Coiled material cutting tool arranging method based on multi-strategy combination optimization and matrix solution

Abstract

The invention discloses a coiled material cutting tool arrangement method based on multi-strategy combination optimization and matrix solution, which comprises the following steps: acquiring a coiled material order demand, including the width and length of a required specification; tool arranging parameters are determined, wherein the tool arranging parameters comprise the total width of coiled materials, allowable errors and the maximum combination number; then enumerating a cutting combination mode meeting the maximum combination number within an effective range according to the width of the required coiled material specification; after priority filtering is carried out on the cutting combination mode, a cutting scheme is generated through matrix solving; and finally, evaluating the cutting scheme by adopting at least one evaluation strategy, and outputting an optimal cutting scheme according to an evaluation result. The technical problems that in the existing sticky note raw material paper cutting process, the material waste rate is high, the production efficiency is low, the tool arrangement scheme is single, and global optimization cannot be achieved can be solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent manufacturing and industrial optimization, and more particularly to a roll cutting and knife arrangement method based on multi-strategy combination optimization and matrix solution, which is particularly suitable for paper processing and sticky note production industries. BACKGROUND

[0002] In the field of sticky note production, efficient cutting of raw material rolls directly determines the production cost and market competitiveness of enterprises. The current industry generally relies on manual experience or traditional material arrangement software to generate a knife arrangement scheme, but both have significant defects: Manual knife arrangement relies on operator visual estimation and is difficult to handle mixed orders of multiple specifications (such as cutting different size sticky notes such as 289mm, 312mm, 509mm at the same time), resulting in a long-term utilization rate of roll paper hovering between 62%-75%, with an average of 18%-25% of edge waste.

[0003] Although the automatic material arrangement software improves the static material utilization rate to 78%85% through optimization models such as genetic algorithms, the core algorithm has fundamental limitations. On the one hand, when faced with complex orders containing 4 or more specifications, the number of effective cutting combinations grows exponentially, and traditional heuristic search is difficult to solve within a reasonable time. The average calculation time for a single order is more than 15 minutes, which cannot meet the real-time response needs of the production line.

[0004] This technical defect causes considerable economic loss. Taking a sticky note manufacturer with a monthly capacity of 12 million as an example, when cutting 5 or even dozens of mixed specifications using 1530mm wide rolls, the traditional knife arrangement scheme produces 27% of non-reusable scraps (less than 12mm in size), and the scrap rate increases due to the problem of raw edges. According to estimates, only the waste of raw materials causes a large economic loss every month, and if the cost of equipment idling, tool replacement, and rework is included, the total loss expands to more than 12% of the production value. This exposes the serious disconnection between the current technical solution and the actual production needs.

[0005] Therefore, how to solve the above technical problems is a problem that those skilled in the art need to solve. SUMMARY

[0006] Therefore, the present application provides a roll cutting and knife arrangement method based on multi-strategy combination optimization and matrix solution; aims to build a new paradigm for roll paper cutting optimization that takes into account real-time, adaptability and economy by integrating multi-strategy evaluation framework and matrix solution algorithm, and provides an upgrade path from "experience-driven" to "algorithm-driven" for the industry.

[0007] To achieve the above purpose, the present application adopts the following technical solutions: A roll cutting and knife arrangement method based on multi-strategy combination optimization and matrix solution, comprising, S1. Obtain the roll material order requirements, including the required width specifications. and length Determine the blade arrangement parameters, including the total width of the roll material. Allowable error And the maximum number of combinations; S2. According to the required roll material width Within the effective range The inner enumeration specifies the cutting and combination methods that satisfy the maximum number of combinations. S3. After priority filtering of the cutting combination methods, a cutting scheme is generated by matrix solving; S4. Evaluate the cutting scheme using at least one evaluation strategy, and output the optimal cutting scheme based on the evaluation results.

[0008] Furthermore, the following type of preprocessing is performed before executing step S2: For each specification in the order, determine whether it can be used independently. If it can be used independently, set an independent use flag; if it cannot be used independently, determine whether it can be sorted in descending order. If yes, generate a descending order combination; otherwise, skip the current specification. Based on the descending arrangement and the specifications having the individually usable mark, a cutting arrangement is generated.

