A rectangular nesting method, device, and medium

Abstract

The specification discloses a rectangular layout method, device and medium, the method comprising: generating a current generation part sequence matrix and a current generation storage matrix by using a random function, the part sequence matrix comprising N kinds of part sequences of the current generation, each part sequence comprising D kinds of parts; performing a lowest level line search algorithm on each part sequence to obtain a nesting scheme of the D kinds of parts in a plate; calculating the current plate utilization rate of each nesting scheme according to an objective function until the objective function meets a termination condition, and outputting the current part sequence matrix; when the objective function does not meet the termination condition, repeatedly performing the following steps: updating the part sequence by using genetic crossover operation and local exchange operation to obtain an updated part sequence matrix and a storage matrix; updating the part sequence matrix and the storage matrix by using a direction change operation, and calculating the maximum value corresponding to the updated part sequence matrix according to the objective function. The application improves the utilization rate of the plate.

Description

Technical Field

[0001] The present specification relates to the technical field of computer-aided nesting, and in particular, to a rectangular nesting method, device and medium. Background Art

[0002] In the laser cutting process, when a nesting result is generated by nesting software equipped with a cutting machine, a large amount of steel scrap is generated, which has the defect of material waste. Optimizing the nesting problem to improve the utilization rate of material resources is one of the key points that need improvement.

[0003] Nesting problems mainly include regular part nesting and irregular part nesting. The rectangular nesting problem is to arrange a series of rectangular parts on a rectangular plate with fixed width and unlimited height. No overlap is allowed between the arranged parts, and all parts must be arranged inside the plate. It is required to find an optimal nesting scheme that maximizes the utilization rate of the plate. The rectangular part nesting problem is an NP-complete combinatorial optimization problem. That is, this type of problem has high computational complexity, and an optimal solution cannot be found within the current computer level and within a time acceptable to people. The two-dimensional nesting problem needs to consider a variety of constraints and geometric combinations, and its theoretical research involves linear programming, dynamic programming, heuristic algorithms, intelligent algorithms and other theories. Among them, intelligent search algorithms have increasingly become the trend for solving two-dimensional nesting problems.

[0004] Regarding the nesting problem, many researchers have continuously studied the nesting problem. Currently, classified according to solution algorithms, research on the rectangular part nesting problem is mainly divided into three categories: deterministic algorithms, heuristic algorithms and meta-heuristic algorithms. However, these three algorithms have problems such as long time consumption and low nesting rate, and none of them can well solve the rectangular nesting problem.

[0005] For combinatorial optimization problems, they can be divided into continuous variable problems and discrete variable problems according to the research object. The rectangular nesting problem belongs to the latter. In solving a single continuous optimization problem, compared with many existing meta-heuristic algorithms, the SAR algorithm can obtain a more accurate solution at a faster speed. However, since the existing SAR algorithm has not been modified for the rectangular nesting problem, the quality of the calculated solution cannot meet the requirement of high nesting rate. Summary of the Invention

[0006] One or more embodiments of the present specification provide a rectangular nesting method, which is used to solve the following technical problem: algorithms in the prior art for solving the rectangular nesting problem cannot ensure a high nesting rate while reducing calculation time and improving calculation efficiency.

[0007] One or more embodiments of the present specification adopt the following technical solutions:

[0008] This specification provides one or more embodiments of a rectangular layout method, the method comprising:

[0009] A random function is used to generate the current part sequence matrix and the current storage matrix. The current part sequence matrix includes the sequence of N parts in the current generation, and each part sequence includes D types of parts.

[0010] The lowest horizontal line search algorithm is performed on each part sequence to obtain D nesting schemes of parts in the sheet metal.

[0011] The current material utilization rate of each nested scheme is calculated based on the objective function. When the objective function does not meet the preset termination condition, the following steps are repeated until the objective function meets the preset termination condition, and the current part sequence matrix is ​​output.

[0012] The part sequence is updated using genetic crossover and local exchange operations to obtain the updated part sequence matrix and the storage matrix.

[0013] The part sequence matrix and the storage matrix are updated using a direction change operation, and the maximum and minimum values ​​corresponding to the updated part sequence matrix are calculated according to the objective function.

[0014] This specification provides one or more embodiments of a rectangular layout device, comprising:

[0015] At least one processor; and,

[0016] A memory communicatively connected to the at least one processor; wherein,

[0017] The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the steps described above.

