout considering template replication. Its purpose is to maximize the material utilization rate while realizing the layout optimization of large-scale rectangular one-cut blanking by considering template replication, improve the production efficiency, and reduce the production cost.

[0005] To achieve the above object, according to one aspect of the present invention, the present invention first provides an optimization method for rectangular one-cut blanking layout considering template replication, and the method includes the following steps:

[0006] (1) Input the part specifications, quantities, and the number of plates, and initialize the solution set;

[0007] (2) Group the rectangular parts to be nested according to their quantity. Parts with the same quantity are divided into a set. At the same time, parts with the same length or width within the set are combined to form block parts;

[0008] (3) Calculate the maximum number of template replications C that the current nesting parts can be replicated based on the part area and the sheet area. If the ratio of the part area to the sheet area does not reach the preset ratio λ, then decrease the maximum number of template replications C. Thus, calculate the subset of parts to be nested that can be template-replicated currently and its corresponding number of template replications C1;

[0009] (4) Select the subset of parts to be nested that can be template-replicated and call the one-cut nesting algorithm based on tree search to construct the nesting result with one-cut constraints on the current template, and iterate until the current sheet is completely nested;

[0010] (5) After calculating the one-cut nesting result of a complete sheet, copy the current template and update the part sequence until all parts that can be template-replicated are nested and then continue to execute the next step. Otherwise, return to step (2);

[0011] (6) Call the one-cut algorithm based on tree search to nest the remaining parts that cannot be template-replicated;

[0012] (7) Considering the number of templates and the sheet utilization rate comprehensively, optimize the part order, part combination method, and C1 according to the current nesting result;

[0013] (8) Generate a new solution set until the iteration termination condition is met and output the final nesting result. Otherwise, continue to execute step (7).

[0014] Preferably, in step (2), when parts with the same length or width within the same set are combined to form block parts, set K as the upper limit of part combination, and K = 4, that is, at most only 4 parts are allowed to be combined into a block.

[0015] Preferably, in step (3), the algorithm for generating the subset of parts to be nested that can be template-replicated is as follows: First, calculate the theoretical maximum number of templates C that the current nesting parts can be replicated by dividing the total part area by the area of a single sheet. If the requirement that the ratio of parts to the sheet on a single sheet is >λ is not met, then decrease the maximum number of templates C to re-determine the number of parts on the sheet until the requirement is met and output the current subset of parts to be nested.

[0016] Preferably, in step (4), the one-cut nesting algorithm based on tree search includes the following steps:

[0017] S41: Initialize the sheet to be nested. At each node in the tree search process, check if the sheet has been completely nested. If so, end the algorithm process; otherwise, continue with the next step.

[0018] S42: Select the last sheet B in the sheet sequence, and calculate the fitness value of each part in the part set obtained by the subset production algorithm for the parts to be nested.

[0019] S43: Select the part with a high fitness value and place it on the current sheet. Then, divide the sheet horizontally or vertically to form new sheets B1 and B2. Delete sheet B from the sheet sequence, and add the new sheets B1 and B2 to the end of the sheet sequence.

[0020] S44: Recursively search and backtrack. Recursively call the one - cut nesting algorithm based on tree search on the new sheet sequence to find the optimal solution. If the current division and placement method cannot find a solution, return to S43 and continue to try the next part in the candidate subset or another division method; if there are no parts or sheets that can be selected in S43, the algorithm ends.

[0021] Preferably, a fitness value function f(i, B) for a part is defined to evaluate the matching degree between the part to be nested and the current sheet to be nested. The part fitness function is expressed as shown in Equation (1):

[0022]

[0023] In Equation (1), w i and h i represent the width and height of the part, w B and h B represent the width and height of the sheet, N i represents the quantity of this part, M i represents the number of parts that the block of parts is composed of; α, β, and Q i are all adjustment coefficients.