[0009] Furthermore, S2 also includes performing normalized sorting and stringification on each of the cutting combinations to ensure its global uniqueness.

[0010] Furthermore, the cutting combination method is prioritized and filtered according to the following formula;

[0011] In the formula, For the priority score of combination C, 、 and These are configurable weighting coefficients. Specifications The number of times it appears in combination C. For specifications The inventory status and production priority are pre-set type weights. The total width of combination C, The score for the reduction strategy is the number of specifications in combination C that can be replaced by reduction strategies.

[0012] Furthermore, the matrix solution includes: Based on the priority-filtered combination set, a subset is selected to construct a coefficient matrix A, where the elements in coefficient matrix A are... representing the number of occurrences of the th combination; constructing a demand vector b, where the element represents the demand length of the i th specification; solving the linear equation system to obtain a vector representing the cutting number of each combination.

[0013] Further, the matrix solving further comprises: verifying the validity of each element x in the solution vector , including checking , and rounding up to the nearest integer for non-integer.

[0014] Further, solving the linear equation system , the steps include: a) performing row transformation on the coefficient matrix A to obtain a row echelon form, identifying the pivot column in the row echelon form to obtain the rank r of the matrix; b) if , is the number of combinations in the subset, then extract the full-rank submatrix of and solve by calculating ; c) if , then determine that the combinations in the current subset are linearly dependent and cannot obtain a unique solution, discard the current subset.

[0015] Further, S3 further comprises generating a hash fingerprint for the path of the current generated cutting scheme; for querying historical records, pruning the path when the same fingerprint exists to avoid repeated calculation.

[0016] The method for generating a unique hash fingerprint is: arranging the IDs of all combinations in the current path in a specific order, and calculating the MD5 or SHA256 hash value.

[0017] Further, the evaluation strategy includes: precise mode, for evaluating according to the total cutting length. The total cutting length is , where represents the cutting number of the th combination. This mode pursues the minimization of the total cutting length, and is suitable for scenarios of strictly single production and pursuit of the highest material utilization rate; downgrade mode, for evaluating the use of wide specifications to replace narrow specifications (where ​material efficiency. After substitution, the demand length of the original specification is converted into the demand length of the new specification according to the area equivalence principle . The evaluation index in this mode is also the total cutting length , which seeks better overall material utilization by allowing downcut substitution; The multi-cut mode is used to evaluate according to the multi-cut part (i.e., the area of excess cutting). The calculation of the multi-cut amount is as follows:

[0018] The first term of the formula calculates the total area of the material actually consumed, which is obtained by accumulating the product of the cutting times of each combination and the total width of the combination , where is the total width of the kth combination; the second term of the formula k calculates the total area required by the order, which is obtained by accumulating the product of the demand length of each specification and its width . The difference between the two is the area of multi-cut waste, and the smaller this value is, the more accurate the scheme is and the higher the material utilization rate is; The waste mode is used to evaluate according to the total waste amount. The calculation of the total waste amount is as follows:

[0019] The total waste amount is composed of edge waste and excess cutting waste. Among them, represents the total width of the roll material, is the total width of the kth cutting combination, which is calculated from the widths of the specifications contained therein and the number of occurrences , is the cutting times of the combination; the other part of the formula is used to calculate the excess cutting waste, indicates the actual total length of the specification , which is obtained by multiplying the number of occurrences of the specification in each combination and the cutting times of the corresponding combination and then summing them up, represents the demand length of the specification, and is the width of the specification. This formula comprehensively quantifies the material waste of the scheme by accumulating the edge waste of all combinations and the excess part of all specifications. ​​​​

[0020] Further, in S1, the row cutter parameter further comprises a maximum calculation time threshold; For real-time monitoring of calculation time, when the maximum calculation time threshold is reached, the calculation process is terminated, and the current optimal solution or feasible solution is output.

[0021] The roll cutting row cutter method and system based on multi-strategy combination optimization and matrix solution provided by the present application aim to solve the technical problems of high material waste rate, low production efficiency, single row cutter scheme and inability to globally optimize in the process of cutting the adhesive note raw material paper.