[0018] This specification provides one or more embodiments of a non-volatile computer storage medium storing computer-executable instructions configured to perform the steps described above.

[0019] The above-described at least one technical solution adopted in the embodiments of this specification can achieve the following beneficial effects:

[0020] To solve the rectangular layout problem, this invention modifies the search and rescue algorithm: genetic crossover and local crossover are used in the population phase of the search and rescue algorithm, and directional change is used in the individual phase. The search and rescue algorithm is a novel heuristic algorithm, demonstrating good performance in continuous problems and, after optimization, also applicable to discrete problems. To verify the algorithm's effectiveness, this paper first uses the Friedman test to check the quality of the swapped part sequence and the utility of the actual layout detection algorithm. The experiments yielded satisfactory results, thus verifying the algorithm's effectiveness. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments or prior art of this specification, the drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0022] Figure 1 A flowchart illustrating a rectangular layout method provided in the embodiments of this specification;

[0023] Figure 2 Statistics on the differences between 7 and 8 types of parts;

[0024] Figure 3 This is a flowchart illustrating the SARO algorithm. Detailed Implementation

[0025] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, and not all embodiments. Based on the embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this specification.

[0026] The SAR algorithm involved in this invention is an optimized search algorithm summarized by researchers based on the first simulation of human behavior. In SAR, the search operation is divided into two phases: a group phase and an individual phase. In the group phase, search and rescue personnel compare the clues they have with those of others to determine their route. If someone else's clue is of higher quality, they discard their own clue and move towards the direction of the better clue. In the individual phase, search and rescue personnel search based on the clues they have.

[0027] This specification provides a rectangular layout method through its embodiments. Figure 1This is a flowchart illustrating a rectangular layout method provided in an embodiment of this specification. Figure 1 As shown, the method mainly includes the following steps:

[0028] Step S101: Generate the current part sequence matrix and the current storage matrix using a random function. The current part sequence matrix includes the sequence of N parts in the current generation, and each part sequence includes D types of parts.

[0029] refer to Figure 3 This invention relies on the SAR algorithm and improves it to handle discrete problems of finding the optimal rectangular nesting. The initial 2N clue matrix C is generated by a random function rand(). In SAR, D represents dimension, X... ij This indicates the location of a search and rescue worker; while in a rectangular layout, D represents the total number of parts, and X... ij A component is represented by a number that is numerically equal to its index in the original set of D types of components. In SAR, matrix X represents the N D-dimensional clues currently held by the search and rescue personnel. In the rectangular layout problem, matrix X represents the order of all N types of components used in the current generation. In SAR, when the rescue personnel find a better clue, matrix M is used to store the discarded clue; in the rectangular layout problem, matrix M is used to store the sequence of components with lower utilization of the plate material discarded in the iteration. In SAR, the clue matrix C is used to store the existing known clue positions, that is, the combination of matrix X and matrix M, and each row of this matrix represents a clue position; while in the rectangular layout problem, the clue matrix C is used to store the existing known component sequences, and each row represents a component sequence. As shown in the following formula (2):

[0030]

[0031] Step S102: Perform the lowest horizontal line search algorithm on each part sequence to obtain D nesting schemes of parts in the sheet metal.

[0032] The lowest horizontal line search strategy is adopted as the part positioning algorithm. Research on algorithms proposed in published literature reveals that the lowest horizontal line algorithm is simple to implement and produces good nesting results.

[0033] The specific algorithm flow of the lowest horizontal line search strategy is as follows:

[0034] Step 1: Set the bottom edge of the board as the initial highest contour line.

[0035] Step 2: When a part is to be nested into a sheet metal block, select the lowest horizontal line from the bottom of the sheet metal block as the placement position for the part. If several lowest horizontal lines exist at the same height, select the leftmost one. Compare the width of the lowest horizontal line with the width of the part block to be nested.

[0036] If the width of the lowest horizontal line is long, the current part can be nested in this location, and then the lowest horizontal line set can be updated.

[0037] Otherwise, find the second lowest horizontal line adjacent to this lowest horizontal line and merge it with the lowest horizontal line. That is, increase the height and length of the lowest horizontal line. Update the set of lowest horizontal lines.

[0038] Step 3: Repeat step 2 until the current part can be nested.

[0039] Step 4: Repeat this process until all parts are nested.

[0040] Step S103: Calculate the current material utilization rate of each nested scheme according to the objective function. When the objective function does not meet the preset termination condition, repeat the following steps until the objective function meets the preset termination condition, and output the current part sequence matrix.