[0024] Preferably, in step (5), after a sheet is completely nested and before copying the current template and updating the part sequence, calculate whether the sheet meets the requirement of the single - sheet utilization rate; if there are still remaining parts after updating the part sequence, this part of the parts will be separately called the one - cut algorithm based on tree search for nesting on a new sheet or on the remaining material of the previously copied template.

[0025] Preferably, in step (7), retain the elite individuals in the current nesting result. The elite individuals are the top 20% of the individuals with the highest fitness values.

[0026] Preferably, in step (7), a fitness function F(x) is used to comprehensively consider the utilization rate of the sheet and the production efficiency. Among them, the utilization rate of the sheet is converted into the number of sheets used and defined as SheetNum, and the production efficiency is defined as the number of template types CopyNum of the template copied. The fitness function F(x) is shown in Equation (2):

[0027]

[0028] where ω and θ are cost coefficients. ω represents the cost generated by using one more sheet, and θ represents the cost generated by replacing the template once.

[0029] According to the second aspect of the present invention, the present invention also provides a rectangular one - cut nesting optimization system considering template replication. The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the above - mentioned rectangular one - cut nesting optimization method considering template replication.

[0030] According to the last aspect of the present invention, the present invention also provides a computer - readable storage medium. The computer - readable storage medium stores machine - executable instructions. When the machine - executable instructions are called and executed by the processor, the machine - executable instructions cause the processor to implement the above - mentioned rectangular one - cut nesting optimization method considering template replication.

[0031] Generally speaking, compared with the prior art by the above - mentioned technical solution conceived by the present invention, the following beneficial effects are mainly achieved:

[0032] 1. The rectangular one - cut nesting optimization method considering template replication provided by the present invention designs a fitness value function that comprehensively considers the least number of sheets used and the least number of template types during the iteration process. While efficiently implementing the rectangular one - cut nesting, the number of templates for nesting is considered as an important parameter index. At the same time, when designing the template replication algorithm, it is considered to evenly distribute the parts to be nested on the current sheet to achieve the high efficiency of template replication, and obtain a solution with fewer template types, breaking the situation where the nesting method on each sheet is different generated by manual nesting or ordinary rectangular one - cut nesting, making the nesting result more in line with the actual needs of large - batch production of enterprises, reducing the production cost of enterprises, and improving the production efficiency.

[0033] 2. In the preferred method of the present invention, it can systematically explore all possible placement and segmentation combinations, and add the generated new space to the sheet sequence, ensuring a comprehensive search of the solution space, improving the utilization rate of the sheet space. At the same time, through the backtracking mechanism, it can be terminated in time when it is determined that a certain search path cannot generate a better solution, reducing unnecessary calculations.

[0034] 3. In the preferred method of the present invention, when performing the one - cut nesting, it is only necessary to sort the fitness values of the part sequences in the subset of parts to be nested. Compared with optimizing all part sequences, the preferred method of the present invention can further adapt to the nesting of a large number of parts.

[0035] 4. In the preferred method of the present invention, by defining the fitness value function of parts, the size, quantity of parts and the matching degree between parts and the current nesting sheet are comprehensively considered. After obtaining the nesting result, the fitness values of parts will be dynamically adjusted to ensure that the parts on the sheet with lower utilization rate can have a certain priority in the subsequent nesting process. At the same time, adjusting the number of new template copies and the combination method of parts helps the algorithm explore more nesting schemes, thus avoiding falling into local optimal solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic flow chart of a rectangular one - cut nesting optimization method considering template replication provided by the present invention.

[0037] Figure 2 It is a schematic diagram of the grouping and combination of parts to be nested provided by the present invention.

[0038] Figure 3 It is a schematic diagram of the one - cut constraint cutting method provided by the present invention.

[0039] Figure 4 It is a schematic diagram of the tree - search construction one - cut algorithm provided by the present invention.

