A two-dimensional layout and cutting path joint method and system based on digital twinning

Abstract

A two-dimensional layout and cutting path combined method based on digital twinning includes the following steps: S100, first, two weights alpha, beta are introduced to combine two-dimensional layout optimization and two-dimensional cutting path problems, and a simultaneous problem model is established; S200, the best solution of the combined problem is solved according to the designed variable neighborhood search algorithm; S300, a digital twinning model is established to simulate production, and production parameter data and external conditions are collected from the simulation production process; S400, the collected production parameter data and external conditions are fed back to the digital twinning system, the weight parameters alpha, beta are adjusted according to the real-time data and external conditions, the dynamic adjustment is carried out in the algorithm according to the change of alpha, beta, the layout efficiency and the cutting length are balanced, and the layout and cutting scheme are optimized; S500, the best solution is calculated according to the weight meeting the actual producer's expectation. The application considers reducing the cutting path, reducing the idle stroke and cutting time, and improving the cutting efficiency and quality in the layout process.

Description

Technical Field

[0001] This invention relates to two-dimensional nesting and cutting technology, and in particular to a method for combining two-dimensional nesting and cutting paths based on digital twins. Background Technology

[0002] With the rapid development of the global economy and the continuous expansion of enterprise production scale, the requirements for resource utilization are becoming increasingly higher. Layout and cutting path planning are crucial in the manufacturing industry, and their rationality is directly related to raw material utilization and production efficiency. However, there are many areas for optimization in existing technologies.

[0003] Current technologies typically plan the cutting path independently after nesting is completed, without organically integrating nesting with the cutting path. This leads to problems such as detours and excessive idle travel in the cutting path, increasing cutting time and costs, and reducing production efficiency. Furthermore, the lack of accurate consideration of the real-time status and processing capacity of the cutting equipment may result in cutting paths exceeding the equipment's processing range or being incompatible with its motion characteristics, affecting cutting quality and equipment lifespan.

[0004] Furthermore, the existing nesting and cutting path planning systems suffer from poor information exchange and low data sharing, resulting in poor collaboration during the production process. For example, adjustments to the nesting scheme may not be promptly reflected in the cutting path planning, or the optimization results of the cutting path may not effectively influence nesting decisions, making it difficult to achieve overall optimization of the entire production process. Summary of the Invention

[0005] To address the aforementioned shortcomings, the present invention aims to propose a method for combining two-dimensional nesting and cutting path planning. Based on digital twin technology, a digital twin model of the physical entity is established and deeply integrated with the cutting path planning during nesting. This approach considers reducing cutting paths, minimizing idle travel and cutting time, thereby improving cutting efficiency and quality.

[0006] To achieve this objective, the present invention adopts the following technical solution:

[0007] A combined method for two-dimensional nesting and cutting paths based on digital twins includes the following steps:

[0008] S100. First, by introducing two weights α and β, the two problems of two-dimensional nesting optimization and two-dimensional cutting path are combined to establish a combined problem model.

[0009] S200. Solve the optimal solution to the joint problem using the designed variable neighborhood search algorithm;

[0010] S300: A digital twin model was established to simulate production, creating a virtual production environment, simulating production parameters, and collecting data on production parameters and external conditions from the simulated production process.

[0011] S400: Feed the collected production parameter data and external conditions back to the digital twin system, adjust the weight parameters α and β according to the real-time data and external conditions, and dynamically adjust them in the algorithm according to the changes in α and β to balance the layout efficiency and cutting length, and optimize the layout and cutting scheme.

[0012] S500, finally take the weights that meet the actual producers' expectations and calculate the optimal solution.

[0013] Preferably, step S100 includes:

[0014] S110, Definition of Two-Dimensional Nesting Optimization Problem:

[0015] Given h planar master templates of fixed width but variable length B1, B2, B3...B h n irregular parts to be arranged: P1, P2, P3...P n Each part is allowed to rotate by t angles r1, r2, r3...r t Then, the parts to be arranged are placed reasonably in the flat mother plate, so that the mother plate generates the least amount of waste, and the following constraints are satisfied: Part P i and P j Cannot overlap; i,j=1,2,…,n; Part P i Within the boundary of the motherboard; i = 1, 2, ..., n; geometric overlap constraint; boundary position matching constraint;

[0016] S120, Definition of Two-Dimensional Cutting Path Problem:

[0017] In the two-dimensional cutting path problem, the common edge refers to the overlapping part of the edges of two or more parts when they are laid out. During the cutting process, the common edge part only needs to be cut once to avoid the loss caused by repeated cutting.

[0018] By introducing variables and parameters related to shared edges, this two-dimensional cutting path problem can be defined as: the set of parts P contains the set of vertices of each part, i.e., P k (1≤k≤|P|) represents the set of vertices of part k. The set of vertices is used to store the vertex information of the part, such as P. kl (1≤l≤|P k |) can be used to represent the vertex l of part k. The set of empty tool edges is E. E The cost C of the edge at this time ij Let the variable x be the length of the edge connecting points i and j. ijIndicate whether points i and j are empty knife edges;

[0019] The following constraints must be met: the out-degree and in-degree of each part with respect to the empty tool edge are equal; the out-degree of each part with respect to the empty tool edge is guaranteed to be 1; sub-loops must be avoided; when there is a shared edge, there are no loops.