[0041] For the sake of convenience in describing the problem, the technical solution of this invention assumes that the width W of the rectangular plate is a fixed value, the height H is unlimited, the total number of parts to be arranged is N, and the length of the i-th part is l_i and the width is w_i. A rectangular coordinate system is established with the lower left corner of the plate as the origin, the width direction as the x-axis, and the height direction as the y-axis. Rectangular parts of specified specifications and quantities are arranged into the plate. The less the plate is used in the height direction after arrangement, the higher its utilization rate.

[0042] The objective function is shown in Formula 1, where the distance between the part and the bottom of the plate is the highest distance.

[0043]

[0044] Step S104: The part sequence is updated using genetic crossover and local exchange operations to obtain the updated part sequence matrix and the storage matrix.

[0045] In the group stage, formulas (5) and (6) are used to update the part sequence matrix X and the storage matrix M, respectively. Given the distribution pattern of the difference between the two part sequences, when the difference between the two sequences is within a certain range... When the distribution curve is in the middle, the crossover strategy in the genetic algorithm is adopted because the genetic algorithm has a strong global search capability and a large "step size". This generates two new part sequences NX1 and NX2. The difference between these two new sequences and the original part sequence is significantly different. If the objective function value of the new part sequence is higher than that of the original part sequence, the new sequence is used to replace the original sequence, thus realizing the operation of the algorithm moving towards a better extreme value. However, sometimes this sequence transformation does not improve the objective function value. In this case, the part sequence is not updated. Therefore, a limit value L needs to be set to force the update. That is, when a part sequence has not been updated for L consecutive times, a new random sequence is used to replace it. This is done to prevent the part sequence from getting trapped in a local extreme value and also to expand the search range, i.e., formula (5).

[0046] Then use formula (6) to update the M matrix.

[0047]

[0048]

[0049] When the difference between the two sequences is in or When the sequence differences between two part sequences are small, a local crossover strategy is adopted. To implement this strategy, first select two sets of part sequences X. i C k The items with the largest single-dimensional differences are then swapped in sequence X. i and sequence C k These terms are used. This is done to ensure that the part sequence searches around the extreme values ​​and does not deviate too much, i.e., using a "small step size". This generates two new part sequences NX1 and NX2. The subsequent update matrix method still uses formulas (5) and (6).

[0050] To accurately measure the differences between two part sequences i and k, this paper directly sums the absolute values ​​of the differences in the position indices of all positions in the two sequences to obtain the SD. i By examining the relationships between the sequences, a formula for the maximum difference (4) is obtained:

[0051]

[0052] refer to Figure 2 After statistically analyzing the differences between any two sequences of 7 and 8 parts in full permutations, we can find that the distribution of the differences between the two part sequences tends to a normal distribution, such as... Figure 1 As shown, the difference between two part sequences after a "subtraction operation" often lies in the middle of a normal distribution curve.

[0053] Step S105: Update the part sequence matrix and the storage matrix using a direction change operation, and calculate the maximum and minimum values ​​corresponding to the updated part sequence matrix according to the objective function.

[0054] In SAR, the individual stage aims to search around itself. For rectangular parts, based on their discrete characteristics, this paper achieves the search operation around itself by changing the orientation of the parts. Formula (7) is used to update the part matrix. Parts with large length-width differences and a quantity of Q are selected and rotated 90 degrees. This operation will generate a new sequence NX1. Similarly, a limit value L needs to be set. When the number of times a part sequence has not been updated exceeds L, a new random sequence is used to replace it. Similarly, the new part sequence with a high objective function value replaces the original part sequence, ensuring that the search moves towards the extreme value. The forced update mechanism expands the search range.

[0055]

[0056] To compare the effectiveness of the algorithms, this paper first performs a Friedman test on the part sequences generated by SARO, GA, and SA. The average rank of the algorithms is calculated to estimate the best-performing algorithm for the generated part sequences; a lower value is better. SARO significantly outperforms the other two algorithms. The algorithm presented in this paper shows the best overall optimization performance compared to the other two algorithms, and its advantage becomes more pronounced as the sample size increases. In this part, the sheet metal utilization rate for rectangular nesting using the SARO algorithm is consistently above 90%, higher than the average utilization rate of other algorithms. Nevertheless, from an algorithmic perspective, SARO requires more iterations than GA, so the SARO algorithm should consume more time than the GA algorithm, but this is still within an acceptable range. The uncertainty in the experiment comes from the randomly generated part sequences, because if the randomly generated sequence corresponds to a good sheet metal utilization rate, the program can terminate without undergoing multiple generations of search.