[0040] Figure 5 It is a schematic diagram of the result of template nesting provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0041] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0042] The embodiment of the present invention provides a rectangular one - cut nesting optimization method considering template replication, and its flow chart is as Figure 1 shown. A rectangular one - cut nesting optimization method considering template replication includes the following steps:

[0043] (1) Input the part specifications, quantities and the number of sheets, and initialize the solution set;

[0044] Specifically, input the lengths, widths and quantities of 10 kinds of parts asFigure 2 as shown in a of ; the length and width of the input sheet material, and the number of single - specification sheets is not limited. Initialize the solution set, set the capacity of the solution set to 10, and continuously update the solution set during the subsequent optimization process.

[0045] (2) Group the rectangular parts to be nested according to the quantity, divide the parts with the same quantity into a set, and at the same time combine the parts with the same length or width within the set to form block parts;

[0046] Specifically, group the rectangular parts to be nested according to the quantity, divide the parts with the same quantity into a set, and combine the parts with the same length or width within the same set to form block parts. Such a combination method can ensure that the parts meet the one - cut constraint. Set a K as the upper limit of part combination. Assume K = 4, that is, at most 4 parts can be combined into a block; the setting of K is an important parameter. If it is too large, the convergence speed will be too slow. If it is too small, the better solution may be missed. Different values can be set according to different actual situations.

[0047] In this specific embodiment, there are a total of 10 types of parts. According to the grouping and combination, a new combination of block parts is finally obtained, as Figure 2 shown in b of .

[0048] (3) Calculate the maximum number of template replications C that the currently nested parts can be replicated according to the part area and the sheet material area. If the ratio of the part area to the sheet material area does not reach the preset ratio λ, then decrease the maximum number of template replications C. Thus, calculate the subset of parts to be nested that can be template - replicated currently and its corresponding number of template replications C1;

[0049] Specifically, only when the number of parts is greater than or equal to 2 is it possible to be a replicated part. The maximum number of template replications C is calculated by dividing the total area of all parts that can be replicated by the area of a single sheet. According to the maximum number of template replications C, the number of each part on the sheet can be obtained, and the remaining parts are put into the next template. The λ value is used to judge whether the selected parts can fill the current sheet. If the calculation result is equal to 1, it means that the total area of the currently selected parts is the same as the area of the sheet. Usually, λ>1 is set. If the calculation result is less than λ, the maximum number of template replications C needs to be reduced to obtain a new set of parts to be placed on the current sheet until the calculation result is greater than or equal to λ, obtaining the subset of parts to be nested that can be template - replicated and its corresponding number of template replications C1. The subset of parts to be nested is the specification and quantity of the parts nested in the current template.

[0050] Among them, if C = 1, it means that all current parts are arranged on one sheet of plate. If C = 0, it means that all current parts cannot fill the current sheet of plate, and these parts are directly added to the non-replicated part set, and the current algorithm ends.

[0051] In this embodiment, the method for selecting the subset of parts to be arranged with template replication is as Figure 3 shown, and mainly includes the following steps:

[0052] S31: Initialize the part candidate set;

[0053] S32: Calculate the initial maximum template replication times C by dividing the total area of all parts that can be replicated by the area of a single sheet of plate. The calculation formula is as follows:

[0054]

[0055] where w i , h i represent the width and height of the i-th part in the set of parts to be arranged, and W, H represent the width and height of a single sheet of plate.

[0056] S33: When the current maximum template replication times is C, all parts with a quantity greater than or equal to C will have the opportunity to be arranged on the plate. Calculate the quantity Num i of each part arranged on the current plate, that is, divide the quantity of the part by the maximum template replication times C and round down to an integer. The calculation formula is as follows:

[0057]

[0058] where n i represents the total quantity of the i-th part in the set of parts to be arranged.

[0059] S34: Judge whether the ratio of the total area of the currently selected parts to the area of the plate meets the requirements. If it exceeds the set λ value, it means that the requirements are met, and continue to execute the next step. Otherwise, decrement C by 1 and return to execute step S33;

[0060] S35: Output the final part candidate set and the template replication times C1.