[0022] Compared with the prior art, the present application has the following beneficial effects: 1. Improve the solving ability: by combining depth-first search with mathematical modeling, automatically generate a large number of feasible row cutter combinations, break through the dependence on artificial experience in traditional methods; use matrix operations to accurately and quantitatively solve the combinations, quickly find the optimal solution or exact solution that meets the order requirements under certain conditions, and fundamentally improve the scientificity and optimality of the scheme.

[0023] 2. Improve the calculation efficiency: through priority filtering, repeated path pruning and other mechanisms, intelligently reduce the search space, greatly reduce the calculation complexity, effectively solve the "combination explosion" problem; introduce a timeout control mechanism to ensure that the algorithm always returns a high-quality feasible solution within a limited time, meeting the stringent real-time requirements of the production site.

[0024] Propose a multi-strategy parallel evaluation mechanism: simultaneously output multiple optimal schemes for different production goals such as accurate delivery, row reduction saving, reserve inventory, and minimizing waste; thereby changing the limitations of traditional methods with single goals, providing rich and visual data support for production decisions, and greatly enhancing the flexibility and scientificity in dealing with complex and variable production scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0025] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are only embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor based on the provided drawings.

[0026] Figure 1 is a flowchart of the roll cutting row cutter method based on multi-strategy combination optimization and matrix solution of the present application; Figure 2 is a flowchart of the pre-processing of the specification type in the embodiment of the present application; Figure 3 is a workflow diagram of the recursive optimization engine in the present application; Figure 4 is a matrix solving flowchart in the present application; Figure 5 is a multi-strategy evaluator workflow chart in the present application; Figure 6 is a result collection and sorting module workflow chart in the present application; Figure 7 is a timeout control module workflow chart in the present application. DETAILED DESCRIPTION

[0027] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0028] In the following description, many specific details are set forth in order to provide a thorough understanding of the present application. However, the present application can be practiced without the specific details that are set forth in the following description, in other manners that are consistent with the spirit and principles of the present application. Therefore, the present application is not limited to the specific embodiments disclosed in the following description.

[0029] The embodiments of the present application disclose a coil cutting and arranging tool method and system based on multi-strategy combination optimization and matrix solving, which aims to break through the three bottlenecks of the new arranging tool technology: 1) solving the combination explosion problem and completing the high-quality solution search of a complex order within 3 minutes; and 2) upgrading from single-target optimization to multi-target cooperation and synchronously optimizing key indicators such as material utilization rate (required to be greater than or equal to 92%) and equipment comprehensive efficiency (tool replacement is less than or equal to 2 times per thousand sheets).

[0030] To achieve the above purpose, the present application adopts a comprehensive technical solution of hierarchical optimization and multi-strategy evaluation, which can realize a complete intelligent decision-making process from data input to scheme output. Specifically, the scheme flowchart is as shown in Figure 1 , and mainly includes the following steps: S1, obtaining a coil order demand, including a required width and a length of a required specification; determining arranging tool parameters, including a total width of the coil , an allowed error , and a maximum combination number; S2, according to the width of the required coil specification , enumerating a cutting combination mode that meets the maximum combination number in an effective range , that is, a combination scheme tree; S3, after priority filtering of the cutting combination mode, a cutting scheme is generated by matrix solution; S4, the cutting scheme is evaluated by at least one evaluation strategy, and the optimal cutting scheme is output according to the evaluation result. In some embodiments, the evaluation strategy includes the accurate mode, the reduced row mode, the multi-cut mode and the waste mode.

[0031] In another embodiment, the cutting scheme obtained in step S3 is subjected to timeout control and repeated detection to improve the calculation efficiency and ensure the response speed.

[0032] In an alternative embodiment, after inputting the required list of roll types, parameter initialization is first performed, and the flow is as shown in Figure 2 ; including: setting the web width, error range, maximum combination length, and time limit.

[0033] Then type preprocessing is performed, the steps including: For each specification in the order, a single use judgment is performed. If it can be used alone, a single use flag is set. If it cannot be used alone, it is judged whether it can be reduced row. If yes, a reduced row combination is generated. If no, the current specification is skipped; According to the reduced row combination and the specification with the single use flag, a combination tree is constructed, and an initial combination tree is generated and output.

[0034] Secondly, an effective initial combination tree is generated. In this embodiment, a depth-first search (DFS) algorithm is used to enumerate all possible and effective cutter combination modes in the search space under the constraint condition ; In this application, each cutting combination mode is uniquely identified by using a data structure, which includes combination ID, width of each specification constituting the combination, occurrence number of each specification, and total width of the combination.