[0020] S130. Combine the two-dimensional layout optimization problem and the two-dimensional cutting path problem: By introducing two weights α and β into the layout problem and the cutting path problem, and since the total area of ​​the parts is a constant, the objective function of the layout problem can be optimized to minimize the total area of ​​the sheet metal used.

[0021] Preferably, in step S130, the simultaneous problem model is as follows:

[0022]

[0023] Where α, β ≥ 0 and α + β = 1. All other constraints remain unchanged.

[0024] When determining the initial weight values, a normalized equivalent contribution method is adopted. After calculating the initial solution L0 for layout and the initial solution G0 for cutting, the following steps are taken: Thus, in the initial solution, αL0 = βG0, making their contributions to the objective Z equal;

[0025] Subsequently, the weights α and β will be dynamically adjusted based on the real-time data collected in the digital twin system and the company's requirements, according to the actual production situation.

[0026] Preferably, in step S200, the solution steps include:

[0027] S210. Define the corresponding neighborhood structure for the nesting problem and the cutting path problem, and then use the goal-driven nesting optimization algorithm to generate a feasible nesting scheme L0.

[0028] S220. On the layout diagram of the layout scheme L0, use a greedy algorithm to find the part cutting order C0 of the cutting path problem, and use a common edge-based cutting algorithm to obtain the point path order G0 of the cutting path problem. The initial solution S0 = (L0, C0, G0). In this algorithm, the material utilization rate is used as the fitness of solution L0, the empty cutting edge of the cutting path is used as the fitness of solution C0, and the sum of all point paths through which the cutting is carried is used as the fitness of solution G0. The fitness of solutions L0 and G0 are multiplied by weights α and β respectively and then added together as the comprehensive fitness.

[0029] S230. Calculate the fitness of each component and the overall fitness, and then perturb C0 using a perturbation algorithm to obtain C. ' 0, then find the optimal part cutting sequence C obtained in the neighborhood structure through a variable neighborhood descent operation.' 0 ' According to C ' 0 ' G is obtained using a shared-edge cutting algorithm. ' 0. Calculate the overall fitness of the new solution, compare the fitness of the two solutions, and update the better one as the best solution;

[0030] S240. Next, a new layout scheme L is obtained by continuously perturbing the layout solution. Under L, new C and G are obtained. The perturbation algorithm, the variable neighborhood descent operation, and the edge-based cutting algorithm are repeated to update the best solution until the perturbation of the layout solution reaches the upper limit of the number of iterations or the upper limit of the running time.

[0031] Furthermore, in step S200, the variable neighborhood search algorithm is a joint algorithm for the two problems of nesting and cutting paths, so different neighborhood structures are defined for each of these two problems.

[0032] For layout problems, there are two methods: part exchange and part rotation. For part exchange, any two parts P in the current layout scheme are selected. i ,P j Swap their positions on the motherboard; rotate the parts as needed for selected part P. i Rotate clockwise according to the allowed angle set;

[0033] For the cutting path problem, there are part swapping, part reversal and part insertion; Part swapping: swap the cutting order of two parts; Part reversal: reverse the order of all parts in the interval between two parts; Part insertion: insert a part before other parts.

[0034] Furthermore, in step S200, the target-driven sorting optimization algorithm includes the following steps:

[0035] First, calculate the minimum number of usable sheets based on the total area of ​​all parts and the sheet specifications as the initial value;

[0036] Then, using a pre-constructed critical polygon and a scan line strategy, the continuous geometric data of each part is converted into discrete pixel representations under this plate number, generating scan lines that scan along the coordinate axis direction to quickly detect local overlaps.

[0037] In conjunction with the horizontal line strategy, the first layer is initialized at the bottom of the board, and the layer height and used width are recorded as 0. The parts are sorted in descending order by height or area, and each part is retrieved sequentially by traversing the existing layers. If the height of a layer is greater than or equal to the height of the part, the remaining width is greater than or equal to the width of the part, and there is no overlap, then the part is placed at the current fill endpoint of the layer and the used width is updated. If none of the conditions are met, a new layer is created at the top of the board and placed there. The layer height is the height of the part or the preset minimum layer height, which quickly determines the placement position of each part.

[0038] If all parts cannot be placed within the limited number of iterations, the number of plates is incremented by one, and the NFP decoding operation and feasibility judgment are repeated. Once a feasible solution is found, the algorithm enters the compression stage. Through multiple iterations, the layout is tightened and gaps are filled by pushing parts to the edge along the X / Y axis, locally exchanging the position of parts, and maximizing space reuse by inserting small parts into plates with remaining space, so as to maximize utilization.

[0039] The final output includes the optimal number of plates, the precise placement coordinates and rotation angles of the parts on each plate, and the overall utilization rate.

[0040] Furthermore, in step S200, in the greedy algorithm, a point in a part is first randomly selected as the first element of the part cutting order. Then, in each iteration, the point with the closest Euclidean distance to the point previously added to the part cutting order is found from the set of part vertices that have not yet been added. This process is repeated until all parts have been added to the part cutting order.

[0041] Furthermore, in step S200, in the edge-based cutting algorithm, the cutting path is optimized by introducing edge-related variables;

[0042] Step 1: After the layout diagram and part cutting sequence are determined, mark all two points that form a common edge as the first point and the second point. When a point is in multiple common edge positions, it can be marked repeatedly.