[0061] (4) Select the subset of parts to be arranged and call the one-cut nesting algorithm based on tree search to construct the nesting result with one-cut constraints on this template, and iterate until the current plate is completely nested. Otherwise, continue to select new parts to be arranged and execute the one-cut algorithm of tree search;

[0062] Specifically, for the one - cut nesting algorithm based on tree search, first, sort the current subset of parts to be nested according to the part fitness value, select the part with the largest fitness value, and try to place each selected part in the space. Split the space into two new spaces by horizontal or vertical cutting, and recursively call itself on the new space list.

[0063] As Figure 3 shown in a of Figure 3 and b of Figure 3 , splitting the space into two new spaces in this cutting manner can make the nesting result meet the one - cut constraint. The formed B1 and B2 will be added as new sheets to the end of the sheet sequence and given priority for use next time, as Figure 3 shown in c of

[0064] and d of Figure 4 . B1 and B2 are further split to produce B11, B12, B21, and B22; B3 and B4 are also re - split.

[0065] S41: Initialize the sheet sequence to be nested. At each node in the tree - search process, check if the sheet has been completely nested. If so, the algorithm ends; otherwise, continue to the next step.

[0066] S42: Select the last sheet B in the sheet sequence, calculate the fitness value of each part in the part set obtained by the part - nesting algorithm for the subset of parts to be nested, and sort them from high to low.

[0067] S43: Select the part with a high fitness value. Judge whether it can be placed in the current sheet. If it can, split the sheet by horizontal or vertical division to form new sheet spaces B1 and B2, delete sheet B from the sheet sequence, and add the new sheets B1 and B2 to the end of the sheet sequence.

[0068] S44: Recursive search and backtracking. Recursively call the one - cut nesting algorithm based on tree search on the new sheet sequence to find the optimal solution. If the current division and placement method cannot find a solution, return to S43 and continue to try the next part in the candidate subset or another division method; if there are no parts or sheets that can be selected in S43, the algorithm ends, and the remaining sheets are regarded as leftovers.

[0069] Specifically, in order to select more suitable parts to be placed on the current sheet, a fitness value function f(i,B) of the part is defined to evaluate the matching degree between the part to be nested and the current sheet to be nested, comprehensively considering the size, quantity of the part, and the size relationship between the part and the current nested sheet. The higher the matching degree, the greater the fitness value. The part fitness function is expressed as in Equation (1):

[0070]

[0071] Among them, w i and h i represent the width and height of the part, w B and h B represent the width and height of the sheet, N i represents the quantity of this part, M i represents the number of parts that the block of parts is composed of. The first and second terms indicate that the parts occupying more space on the sheet in terms of length and width have higher priorities. The third term indicates that the parts with larger areas will be assigned higher priorities; α and β are relatively small coefficients, indicating that the parts with larger quantities will be assigned higher priorities, and the parts forming more blocks will be assigned higher priorities. Q i is the adjustment coefficient of the fitness value function.

[0072] (5) After calculating the one - cut nesting result of a complete sheet, copy the current template and update the part and sheet sequences until the nesting of all parts that can be template - copied is completed, then continue to execute step (6), otherwise return to step (2).

[0073] Specifically, when a sheet is nested, calculate whether it meets the requirement of the single - sheet utilization rate. If it meets the requirement, copy the template C times according to the current nesting method, that is, the placement positions of the parts on each sheet are the same, until some parts have been nested, and then end the current template copying.

[0074] Among them, because when executing the one - cut nesting algorithm based on tree search, not all parts in the candidate subset of parts to be nested will be nested into the current template, so there will be remaining parts. Therefore, it is necessary to update the information of the remaining parts and return to step S2 to regroup and combine the parts. At the same time, during the one - cut process, when the sheet cannot be utilized 100%, there will be leftover materials, so it is also necessary to update the sheet sequence information.

[0075] (6) Call the one - cut algorithm based on tree search to nest the remaining parts that cannot be template - copied.