[0035] As a preferred, each of the cutting combination modes is subjected to normalized sorting and string processing, that is, the internal combination is sorted and converted into a string form for storage and comparison, so as to realize global deduplication and ensure its global uniqueness.

[0036] In an embodiment, the initial combination tree is used as a candidate solution space, and recursive search is performed to find the optimal cutter arrangement scheme, as shown in Figure 3 , the steps including: S31, in order to solve the combination explosion problem, based on the preset optimization strategy, the type weight is calculated, and a priority score P(C) is calculated for each cutting combination in the combination scheme tree, and the calculation formula is:

[0037] In the formula, is the priority score of combination C, 、 and is a configurable weighting coefficient, is the specification occurrence in combination C, is the inventory status and production priority based specification type weight pre-set, is the total width of combination C, is the drop-ranking strategy score, which is the number of specifications in the combination that can be replaced by drop-ranking.

[0038] The formula can prioritize more urgent, more material-saving, and more flexible combinations, greatly reducing the search space.

[0039] S32, check the termination condition, if the combination is empty, drop the special processing, and output the processing result; if the combination is not empty, execute step S33 matrix solution; S33, matrix solution, for the high-priority combination filtered out, convert it into a linear equation system for accurate solution, the steps are as follows Figure 4 , specifically including: Based on the combination set filtered by priority, select a subset to construct the coefficient matrix A, the elements in the coefficient matrix A represent the occurrence of specification in the th combination; in this embodiment, from the filtered high-priority combination, select combinations to construct the coefficient matrix of , wherein, is the total number of specifications; Construct demand vector b, the elements in the demand vector b represent the demand length of the i th specification; Solve the linear equation system to get the vector representing the cutting times of each combination, the steps include: a) Perform row transformation on the coefficient matrix A to get the row echelon form, identify the pivot column in the row echelon form to get the rank r of the matrix; b) If , is the number of combinations in the subset, then extract the full-rank submatrix of , and solve it by calculating ; c) If If so, it is determined that the combination in the current subset is linearly dependent and cannot get a unique solution, and the current subset is discarded, and the empty set is returned.

[0040] Further, verify the validity of the solution: for each element in the solution vector x , perform validity verification, including checking , and is an integer, and if not, round up. When the solution is valid, update the current solution, and if not, skip this combination.

[0041] And repeat detection: generate a unique hash fingerprint for the path of the current cutting plan; used to query the history record, if the fingerprint already exists in the history record, terminate the further search of the current path, realize pruning, so as to avoid repeated calculation, and further improve the efficiency.

[0042] The method of generating a unique hash fingerprint is: arrange the IDs of all combinations in the current path in a specific order, and calculate the MD5 or SHA256 hash value.

[0043] In one embodiment, as Figure 5 , the feasible solutions obtained by the recursive optimization solving step are sent into a multi-strategy evaluator in parallel to perform the following four modes of evaluation to meet the needs of different production scenarios: Accurate mode, used for evaluation according to the total cutting length. The total cutting length is , where represents the cutting times of the th combination. This mode pursues the minimization of the total cutting length, and is suitable for scenarios that strictly follow single production and pursue the highest material utilization rate; Downgrade mode, used for evaluating the material efficiency when replacing narrow specifications with wide specifications (where ). After replacement, the required length of the original specification is converted to the required length of the new specification according to the area equivalence principle, where is the rounding up function. The evaluation index in this mode is also the total cutting length , which seeks better overall material utilization rate by allowing downgrade replacement; Multi-cut mode, used for evaluation according to the multi-cut part (i.e. the area of excess cutting). The calculation method of the multi-cut amount is as follows:

[0044] where the first term of the formula ​The calculation measures the total area of ​​material actually consumed, by summing the number of cuts for each combination. Total width of the combination The product of is obtained, where The total width of the k-th combination; the second term of the formula Calculated is The total area required by the order is calculated by summing the required length for each specification. Its width The product of the two is obtained. The difference between the two is... This refers to the area of ​​waste from excessive cutting. The smaller this value, the more precise the solution and the higher the material utilization rate. Waste mode, used to assess based on total waste. Total waste The calculation method is as follows:

[0045] The total waste consists of two parts: edge material waste and excessive cutting waste. Represents the total width of the roll material. Let be the total width of the k-th cutting combination, which is composed of the widths of each specification within it. With the number of occurrences Calculations show that This refers to the number of cuts in the combination; another part of the formula is used to calculate waste from excessive cutting. Specifications The actual total cutting length is determined by the number of times it appears in each combination. Number of cuts in the corresponding combination Multiply and then sum to get the result. This represents the required length for this specification in the order. This represents the width of that specification. This formula comprehensively quantifies material waste in a given solution by summing up the excess material from all combinations and the overproduction from all specifications.

[0046] Furthermore, the top 5 solutions for each strategy collected by the results collector are sorted, formatted, and a detailed report is generated to obtain the final optimization solution. See details below. Figure 6 The plan includes detailed information on the blade arrangement, number of cuts, and expected waste, which is used by production personnel for final decision-making.

[0047] Furthermore, in S1, the tool distribution parameters also include a maximum computation time threshold. Used for performing timeout control: Real-time monitoring of the time t elapsed since the start of the calculation, and comparison with the preset maximum allowable time. Compare; if If so, the recursive optimization solving process is terminated immediately and the current optimal result is returned, ensuring the responsiveness of the system. In an embodiment, the monitoring process is as shown in FIG. 6, determining whether the timeout occurs, if so, terminating the current calculation and outputting the current optimal solution, if not, continuing to execute and returning control. Figure 7

[0048] The cutting method provided by the present application adopts a layered architecture, runs from data input to result output, and passes through multiple optimization and processing stages in the middle. The architecture has high scalability, and each layer can be upgraded and optimized independently without affecting the normal operation of the entire process. Compared with the prior art, the present application has the following significant advantages: Global optimization, significant effect: By combining recursive search with mathematical programming, the cutting method can jump out of the local optimum and find a nearly globally optimal cutting scheme, thereby greatly improving material utilization and directly reducing raw material costs.

[0049] Efficient calculation and rapid response: Through priority filtering and repeated pruning mechanisms, the cutting method intelligently narrows down the solution space, and then quickly solves it by combining matrix operations, while ensuring real-time performance through timeout control, which can meet the modern production rhythm.

[0050] Flexible strategy and strong adaptability: The four evaluation modes (precision, reduced cutting, multiple cutting, and waste) provided by the cutting method cover a variety of actual production scenarios, and users can select the most suitable production scheme according to real-time requirements (such as delivery time, cost, and inventory), thereby enhancing the practicality and flexibility of the system.

[0051] High degree of automation: The cutting method realizes full-process automation from order input to scheme output, reduces the dependence on human experience, reduces human errors, and improves the consistency of production efficiency.

[0052] In an exemplary embodiment, the above cutting method can be converted into a hardware system, which includes: a data input module for receiving order demand data and system parameters; a combination generation module connected to the data input module for generating the initial combination scheme tree; a recursive optimization engine connected to the combination generation module, which includes a priority filtering submodule, a matrix solving submodule, and a repeated detection and pruning submodule; a multi-strategy evaluator connected to the recursive optimization engine for evaluating the combination results; a timeout control module connected to the recursive optimization engine; a result output module connected to the multi-strategy evaluator.

[0053] ​In addition, the matrix solver submodule can call external linear algebra libraries (EJML) to perform matrix row transformations, rank calculations, and inversion operations.

[0054] In one specific embodiment, Step 1: Configure the following key operating parameters through the system configuration interface: 1. Width of roll material ( ): 1530mm, this parameter is based on industry standard roll material specifications; 2. Cutting tolerance ( ): 12mm (meaning the effective total width of the combination must be within the range of [1518mm, 1530mm]), this error range takes into account the equipment accuracy and material properties; 3. Maximum combined capacity ( ): 8 (a single combination can contain a maximum of 8 different specifications), this parameter balances computational complexity and scheme diversity; 4. Timeout period ( T_max 120 seconds (maximum algorithm execution time limit) to meet the real-time requirements of the production site.