[0043] Step 2: First, cut the first part along its outline;

[0044] Step 3: According to the obtained cutting order of the parts, when the part to be cut and the part already cut do not share an edge, the empty cutting edge is the point with the shortest distance from the exit point of the previous cutting part to all points of the part to be cut; when the part to be cut and the part already cut share an edge, the empty cutting edge is the point with the shortest distance from the exit point of the previous cutting part to the two marked points of the longest shared edge between the part to be cut and the part already cut, and this point is marked as the entry point, and the other corresponding point is marked as the exit point;

[0045] Step 4: Continue cutting along the part outline. When the part to be cut and the part already cut do not share an edge, cut the entire part outline directly. When the part to be cut and the part already cut share an edge, cut in the opposite direction from the current entry point to the exit point until the current exit point.

[0046] Step 5: Repeat steps 3 and 4 until all parts have been cut.

[0047] Furthermore, in step S200, the perturbation algorithm performs perturbation operations on both the layout scheme and the part cutting order. In each iteration, a neighborhood structure is randomly selected to change the two parts related to the current solution. After 10 iterations of perturbation, a perturbed solution is obtained.

[0048] In the variable neighborhood descent algorithm, this algorithm is used to find the optimal part cutting sequence under the current nesting scheme and minimize the length of the empty tool edge;

[0049] First, the order of three neighborhood structures in the neighborhood structure set of the part cutting order is randomly shuffled to facilitate the process of diversified local search;

[0050] Then, the shuffled neighborhood structures are searched sequentially. In each neighborhood structure, all possible perturbations are traversed. Once the first perturbation that can improve the target is found, it is immediately accepted and saved. If no further improvement can be made in the current neighborhood, the search is switched to the next neighborhood. The algorithm terminates when all neighborhoods have completed a traversal without improvement.

[0051] Furthermore, in step S300, a digital twin model is established to simulate layout, cutting paths, etc., to create a model of the production environment, to collect real-time data from the production process and to feed it back to the digital twin system, and to use the data analysis capabilities in the digital twin model to dynamically adjust the weight parameters α and β according to the actual production situation.

[0052] The algorithm dynamically adjusts the fitness function based on the changes in α and β to balance the nesting efficiency and cutting length. Based on the subjective preferences of different enterprises for different costs, it predicts the balance benefits under different α and β values. After multiple adjustments, the optimal solution is selected for nesting and cutting in actual production so that the final result meets the producer's expectations.

[0053] If current production data indicates low material utilization, the weight parameter α can be increased appropriately to make the optimization algorithm focus more on improving material utilization efficiency, thereby reducing material waste. If the cutting path is long and the cutting efficiency is low, the weight parameter β can be increased to make the optimization algorithm focus more on reducing the cutting path, thereby reducing the total length of the cutting path and the cutting time.

[0054] One of the aforementioned technical solutions includes the following beneficial effects: This method and system, by establishing a digital twin model, utilizes the information provided by the digital twin model during the nesting process to generate an efficient and reasonable nesting plan, thereby improving raw material utilization. Simultaneously, it deeply integrates the nesting plan with the cutting path planning, considering the reduction of cutting paths during the nesting process while ensuring high material utilization. Through digital twin technology, real-time information interaction and data sharing between the nesting and cutting path planning systems are achieved, enabling them to collaboratively optimize and thus improve the efficiency and effectiveness of the entire production process. Attached Figure Description

[0055] Figure 1 This is a flowchart of the overall steps of one embodiment of the present invention;

[0056] Figure 2 This is a schematic diagram of the cutting path when common-edge cutting is not used;

[0057] Figure 3 This is a schematic diagram of the cutting path when using common-edge cutting;

[0058] Figure 4 This is a flowchart of a common-edge variable neighborhood search algorithm for nesting and cutting.

[0059] Figure 5 This is a flowchart based on the common-edge cutting path algorithm;

[0060] Figure 6 This is a schematic diagram of cutting based on the common edge cutting path algorithm. Detailed Implementation

[0061] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0062] like Figure 1 As shown, a joint method for two-dimensional nesting and cutting paths based on digital twins includes the following steps:

[0063] S100. First, by introducing two weights α and β, the two problems of two-dimensional nesting optimization and two-dimensional cutting path are combined to establish a combined problem model.

[0064] S200. Solve the optimal solution to the joint problem using the designed variable neighborhood search algorithm;

[0065] S300: A digital twin model was established to simulate production, creating a virtual production environment, simulating production parameters, and collecting data on production parameters and external conditions from the simulated production process.

[0066] S400: Feed the collected production parameter data and external conditions back to the digital twin system, adjust the weight parameters α and β according to the real-time data and external conditions, and dynamically adjust them in the algorithm according to the changes in α and β to balance the layout efficiency and cutting length, and optimize the layout and cutting scheme.

[0067] S500, finally take the weights that meet the actual producers' expectations and calculate the optimal solution.