[0076] Specifically, after the nesting of all parts that can be template - replicated is completed, update the part sequence. If there are parts with a quantity of 1 or the total area of all current parts is less than the area of the sheet, consider this part of the parts that cannot be template - replicated separately. Call the one - cut - off algorithm based on tree search to perform nesting on a new sheet or on the remaining material from the previous template replication. The method is the same as step four. The only difference is that this part is executed until all parts are nested and completed.

[0077] (7) Comprehensively consider the number of templates and material utilization rate, and optimize the part order, part combination method, and C1 according to the current nesting result.

[0078] (8) Generate a new solution set until the iteration termination condition is met and output the final nesting result; otherwise, continue to execute step (7).

[0079] Specifically, define a fitness function F(x) that comprehensively considers the utilization rate of the sheet and production efficiency, as shown in Equation (2). The utilization rate of the sheet can be converted into the number of sheets used SheetNum, and the production efficiency can be converted into the number of template types CopyNum produced by template replication.

[0080]

[0081] Where ω and θ are the corresponding cost coefficients. ω represents the cost generated by using one more sheet, and θ represents the cost generated by changing the template once. Different cost coefficients can be set according to the actual situation of the enterprise to represent the priorities of utilization rate and efficiency.

[0082] Evaluate the quality of the solution by calculating the fitness value of each individual in the solution set, and retain the top 20% of the individuals with the highest fitness values in the solution set as elite individuals, that is, retain the results with a higher sheet utilization rate and fewer templates generated.

[0083] Specifically, to generate a new solution set based on the current solution set, it mainly includes three levels of optimization and improvement:

[0084] 1. Optimize the part order, and change the adjustment coefficient Q of the part according to the nesting result i Dynamically adjust the fitness value of the part. Increase the fitness value of the parts in the template with a lower sheet utilization rate, because a low sheet utilization rate indicates that the current part combination is not good. After the increase, it can ensure that the parts can be nested preferentially in the next nesting.

[0085] 2. Optimize the part combination method. For example Figure 2 in b, the part block of ×100 is changed from being composed of parts 1, 2, and 3 combined together to parts 1 and 2 combined together, and 3 becomes a separate part;

[0086] 3. Optimize the number of template replications, select a new number of template replications C1, and a new subset of parts to be nested can be obtained by changing the number of template replications C1.

[0087] The optimizations at the above three levels occur randomly, and a new solution set is recalculated based on the changed results. It is judged whether the algorithm termination condition is satisfied. If not, continue to execute step S7 to optimize the part order, part combination method, and the number of template replications. If satisfied, output the nesting result. As Figure 5 shown, a total of 3 templates are generated. The first template is replicated 45 times, the second template is replicated 10 times, and the third template is replicated 5 times, using a total of 60 sheets of sheet material.

[0088] It is easy for those skilled in the art to understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included within the protection scope of the present invention.

Claims

1. A rectangular one-size-fits-all layout optimization method considering template replication, characterized in that: The method comprises the following steps: (1) Input the part specifications, quantity, and number of plates to initialize the solution set; (2) The rectangular parts to be arranged are grouped according to their quantity, and the parts with the same quantity are divided into a set, and the parts with the same length or width in the set are combined to form block parts; (3) Calculate the maximum number of template replications C that can be replicated for the current nested part based on the part area and the plate area. If the part area and the plate area do not reach the preset ratio λ, then decrease the maximum number of template replications C. Thus, calculate the subset of parts to be nested that can be replicated and its corresponding number of template replications C1. (4) Selecting a subset of parts to be nested that can be copied from the template and calling a one-size-fits-all nesting algorithm based on tree search to construct a nesting result of the one-size-fits-all constraints on the current template, iterating until the current plate is nested; (5) After calculating the one-size-fits-all nesting result of a complete plate, copy the current template and update the part sequence until all parts that can achieve template copying are nested and proceed to the next step, otherwise return to step (2); (6) Calling a one-size-fits-all algorithm based on tree search to arrange the remaining parts that cannot be copied by template; (7) Comprehensively consider the number of templates and the utilization rate of the plate, and optimize the part sequence, part combination method and C1 according to the current layout results; (8) Generate a new solution set until the iteration termination condition is met and output the final nesting result, otherwise continue to execute step (7).