[0055] Then, the input order requirement data is received and verified. This embodiment uses the following specifications, which are derived from actual production scenarios: Specification A: Width 509mm, Required length 61,500 meters; Specification B: Width 301mm, required length 5142 meters; Specification C: Width 209mm, Required length 21100 meters; Specification D: Width 248mm, Required length 76427 meters; Specification E: Width 250mm, required length 13200 meters; Specification F: Width 289mm, Required length 128390 meters; Specification G: Width 217mm, Required length 73436 meters; Specification H: Width 312mm, Required length 16480 meters.

[0056] The system performs multiple validations on the input data: first, it performs format validation to ensure the correctness of the data type; second, it performs logical validation to verify the rationality between parameters; and finally, it performs business rule validation to ensure that the width and length of all specifications are positive values ​​and that the total required length is within the processing capacity of the equipment.

[0057] Step 2: Enumerate the cutting and combination methods; First, we determine whether each specification can be used independently, which involves precise mathematical calculations and feasibility analysis for each specification: 1. Size A (509mm): Integer programming calculation, 1530 / 509 ≈ 3.007, rounded to 3, 3x509=1527mm, which falls within the valid range [1518,1530], so it is marked as individually usable; 2. Size B (301mm): Calculate 1530 / 301 ≈ 5.083, rounded to 5, 5x301=1505mm, which is less than the minimum requirement of 1518mm, not meeting the constraint; 3. Check the possibility of reducing the row: analyze the use of 301mm size for reducing the row to determine the range of alternative sizes that can be used; 4. Size H (312mm): Calculate 1530 / 312 ≈ 4.904, rounded to 4, 4x312=1248mm, which is much smaller than the requirement of 1518mm, marked as not individually usable, and needs to be combined with other sizes.

[0058] Further, all valid combinations that meet the width constraint are generated by the optimized depth-first search algorithm, including: Using recursive DFS algorithm, search depth limit is This depth ensures the diversity of combinations; Real-time calculation of the total width of the current combination: Dynamic programming method is used to improve the calculation efficiency; Constraint condition check: strictly ensure This range ensures the maximum utilization of materials; Combination normalization processing: arrange each combination internally in descending order of width to ensure the uniqueness of the combination; Stringification and deduplication: convert normalized combinations to strings for global deduplication, using hash table for fast lookup.

[0059] The generated valid combination examples demonstrate the effectiveness of the algorithm: Combination C1: [509, 509, 509] (total width 1527mm) Combination C2: [509, 509, 301, 209] (total width 1528mm) Combination C3: [509, 509, 250, 250] (total width 1518mm) Step 3, respectively execute priority filtering and matrix solving; Priority filtering: calculate the comprehensive priority score for each combination, using a multi-factor weighted evaluation model:

[0060] Which contains multiple optimization dimensions: : Dynamic calculation of weights based on specification demand length, using exponential weighted moving average method to update weights; the greater the demand length, the higher the weight, ensuring that important orders are prioritized to meet; : Edge material waste penalty term, using a quadratic function to increase the punishment for large waste; : Score of reduction strategy, considering the technical feasibility and economic benefits of specification substitution; : Configurable weighting coefficients (default ), these coefficients can be optimized through machine learning.

[0061] Matrix solution, steps include: 1. Construct the coefficient matrix A: Matrix dimension: (m=8 specifications, n=500 combinations), use sparse matrix storage to save memory, matrix elements are the number of the th specification in the th combination, accurately record the composition of each combination.

[0062] 2. Construct demand vector b: Vector dimension: , containing the demand of all specifications, vector elements : the demand length of the th specification, maintain unit consistency.

[0063] 3. Solve the linear equation set:

[0064] Use full pivot Gaussian elimination method to ensure numerical stability; Calculate the rank of the matrix , judge whether it is full rank, handle the case of ill-conditioned matrix; If full rank, extract the submatrix and solve the inverse, use decomposition to improve efficiency; Calculate the cutting frequency vector: , get the accurate cutting scheme.

[0065] 4. Verify the validity of the solution: Check , exclude negative solutions; Round up non-integer solutions, consistent with production reality; Verify that it meets the order demand, ensuring the feasibility of the solution.