[0068] Beneficial Effects: This method and system, by establishing a digital twin model, utilizes the information provided by the digital twin model during the nesting process to generate efficient and reasonable nesting schemes, improving raw material utilization. Simultaneously, it deeply integrates the nesting scheme with cutting path planning, considering the reduction of cutting paths during the nesting process while ensuring high material utilization. Through digital twin technology, real-time information interaction and data sharing between the nesting and cutting path planning systems are achieved, enabling them to collaboratively optimize and thus improve the efficiency and effectiveness of the entire production process. Production information includes sheet metal ID and dimensions, part rotation angle, placement coordinates, part cutting sequence, cutting path length, material utilization, tool life, part rotation angle, part placement coordinates, material utilization, part cutting path, empty tool edge path, tool position, feed rate, spindle speed, load, and wear information; external environmental information includes workshop temperature and humidity, dust, power status, order requirements and schedules, machine tool maintenance plans, market demand data, and data on changes in user demand.

[0069] Step S100 includes:

[0070] S110, Definition of Two-Dimensional Nesting Optimization Problem:

[0071] Given h planar master templates of fixed width but variable length B1, B2, B3...B h n irregular parts to be arranged: P1, P2, P3...P n Each part is allowed to rotate by t angles r1, r2, r3...r t Then, the parts to be arranged are placed reasonably in the flat mother plate, so that the mother plate generates the least amount of waste, and the following constraints are satisfied: Part P i and P j Cannot overlap; i,j=1,2,…,n; Part P i Within the boundary of the motherboard; i = 1, 2, ..., n; geometric overlap constraint; boundary position matching constraint;

[0072] Its mathematical model is:

[0073]

[0074] i≠j, i,j=1…n (4)

[0075] Collection of permissible rotation angles for parts:

[0076] Rotation angle of each part: δ(i)=r(k(i)) (6)

[0077] Where, p i and p j It is the set of geometric positions of the two parts;

[0078] S120, Definition of Two-Dimensional Cutting Path Problem:

[0079] In the two-dimensional cutting path problem, the common edge refers to the overlapping part of the edges of two or more parts when they are laid out. During the cutting process, the common edge part only needs to be cut once to avoid the loss caused by repeated cutting.

[0080] By introducing variables and parameters related to shared edges, this two-dimensional cutting path problem can be defined as: the set of parts P contains the set of vertices of each part, i.e., P k (1≤k≤|P|) represents the set of vertices of part k. The set of vertices is used to store the vertex information of the part, such as P. kl (1≤l≤|P k |) can be used to represent the vertex l of part k. The set of empty tool edges is E. E The cost C of the edge at this time ij Let the variable x be the length of the edge connecting points i and j. ij Indicate whether points i and j are empty knife edges;

[0081] The following constraints must be met: the out-degree and in-degree of each part with respect to the empty tool edge are equal; the out-degree of each part with respect to the empty tool edge is guaranteed to be 1; sub-loops must be avoided; when there is a shared edge, there are no loops.

[0082] Its mathematical model is:

[0083]

[0084] Where C0 is the total length of all cut edges of the parts, which is a constant. ij For the introduced common-edge related variables, E T Let M be a set sharing an edge. M is a sufficiently large positive real number.

[0085] Figure 2This is a schematic diagram of the cutting path when common-edge cutting is not used. For each part, an entry point is selected, which is also the exit point. The starting cutting device starts from this point, circles the part's outline clockwise, and then exits from that point. The selected points for each part are then connected to form a loop connecting all parts. In the diagram, 1-2-3-4, 6-7-8-9, and 11-12-13 are the cutting edges, and 5-10-14 are the uncut edges.

[0086] Figure 3 This is a schematic diagram of the cutting path after using edge-sharing. After referencing edge-sharing, you can... Figure 2 The common edge is 9-13, therefore the new cutting path is as follows: Figure 3 As shown, the cutting edges are 1-2-3-4, 6-7-8, and 10-11, and the empty cutting edge is 5-9-12, which is significantly shorter than the cutting path when common edge cutting is not used.

[0087] S130. Combine the two-dimensional layout optimization problem and the two-dimensional cutting path problem: By introducing two weights α and β into the layout problem and the cutting path problem, and since the total area of ​​the parts is a constant, the objective function of the layout problem can be optimized to minimize the total area of ​​the sheet metal used.

[0088] By solving the problem together, the layout scheme and cutting path planning are deeply integrated to balance material utilization and cutting efficiency, thereby improving overall production efficiency and comprehensive benefits.

[0089] In step S130, the simultaneous problem model is as follows:

[0090]

[0091] Where α,β≥0 and a+β=1. All other constraints remain unchanged.

[0092] When determining the initial weight values, a normalized equivalent contribution method is adopted. After calculating the initial solution L0 for layout and the initial solution G0 for cutting, the following steps are taken: Thus, in the initial solution, ɑL0=βG0, making their contributions to the objective Z the same;

[0093] Subsequently, the weights α,β will be dynamically adjusted based on the real-time data collected in the digital twin system and the company's requirements, according to the actual production situation.

[0094] Beneficial effects: Digital twin closed-loop adaptive optimization and the use of normalized equivalent contribution method to balance the initial optimization direction reduce parameter tuning costs, improve convergence speed and stability, and facilitate subsequent adaptive adjustment.

[0095] like Figure 4 As shown, in step S200, the solution steps include:

[0096] S210. Define the corresponding neighborhood structure for the nesting problem and the cutting path problem, and then use the goal-driven nesting optimization algorithm to generate a feasible nesting scheme L0.