[0057] In summary, to solve the rectangular layout problem, this invention modifies the search and rescue algorithm: genetic crossover and local crossover are used in the population phase of the search and rescue algorithm, and directional change is used in the individual phase. The search and rescue algorithm is a novel heuristic algorithm, demonstrating good performance in continuous problems and, after optimization, also applicable to discrete problems. To verify the algorithm's effectiveness, this paper first uses the Friedman test to check the quality of the swapped part sequence and the utility of the actual layout detection algorithm. The experiments yielded satisfactory results, thus verifying the algorithm's effectiveness.

[0058] This specification also provides a rectangular layout device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to:

[0059] A random function is used to generate the current part sequence matrix and the current storage matrix. The current part sequence matrix includes the sequence of N parts in the current generation, and each part sequence includes D types of parts.

[0060] The lowest horizontal line search algorithm is performed on each part sequence to obtain D nesting schemes of parts in the sheet metal.

[0061] The current material utilization rate of each nested scheme is calculated based on the objective function. When the objective function does not meet the preset termination condition, the following steps are repeated until the objective function meets the preset termination condition, and the current part sequence matrix is ​​output.

[0062] The part sequence is updated using genetic crossover and local exchange operations to obtain the updated part sequence matrix and the storage matrix.

[0063] The part sequence matrix and the storage matrix are updated using a direction change operation, and the maximum and minimum values ​​corresponding to the updated part sequence matrix are calculated according to the objective function.

[0064] This specification also provides a non-volatile computer storage medium storing computer-executable instructions, wherein the computer-executable instructions are configured as follows:

[0065] A random function is used to generate the current part sequence matrix and the current storage matrix. The current part sequence matrix includes the sequence of N parts in the current generation, and each part sequence includes D types of parts.

[0066] The lowest horizontal line search algorithm is performed on each part sequence to obtain D nesting schemes of parts in the sheet metal.

[0067] The current material utilization rate of each nested scheme is calculated based on the objective function. When the objective function does not meet the preset termination condition, the following steps are repeated until the objective function meets the preset termination condition, and the current part sequence matrix is ​​output.

[0068] The part sequence is updated using genetic crossover and local exchange operations to obtain the updated part sequence matrix and the storage matrix.

[0069] The part sequence matrix and the storage matrix are updated using a direction change operation, and the maximum and minimum values ​​corresponding to the updated part sequence matrix are calculated according to the objective function.

[0070] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the embodiments of apparatus, devices, and non-volatile computer storage media are basically similar to the method embodiments, so the descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0071] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0072] The devices, media, and methods provided in the embodiments of this specification are one-to-one correspondences. Therefore, the devices and media also have similar beneficial technical effects as their corresponding methods. Since the beneficial technical effects of the methods have been described in detail above, the beneficial technical effects of the devices and media will not be repeated here.

[0073] Those skilled in the art will understand that embodiments of this specification can be provided as methods, systems, or computer program products. Therefore, this specification may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this specification may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0074] This specification is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this specification. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0075] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0076] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0077] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0078] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0079] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0080] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0081] The above description is merely one or more embodiments of this specification and is not intended to limit this specification. Various modifications and variations can be made to the one or more embodiments of this specification by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of one or more embodiments of this specification should be included within the scope of the claims of this specification.