[0066] In addition, this step also includes efficient repeated detection and pruning strategy, including: 1. Generate SHA256 hash fingerprints for solution paths to ensure uniqueness; 2. Maintain a sliding window history (last 1000 solutions) using a circular buffer; 3. Prune immediately upon detecting duplicate fingerprints to avoid redundant calculations; 4. Continue recursive optimization for non-duplicate solutions to maintain search diversity.

[0067] Step 4: Execute four evaluation strategies using parallel processing architecture: 1) Exact mode evaluation; Calculate total cutting length: , accurate to the nearest millimeter; Evaluation criteria: , aim for maximum production efficiency; Applicable scenarios: tight delivery deadlines, maximum production efficiency; Additional considerations: equipment wear and tear, energy consumption, and overall cost.

[0068] 2) Down-gauge mode evaluation Core indicator: total cutting length .

[0069] Implementation: According to the predefined down-gauge rule table, convert narrow-gauge requirements to equivalent area of wide-gauge requirements , re-solve and compare total cutting length.

[0070] Constraints: (only replace with wider gauge), ensure product quality.

[0071] Economic benefit analysis: Calculate the payback period and net present value of investment.

[0072] 3) Multi-cut mode evaluation Calculate excess cutting amount: ; Inventory optimization: Use ARIMA time series analysis based on historical data prediction models; Balance current costs and future benefits, considering the time value of money; Risk assessment: Analyze market demand changes and inventory accumulation risks.

[0073] 4) Waste mode evaluation Calculate total waste amount: ; First item: edge waste, use real-time monitoring to reduce waste; second item: excess cutting waste, reduce loss through precise control; Optimization goal: , realize green manufacturing; Environmental impact assessment: calculate carbon footprint and environmental impact index.

[0074] Finally, collect results and sort by different indicators: 1. Precision mode: ascending order of cutting length, prefer efficient solutions; 2. Emission reduction mode: ascending order of cutting length, prefer efficient solutions; 3. Multi-cut mode: sort by inventory value score, balance current and future; 4. Waste mode: ascending order of total waste, emphasize sustainable development.

[0075] And generate a report: use a standardized template to generate a structured and detailed report, including solution details, evaluation indicators, recommended levels; and output the optimal solution of the four strategies, provide decision support, and additional economic benefit analysis and implementation suggestions.

[0076] To further optimize the above technical solutions, start a global timer, with millisecond-level precision, to monitor the time consumption of each processing stage, establish a performance baseline; and display the remaining time in real time, provide progress prompts, and record historical data to optimize time allocation; In this embodiment, hierarchical termination is implemented, that is, when the time reaches the 90% threshold, the new combination generation is suspended and the current calculation is completed; when the time reaches the 95% threshold, the current matrix solution is completed and the output is prepared; when the time reaches the 100% threshold, it is immediately terminated and the result is output, ensuring real-time performance.

[0077] In some embodiments, it also includes providing abnormal situation handling for providing various emergency solutions, including: Numerical calculation exception: switch to heuristic algorithm to ensure continuity; Logical error: enable emission reduction processing mode to maintain basic functions; System failure: save the current state and restore to ensure data security; Performance monitoring: real-time monitoring of system load, automatic adjustment of parameters.

[0078] Through the above embodiments, laboratory environment tests and simulation operation verification, the present application is expected to achieve significant results in actual production: material utilization can be improved from 85% of the industry average level to more than 93% through multi-strategy optimization algorithm, reaching the international advanced level; intelligent tool setting algorithm can improve production efficiency by more than 25%, greatly reducing production cost, among which automatic tool setting can save about 75% of production preparation time compared with manual tool setting, and production line switching efficiency is improved by 40%; under standard hardware configuration, the system calculation time is stably controlled within 120 seconds, fully meeting the real-time requirements of production site, and even in the most complex scenario (more than 10 specifications combination), the calculation time can still be maintained within 180 seconds; the system supports four optimization strategies and can successfully adapt to various production modes including emergency order, batch production and sample trial production; compared with the traditional manual tool setting method, it can reduce more than 90% of manual intervention, the decision accuracy rate is improved to more than 95%, and the quality fluctuation caused by the difference in manual experience is greatly reduced; based on the simulation operation data, it is estimated that the annual raw material cost can be saved by about 1.2 million yuan, and the investment recovery period is less than 6 months; through the standardized tool setting algorithm, the product size consistency can be improved by 30%, and the quality problems caused by tool setting error can be reduced by more than 85%; at the same time, the system supports rapid order switching, which shortens the production line changeover time by 50%, and better meets the flexible manufacturing demand of multi-variety and small batch.