[0097] S220. On the layout diagram of the layout scheme L0, use a greedy algorithm to find the part cutting order C0 of the cutting path problem, and use a common edge-based cutting algorithm to obtain the point path order G0 of the cutting path problem. The initial solution S0 = (L0, C0, G0). In this algorithm, the material utilization rate is used as the fitness of solution L0, the empty cutting edge of the cutting path is used as the fitness of solution C0, and the sum of all point paths through which the cutting is carried is used as the fitness of solution G0. The fitness of solutions L0 and G0 are multiplied by weights α and β respectively and then added together as the comprehensive fitness.

[0098] S230. Calculate the fitness of each component and the overall fitness, and then perturb C0 using a perturbation algorithm to obtain C. ' 0, then find the optimal part cutting sequence C obtained in the neighborhood structure through a variable neighborhood descent operation. ' 0 ' According to C ' 0 ' G is obtained using a shared-edge cutting algorithm. ' 0. Calculate the overall fitness of the new solution, compare the fitness of the two solutions, and update the better one as the best solution;

[0099] S240. Next, a new layout scheme L is obtained by continuously perturbing the layout solution. Under L, new C and G are obtained. The perturbation algorithm, the variable neighborhood descent operation, and the edge-based cutting algorithm are repeated to update the best solution until the perturbation of the layout solution reaches the upper limit of the number of iterations or the upper limit of the running time.

[0100] Beneficial effects: Using the variable neighborhood search algorithm as a framework, combined with various optimization algorithms, it achieves efficient collaborative optimization across problems.

[0101] To further explain the above technology, in step S200, the variable neighborhood search algorithm is an algorithm that addresses both the nesting and cutting path problems. Therefore, it defines different neighborhood structures for each of these two problems.

[0102] For layout problems, there are two methods: part exchange and part rotation. For part exchange, any two parts P in the current layout scheme are selected. i ,P j Swap their positions on the motherboard; rotate the parts as needed for selected part P. i Rotate clockwise according to the allowed angle set;

[0103] For the cutting path problem, there are part swapping, part reversal and part insertion; Part swapping: swap the cutting order of two parts; Part reversal: reverse the order of all parts in the interval between two parts; Part insertion: insert a part before other parts.

[0104] Beneficial effects: The above-mentioned domain structure can be used in subsequent steps to achieve cross-problem collaborative optimization through diverse neighborhood combinations under the same framework, thereby enhancing global search capabilities.

[0105] As a supplement to the above technology, step S200, the target-driven nesting optimization algorithm includes the following steps:

[0106] First, calculate the minimum number of usable sheets based on the total area of ​​all parts and the sheet specifications as the initial value;

[0107] Then, using a pre-constructed critical polygon and a scan line strategy, the continuous geometric data of each part is converted into discrete pixel representations under this plate number, generating scan lines that scan along the coordinate axis direction to quickly detect local overlaps.

[0108] In conjunction with the horizontal line strategy, the first layer is initialized at the bottom of the board, and the layer height and used width are recorded as 0. The parts are sorted in descending order by height or area, and each part is retrieved sequentially by traversing the existing layers. If the height of a layer is greater than or equal to the height of the part, the remaining width is greater than or equal to the width of the part, and there is no overlap, then the part is placed at the current fill endpoint of the layer and the used width is updated. If none of the conditions are met, a new layer is created at the top of the board and placed there. The layer height is the height of the part or the preset minimum layer height, which quickly determines the placement position of each part.

[0109] If all parts cannot be placed within the limited number of iterations, the number of plates is incremented by one, and the NFP decoding operation and feasibility judgment are repeated. Once a feasible solution is found, the algorithm enters the compression stage. Through multiple iterations, the layout is tightened and gaps are filled by pushing parts to the edge along the X / Y axis, locally exchanging the position of parts, and maximizing space reuse by inserting small parts into plates with remaining space, so as to maximize utilization.

[0110] The final output includes the optimal number of plates, the precise placement coordinates and rotation angles of the parts on each plate, and the overall utilization rate.

[0111] Beneficial effects: Generates an initial solution for the layout, which has high quality, high efficiency, good applicability and scalability, and is used in step S210.

[0112] As a supplement to the above technology, in step S200, in the greedy algorithm, a point in a part is first randomly selected as the first element of the part cutting order. Then, in each iteration, the point with the closest Euclidean distance to the point previously added to the part cutting order is found from the set of part vertices that have not yet been added. This process is repeated until all parts have been added to the part cutting order.

[0113] Beneficial effect: In step S220, a better part cutting sequence solution is quickly generated by the greedy algorithm, reducing empty tool paths.

[0114] like Figure 5 As shown, in step S200, in the edge-based cutting algorithm, the cutting path is optimized by introducing edge-related variables;

[0115] Step 1: After the layout diagram and part cutting sequence are determined, mark all two points that form a common edge as the first point and the second point. When a point is in multiple common edge positions, it can be marked repeatedly.

[0116] Step 2: First, cut the first part along its outline;

[0117] Step 3: According to the obtained cutting order of the parts, when the part to be cut and the part already cut do not share an edge, the empty cutting edge is the point with the shortest distance from the exit point of the previous cutting part to all points of the part to be cut; when the part to be cut and the part already cut share an edge, the empty cutting edge is the point with the shortest distance from the exit point of the previous cutting part to the two marked points of the longest shared edge between the part to be cut and the part already cut, and this point is marked as the entry point, and the other corresponding point is marked as the exit point;

[0118] Step 4: Continue cutting along the part outline. When the part to be cut and the part already cut do not share an edge, cut the entire part outline directly. When the part to be cut and the part already cut share an edge, cut in the opposite direction from the current entry point to the exit point until the current exit point.