Claims

1. A rectangular layout method, characterized in that, The method includes: A random function is used to generate the current part sequence matrix and the current storage matrix. The current part sequence matrix includes the sequence of N parts in the current generation, and each part sequence includes D types of parts. The lowest horizontal line search algorithm is performed on each part sequence to obtain D nesting schemes of parts in the sheet metal. The current material utilization rate of each nested scheme is calculated based on the objective function. When the objective function does not meet the preset termination condition, the following steps are repeated until the objective function meets the preset termination condition, and the current part sequence matrix is ​​output. The part sequence is updated using genetic crossover and local exchange operations to obtain the updated part sequence matrix and the storage matrix, including: Calculate the difference between the part sequences. When the difference is between a first preset threshold and a second preset threshold, use a genetic crossover operation to generate two sets of updated part sequences. When the difference is not between the first preset threshold and the second preset threshold, a local exchange operation is used to generate two sets of part sequences. Two sets of part sequences are selected, and several part elements corresponding to the sequences are interchanged to obtain the first updated part sequence and the second updated part sequence. The objective function is used to calculate the current material utilization rate of the current part sequence, the first updated material utilization rate corresponding to the first updated part sequence, and the second updated material utilization rate corresponding to the second updated part sequence. The current material utilization rate, the first updated material utilization rate, and the second updated material utilization rate are compared, and the part sequence matrix and the storage matrix are updated accordingly. When the utilization rate of the first updated sheet material is higher than the utilization rate of the second updated sheet material and higher than the current sheet material utilization rate, the current part sequence matrix is ​​updated to the updated part sequence matrix corresponding to the first set of updated part sequence matrices; When the utilization rate of the second updated sheet material is higher than the utilization rate of the updated sheet material and higher than the utilization rate of the current sheet material, the current part sequence matrix is ​​updated to the second updated part sequence matrix corresponding to the second group of updated part sequences; When the utilization rates of the first and second updated sheet materials are lower than the current sheet material utilization rate, and the number of times the current part sequence is updated is lower than a third preset threshold, the current part sequence matrix is ​​updated to the current part sequence matrix. When the utilization rates of the first and second updated sheet materials are lower than the current sheet material utilization rate, and the number of updates to the current part sequence is higher than the third preset threshold, the random function is used to generate a matrix as the current part sequence matrix. If the first update part sequence and / or the second update part sequence are updated to the current part sequence, the storage matrix is ​​updated to the current part sequence matrix; otherwise, the current storage matrix is ​​maintained. The part sequence matrix and the storage matrix are updated using a direction change operation, and the maximum and minimum values ​​corresponding to the updated part sequence matrix are calculated according to the objective function.

2. The rectangular layout method according to claim 1, characterized in that, The step of updating the part sequence matrix and the storage matrix using a direction change operation includes: Select a number of parts with large length and width differences, rotate the orientation of the parts by 90°, and generate a third updated part sequence; The objective function is used to calculate the utilization rate of the third updated sheet metal corresponding to the third updated part sequence; When the utilization rate of the third updated sheet material is lower than the utilization rate of the current sheet material, the current part sequence matrix is ​​updated to the updated part sequence matrix corresponding to the third updated part sequence. If the number of updates to the current part sequence is higher than a third preset threshold, then the current part sequence matrix is ​​maintained. If the number of times the current part sequence is updated is less than a third preset threshold, then a random function is used to generate the current part sequence matrix.

3. A rectangular layout device, employing the rectangular layout method as described in any one of claims 1-2, characterized in that, The device includes: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the at least one processor, which, when executed by the at least one processor, enable the at least one processor to: A random function is used to generate the current part sequence matrix and the current storage matrix. The current part sequence matrix includes the sequence of N parts in the current generation, and each part sequence includes D types of parts. The lowest horizontal line search algorithm is performed on each part sequence to obtain D nesting schemes of parts in the sheet metal. The current material utilization rate of each nested scheme is calculated based on the objective function. When the objective function does not meet the preset termination condition, the following steps are repeated until the objective function meets the preset termination condition, and the current part sequence matrix is ​​output. The part sequence is updated using genetic crossover and local exchange operations to obtain the updated part sequence matrix and the storage matrix. The part sequence matrix and the storage matrix are updated using a direction change operation, and the maximum and minimum values ​​corresponding to the updated part sequence matrix are calculated according to the objective function.

4. A non-volatile computer storage medium storing computer-executable instructions, characterized in that, The computer-executable instructions are configured as a rectangular layout method as described in any one of claims 1-2, specifically including: A random function is used to generate the current part sequence matrix and the current storage matrix. The current part sequence matrix includes the sequence of N parts in the current generation, and each part sequence includes D types of parts. The lowest horizontal line search algorithm is performed on each part sequence to obtain D nesting schemes of parts in the sheet metal. The current material utilization rate of each nested scheme is calculated based on the objective function. When the objective function does not meet the preset termination condition, the following steps are repeated until the objective function meets the preset termination condition, and the current part sequence matrix is ​​output. The part sequence is updated using genetic crossover and local exchange operations to obtain the updated part sequence matrix and the storage matrix. The part sequence matrix and the storage matrix are updated using a direction change operation, and the maximum and minimum values ​​corresponding to the updated part sequence matrix are calculated according to the objective function.

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