[0079] The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same or similar parts between the various embodiments can be referred to each other. For the device disclosed by the embodiments, since it corresponds to the method disclosed by the embodiments, the description is relatively simple, and the related parts can be referred to the method part.

[0080] The above description of the disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to these embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for roll cutting tool arrangement based on multi-strategy combination optimization and matrix solution, characterized in that, Comprise: S1, obtaining the roll material order requirement, including the width and length of the required specification ;​ Determining the parameters of the row of knives, including the total width of the web , the allowable error , and the maximum number of combinations; S2, width according to the required roll format within the effective range enumerating cutting combination manners satisfying the maximum combination number; S3, after priority filtering of the cutting combination mode, generate a cutting scheme by matrix solving; S4, evaluate the cutting scheme by at least one evaluation strategy, and output the optimal cutting scheme according to the evaluation result.

2. The method of claim 1, wherein, Before step S2, the following type of preprocessing is performed: Judge whether each specification in the order can be used alone, and set the flag of being able to be used alone if it can be used alone; if it cannot be used alone, judge whether it can be reduced in row, and if it can, generate a reduced row combination, and if it cannot, skip the current specification; Generate a cutting combination mode according to the reduced row combination and the specification with the flag of being able to be used alone.

3. The method of claim 1, wherein, S2 further comprises normalizing and string processing of each cutting combination mode to ensure its global uniqueness.

4. The method of claim 1, wherein, The cutting combination mode is filtered according to the following formula: wherein, is the priority score of combination C, 、 and is a configurable weighting factor, is the specification number of occurrences in combination C, is the type weight pre-set based on the inventory status and production priority of specification , and is the total width of combination C, is the down-ranking strategy score, which is the number of specifications in combination C that can be replaced by down-ranking.

5. The method of claim 1 wherein, The matrix solving comprises: Based on the combination set filtered by priority, a subset is selected to construct a coefficient matrix A, wherein elements in the coefficient matrix A represent the number of times of appearance of specifications in the jth combination . th combination . A demand vector b is constructed, where the elements of the demand vector b represent the length of demand for a particular size i ​​ Solving linear equation systems , resulting in a vector representing the number of cuts for each combination .

6. The method of claim 5, wherein, The matrix solution also includes: processing the solution vector x Each element in Perform validity verification, including checking And round up any non-integer values.

7. The method of claim 5, wherein, Solving linear equations The steps include: a) perform row transformation on the coefficient matrix A to obtain a row echelon form, and identify the pivot column in the row echelon form to obtain the rank r of the matrix; b) if , is the number of combinations in the subset, then the full rank submatrix of is extracted and solved by computing​ c) if then determine that the combination in the current subset is linearly dependent and no unique solution can be obtained, and discard the current subset.

8. The method of claim 1, wherein, S3 further comprises generating a hash fingerprint for the path of the current cutting scheme to query the historical record, and pruning the current path when the same fingerprint exists to avoid repeated calculation.

9. The method of claim 1 wherein, The evaluation strategy comprises: The exact mode, for evaluation according to the total cutting length, the total cutting length being ， represents the number of cuts for the th combination; Downgauging mode for evaluating material efficiency using wide gauges instead of narrow gauges with total cut length as the indicator after which the gauge is replaced is a ceiling function; Multi-cut mode, for evaluation according to multi-cut area, multi-cut amount The calculation method is as follows: Among them, the first item This represents the total area of ​​materials actually consumed. This represents the number of cuts for the k-th combination. Indicates the first k Total width of each combination; second item The total area required for the order. Let i be the required length for the i-th specification in the order. Let be the width of the i-th specification; Waste mode, for evaluation based on total waste amount, total waste amount is calculated as: wherein, represents the total width of the web, represents the gauge of the actual cut length, represents the gauge of the order demand length.

10. The method of claim 1, wherein, In S1, the row cutter parameters further comprise a maximum calculation time threshold; When the maximum calculation time threshold is reached during real-time monitoring of the calculation time, the calculation process is terminated in stages, and the current optimal solution or feasible solution is output.

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