[0119] Step 5: Repeat steps 3 and 4 until all parts have been cut.

[0120] Beneficial effects: It effectively balances maximizing the utilization of shared edges with minimizing the empty tool path, improves the continuity of the cutting path, and enhances both cutting efficiency and accuracy. The shared edge-based cutting algorithm is used in steps S220, S230, and S240.

[0121] like Figure 6As shown, there are four parts to be cut on the sheet metal. The numbers 1-4 indicate their cutting order. The thick lines in the left diagram represent three common edges, each with two marked points. For example, (1,1,2) represents the set of the first and second marked points on the first common edge. The right diagram shows the entire cutting process. Solid arrows indicate the cutting edge and direction, while dashed arrows indicate the empty cutting edge and direction. Starting from the upper left corner of part 1, after cutting the first part in the order abcd, the exit point is still the upper left corner of part 1. Because the first marked point on the left side of the common edge (1,1,2) between part 2 and part 1 coincides with this point, and the distance is 0, this point is also the entry point for the next part to be cut. The length of the empty cutting edge between the two parts is... The degree is 0, and since its direction to the corresponding other point (which is now updated to the exit point) is counterclockwise, the cutting direction of this part is clockwise. Cutting along the part contour to the exit point stops, i.e., efg; The cutting of part 3 is similar to that of part 2, but since parts 1 and 2 have already been cut and share an edge with part 3, the longer shared edge needs to be selected, i.e., the shared edge between parts 1 and 3. The final cutting order is hij; Since part 4 does not share an edge with other parts, the empty cutting edge is the point with the shortest distance from the exit point of part 3 to each point of part 4, i.e., the dashed arrow k. The point at the lower right corner of part 4 is used as the new entry point and exit point. Cutting is performed in the order of lmn. At this point, all parts have been cut and the algorithm ends.

[0122] Furthermore, in step S200, the perturbation algorithm performs perturbation operations on both the layout scheme and the part cutting order. In each iteration, a neighborhood structure is randomly selected to change the two parts related to the current solution. After 10 iterations of perturbation, a perturbed solution is obtained.

[0123] In the variable neighborhood descent algorithm, this algorithm is used to find the optimal part cutting sequence under the current nesting scheme and minimize the length of the empty tool edge;

[0124] First, the order of three neighborhood structures in the neighborhood structure set of the part cutting order is randomly shuffled to facilitate the process of diversified local search;

[0125] Then, the shuffled neighborhood structures are searched sequentially. In each neighborhood structure, all possible perturbations are traversed. Once the first perturbation that can improve the target is found, it is immediately accepted and saved. If no further improvement can be made in the current neighborhood, the search is switched to the next neighborhood. The algorithm terminates when all neighborhoods have completed a traversal without improvement.

[0126] The efficient local extraction of variable neighborhood descent, the diversification of perturbation operations, and the dual-layer search collaboration take into account both material utilization and cutting efficiency.

[0127] Because the cutting path can only be determined after the layout scheme is generated in this invention, a decrease in the quality of the layout solution may lead to an increase in the quality of the cutting path solution, and the ultimate requirement is the combined benefit of the layout and cutting path problems. Therefore, instead of performing a variable neighborhood descent operation on the layout scheme, only a perturbation operation is performed to expand the search range and reduce the algorithm's running time and complexity, achieving a better overall benefit; the perturbation algorithm is used in steps S230 and S240.

[0128] In addition, in step S300, a digital twin model is established to simulate layout, cutting path, etc., to create a model of the production environment, collect real-time data from the production process, and feed it back to the digital twin system. The data analysis capabilities in the digital twin model are used to dynamically adjust the weight parameters α and β according to the actual production situation.

[0129] The algorithm dynamically adjusts the fitness function based on the changes in α and β to balance the nesting efficiency and cutting length. Based on the subjective preferences of different enterprises for different costs, it predicts the balance benefits under different α and β values. After multiple adjustments, the optimal solution is selected for nesting and cutting in actual production so that the final result meets the producer's expectations.

[0130] If current production data indicates low material utilization, the weight parameter α can be increased appropriately to make the optimization algorithm focus more on improving material utilization efficiency, thereby reducing material waste. If the cutting path is long and the cutting efficiency is low, the weight parameter β can be increased to make the optimization algorithm focus more on reducing the cutting path, thereby reducing the total length of the cutting path and the cutting time.

[0131] By dynamically adjusting the balance between the weighting parameters α and β, the material utilization rate and cutting path length are comprehensively optimized to adapt to different production conditions and needs, thereby maximizing production efficiency and resource utilization.

[0132] The technical principles of the present invention have been described above with reference to specific embodiments. These descriptions are merely for explaining the principles of the invention and should not be construed as limiting the scope of protection of the invention in any way. Based on this explanation, those skilled in the art can readily conceive of other specific embodiments of the invention without inventive effort, and these embodiments will all fall within the scope of protection of the present invention.