2. The rectangular one-size-fits-all layout optimization method considering template replication as claimed in claim 1, characterized in that: In step (2), when parts of the same length or width in the same set are combined to form block parts, K is set as the upper limit of the part combination, and at most K parts are allowed to be combined into a block.

3. The rectangular one-size-fits-all layout optimization method considering template replication as claimed in claim 1, characterized in that: In step (3), the algorithm for generating a subset of parts to be arranged that can be copied by template is as follows: first, the maximum number of template copies C that can be copied for the current arrangement parts is calculated by dividing the total area of ​​the parts by the area of ​​a single plate; if the requirement of the ratio of parts to plates > λ is not met on a single plate, the maximum number of template copies C is decreased to redetermine the number of parts on the plate until the requirement is met and the current subset of parts to be arranged is output.

4. The rectangular one-size-fits-all layout optimization method considering template replication as claimed in claim 1, characterized in that: In step (4), the one-size-fits-all sorting algorithm based on tree search includes the following steps: S41: Initialize the plates to be arranged. At each node in the tree search process, check whether the plates have been arranged. If yes, the algorithm ends. Otherwise, proceed to the next step. S42: Select the last plate B in the plate sequence, and calculate the fitness value of each part in the part set obtained by the production algorithm of the subset of parts to be arranged; S43: Select parts with high fitness values ​​and put them into the current plate, and divide the plate into new plates B1 and B2 by horizontal or vertical division, delete plate B from the plate sequence, and add the new plates B1 and B2 to the end of the plate sequence; S44: Recursive search and backtracking. Recursively call the one-size-fits-all arrangement algorithm based on tree search to find the optimal solution for the new plate sequence. If the current segmentation and placement method cannot find a solution, return to S43 and continue to try the next part in the candidate subset or another segmentation method. If there is no part or plate that can be selected in S43, the algorithm ends.

5. The rectangular one-size-fits-all layout optimization method considering template replication according to claim 1, characterized in that: A fitness value function f(i, B) of a part is defined to evaluate the matching degree between the part to be arranged and the current plate to be arranged. The fitness function of the part is expressed as shown in formula (1): In formula (1), w i 、h i Represents the width and height of the part, w B 、h B Represents the width and height of the plate, N i Represents the number of parts, M i represents the number of parts that a block is composed of; α, β, Q i Both are adjustment factors.

6. The rectangular one-size-fits-all layout optimization method considering template replication as claimed in claim 1, characterized in that: In step (5), after a sheet is arranged and before the current template is copied and the part sequence is updated, it is calculated whether the sheet meets the single sheet utilization requirement; If there are still remaining parts after updating the part sequence, these parts will be nested on the new plate or on the remaining parts copied from the previous template using a one-size-fits-all algorithm based on tree search.

7. The rectangular one-size-fits-all layout optimization method considering template replication as claimed in claim 1, characterized in that: In step (7), the elite individuals in the current sorting result are retained, and the elite individuals are the first 20% of individuals in terms of fitness value from high to low.

8. The rectangular one-size-fits-all layout optimization method considering template replication according to claim 1 or 7, characterized in that: In step (7), the fitness function F(x) is used to comprehensively consider the utilization rate and production efficiency of the sheet material, wherein the utilization rate of the sheet material is converted into the number of sheets used and defined as SheetNum, and the production efficiency is defined as the number of template types copied by the template CopyNum. The fitness function F(x) is shown in formula (2): In formula (2), ω and θ are cost coefficients, ω represents the cost of using one more sheet, and θ represents the cost of replacing a template.

9. A rectangular one-size-fits-all layout optimization system considering template replication, characterized by: The system includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the rectangular one-size-fits-all layout optimization method considering template replication according to any one of claims 1 to 8 is executed.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions prompt the processor to implement the rectangular one-size-fits-all layout optimization method considering template replication as described in any one of claims 1-8.

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