Claims

1. A combined method for two-dimensional nesting and cutting paths based on digital twins, characterized in that, Includes the following steps: S100, First, introduce two weights By combining the two problems of 2D nesting optimization and 2D cutting path, a combined problem model is established; S200. Solve the optimal solution to the joint problem using the designed variable neighborhood search algorithm; S300: A digital twin model was established to simulate production, creating a virtual production environment, simulating production parameters, and collecting data on production parameters and external conditions from the simulated production process. S400 feeds the collected production parameter data and external conditions back to the digital twin system, adjusting the weight parameters based on real-time data and external conditions. In the algorithm, according to The layout and cutting schemes are dynamically adjusted to balance the efficiency of the layout and the cutting length, thereby optimizing the layout and cutting schemes. S500, finally take the weights that meet the actual producers' expectations and calculate the optimal solution.

2. The method for combined two-dimensional nesting and cutting paths based on digital twins according to claim 1, characterized in that, Step S100 includes: S110, Definition of Two-Dimensional Nesting Optimization Problem: Given h planar masters of fixed width but variable length n irregular parts to be arranged And each part is allowed to rotate t angles Then, the parts to be arranged are placed reasonably in the flat mother plate, so that the mother plate generates the least amount of waste and satisfies the following constraints: parts and Cannot overlap; ;Component Within the boundary of the motherboard; Geometric overlap constraints; Boundary position matching constraints; S120, Definition of Two-Dimensional Cutting Path Problem: In the two-dimensional cutting path problem, the common edge refers to the overlapping part of the edges of two or more parts when they are laid out. During the cutting process, the common edge part only needs to be cut once to avoid the loss caused by repeated cutting. By introducing variables and parameters related to shared edges, this two-dimensional cutting path problem can be defined as: the set of parts P contains the set of vertices of each part, i.e. This represents the set of vertices of part k. A part vertex set is a collection used to store vertex information of a part. The vertex l is used to represent part k. The empty knife edge collection is The cost of the edge Introduce a variable to represent the length of the edge connecting points i and j. Indicate whether points i and j are empty knife edges; The total length of the cut edges of all parts is a constant. For the introduced common-edge related variables, It is a set sharing an edge; The following constraints must be met: the out-degree and in-degree of each part with respect to the empty tool edge are equal; the out-degree of each part with respect to the empty tool edge is guaranteed to be 1; sub-loops must be avoided; when there is a shared edge, there are no loops. S130. Simultaneously solve the two-dimensional nesting optimization problem and the two-dimensional cutting path problem: by introducing two weights into the nesting problem and the cutting path problem. Furthermore, since the total area of ​​the parts is a constant, the objective function of the layout problem can be optimized to minimize the total area of ​​the sheet metal used.

3. The method for combined two-dimensional nesting and cutting paths based on digital twins according to claim 2, characterized in that, In step S130, the simultaneous problem model is as follows: Equation (15); in, and All other constraints remain unchanged. When determining the initial weight values, a normalized equivalent contribution method is adopted, after calculating the initial solution for the layout. and cutting initial solution Afterwards, , Thus, in the initial solution there is This ensures that both contribute equally to the objective Z; Subsequently, weight It will also make dynamic adjustments based on the real-time data collected in the digital twin system and the company's requirements, according to the actual production situation.

4. The method for combined two-dimensional nesting and cutting paths based on digital twins according to claim 3, characterized in that, In step S200, the solution steps include: S210. Define the corresponding neighborhood structure for the nesting problem and the cutting path problem, and then use a goal-driven nesting optimization algorithm to generate a feasible nesting scheme. ; S220, in the layout scheme Using a greedy algorithm to find the cutting path and cutting order of parts on the layout diagram And according to The point path order for the cutting path problem is obtained using a common-edge-based cutting algorithm. Initial solution In this algorithm, the material utilization rate is used as the solution. The adaptability and the empty edge of the cutting path are the solutions. The fitness and the sum of the paths through all points traversed by the cut are the solution. The fitness of, and will solve and The fitness values ​​are multiplied by the weights respectively. The summation is then used as the overall fitness. S230, calculate the fitness of each component and the overall fitness, and then apply the perturbation algorithm to... Perturbation to obtain Then, the optimal part cutting sequence obtained in the neighborhood structure is found through a variable neighborhood descent operation. ,according to Using a shared-edge cutting algorithm to obtain Calculate the overall fitness of the new solution, compare the fitness of the two solutions, and update the better one as the best solution; S240. Next, a new layout scheme is obtained by continuously perturbing the layout solution. ,exist Get new and Repeat the perturbation algorithm, variable neighborhood descent operation, and edge-based cutting algorithm to update the best solution until the perturbation of the sorted solution reaches the upper limit of the number of iterations or the upper limit of the running time.

5. The method for combined two-dimensional nesting and cutting paths based on digital twins according to claim 4, characterized in that, In step S200, the variable neighborhood search algorithm is an algorithm that addresses both the nesting and path cutting problems. Therefore, it defines different neighborhood structures for each of these two problems. For layout problems, this includes part exchange methods and part rotation methods; for part exchange methods, any two parts can be selected from the current layout scheme. Swap their positions on the motherboard; part rotation mode, for selected parts. Rotate clockwise according to the allowed angle set; For cutting path problems, including part swapping, part reversal, and part insertion; Part swapping: swapping the cutting order of two parts; Part Reversal: Reverse the order of all parts within the interval between two parts; Part insertion: Inserting a part before other parts.

6. The method for combined two-dimensional nesting and cutting paths based on digital twins according to claim 4, characterized in that, In step S200, the target-driven nesting optimization algorithm includes the following steps: First, calculate the minimum number of usable sheets based on the total area of ​​all parts and the sheet specifications as the initial value; Then, using a pre-constructed critical polygon and a scan line strategy, the continuous geometric data of each part is converted into discrete pixel representations under this plate number, generating scan lines that scan along the coordinate axis direction to quickly detect local overlaps. In conjunction with the horizontal line strategy, initialize the first layer at the bottom of the board, recording the layer height and used width. The parts are sorted in descending order by height or area. When retrieving parts, the existing layers are traversed. If the height of a layer is greater than or equal to the height of the part, the remaining width is greater than or equal to the width of the part, and there is no overlap, then the part is placed at the current fill endpoint of the layer and the used width is updated. If none of the layers meet the requirements, a new layer is created on top of the board and then placed in the layer. The layer height is the height of the part or the preset minimum layer height, which quickly determines the placement position of each part. If all parts cannot be placed within the limited number of iterations, increment the number of boards by one and repeat the NFP decoding operation and feasibility assessment. Once a feasible solution is found, the algorithm enters the compression phase, which uses multiple iterations to tighten the layout and fill gaps by pushing parts to the edge along the X / Y axis, locally exchanging the positions of parts, and maximizing space reuse by inserting small parts into plates with remaining space, in order to maximize utilization. The final output includes the optimal number of plates, the precise placement coordinates and rotation angles of the parts on each plate, and the overall utilization rate.

7. The method for combined two-dimensional nesting and cutting paths based on digital twins according to claim 4, characterized in that, In step S200, the greedy algorithm first randomly selects a point from a part as the first element of the part cutting order. Then, in each iteration, it finds the point with the closest Euclidean distance to the point previously added to the part cutting order from the set of vertices of the parts that have not yet been added. This process is repeated until all parts have been added to the part cutting order.

8. The method for combined two-dimensional nesting and cutting paths based on digital twins according to claim 4, characterized in that, In step S200, the cutting algorithm based on shared edges optimizes the cutting path by introducing variables related to shared edges. Step 1: After the layout diagram and part cutting sequence are determined, mark all two points that form a common edge as the first point and the second point. When a point is in multiple common edge positions, it can be marked repeatedly. Step 2: First, cut the first part along its outline; Step 3: According to the obtained cutting order of the parts, when the part to be cut and the part already cut do not share an edge, the empty cutting edge is the point with the shortest distance from the exit point of the previous cutting part to all points of the part to be cut; when the part to be cut and the part already cut share an edge, the empty cutting edge is the point with the shortest distance from the exit point of the previous cutting part to the two marked points of the longest shared edge between the part to be cut and the part already cut, and this point is marked as the entry point, and the other corresponding point is marked as the exit point; Step 4: Continue cutting along the part outline. When the part to be cut and the part already cut do not share an edge, cut the entire part outline directly. When the part to be cut and the part already cut share an edge, cut in the opposite direction from the current entry point to the exit point until the current exit point. Step 5: Repeat steps 3 and 4 until all parts have been cut.

9. The method for combined two-dimensional nesting and cutting paths based on digital twins according to claim 4, characterized in that, In step S200, the perturbation algorithm performs perturbation operations on the layout scheme and the cutting order of the parts; in each iteration, a neighborhood structure is randomly selected to change the two parts related to the current solution, and a perturbation solution is obtained after 10 iterations. In the variable neighborhood descent algorithm, this algorithm is used to find the optimal part cutting sequence under the current nesting scheme and minimize the length of the empty tool edge; First, the order of three neighborhood structures in the neighborhood structure set of the part cutting order is randomly shuffled to facilitate the process of diversified local search; Then, the shuffled neighborhood structures are searched sequentially. In each neighborhood structure, all possible perturbations are traversed. Once the first perturbation that can improve the target is found, it is immediately accepted and saved. If no further improvement can be made in the current neighborhood, the search is switched to the next neighborhood. The algorithm terminates when all neighborhoods have completed a traversal without improvement.

10. The method for combined two-dimensional nesting and cutting paths based on digital twins according to claim 3, characterized in that, In step S300, A digital twin model is established to simulate layout and cutting paths, creating a model of the production environment. Real-time data is collected from the production process and fed back to the digital twin system. The data analysis capabilities of the digital twin model are used to dynamically adjust weight parameters based on actual production conditions. ; According to the algorithm The fitness function is dynamically adjusted to balance nesting efficiency and cutting length, and predictions are made based on different companies' subjective preferences for different costs. The balance of benefits under the given value is determined by selecting the optimal solution after multiple adjustments and then using it for layout and cutting in actual production so that the final result meets the producer's expectations. If current production data indicates low material utilization, the weighting parameter can be appropriately increased. This allows optimization algorithms to focus more on improving material utilization efficiency, thereby reducing material waste. If the cutting path is long and the cutting efficiency is low, the weighting parameter can be increased. This makes the optimization algorithm focus more on reducing the cutting path, so as to reduce the total length of the cutting path and the cutting time.

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