A stone defect area layout method and system based on multi-objective optimization

Abstract

The present application relates to the field of artificial intelligence auxiliary stone processing, aiming at the problem that the defective stone plate cannot be effectively processed in stone processing, the present application provides a stone defect area layout method and system based on multi-objective optimization, which comprises: collecting stone image and accurately identifying defect area through deep learning model; establishing a characteristic space coordinate system to vectorize the defect area; using an improved adaptive grid search strategy to prioritize the rectangular workpiece; executing a space allocation algorithm combining depth-first search and backtracking mechanism to determine the best position of the workpiece; and verifying the layout scheme through continuous cutting path to ensure that it fully meets the actual processing process requirements. The present application can not only realize accurate avoidance of the defect area, improve material utilization, adapt to various complex cutting processes, and provide visual simulation and direct interface for numerical control processing.

Description

Technical Field

[0001] This invention relates to the fields of intelligent manufacturing and computer-aided optimization technology, and in particular to an intelligent layout method and system for stone defect areas based on multi-objective optimization, which is applicable to the efficient utilization of slabs containing natural defects in the processing of natural stone such as marble and granite. Background Technology

[0002] As an important building and decorative material, natural stone inevitably exhibits defects such as abnormal textures, color variations, cracks, and pores during its formation. These defective areas are usually unsuitable for producing high-quality finished products and must be avoided during processing. The traditional stone processing industry faces two major challenges: first, how to accurately identify various complex defects; and second, how to rationally arrange processing plans to maximize material utilization while avoiding defects.

[0003] Currently, the industry commonly relies on experienced technicians for manual layout planning. This approach suffers from issues such as high subjectivity, low efficiency, and limited optimization. With the development of computer vision and optimization algorithms, some companies have begun using simple computer-aided layout systems. However, these systems typically suffer from the following shortcomings: low defect recognition accuracy, unable to handle complex defects; layout algorithms lack in-depth consideration of actual processing techniques, resulting in solutions that are often difficult to apply directly to production; overly simplistic algorithm design, failing to fully consider space utilization optimization, leading to material waste; and a lack of flexible adjustment mechanisms, unable to cope with dynamic changes in the layout process.

[0004] Therefore, developing a layout method and system that can accurately identify defects, deeply integrate with processing technology, efficiently optimize space utilization, and has flexible adjustment capabilities is of great significance for improving the automation level and economic benefits of the stone processing industry. Summary of the Invention

[0005] The purpose of this invention is to solve the problems of inaccurate stone defect identification, insufficient layout optimization, and poor process adaptability in the prior art. It provides a method and system for intelligent layout of stone defect areas based on multi-objective optimization, in order to maximize the utilization rate of the slab while accurately avoiding defects, and to ensure that the layout scheme fully meets the actual processing requirements.

[0006] To achieve the above objectives, the technical solution adopted by this invention is as follows: A method for layout of stone defect areas based on multi-objective optimization, comprising the following steps:

[0007] S1: Obtain the external dimensions, defect boundaries, and list of workpieces to be arranged for the stone to be laid out;

[0008] S2: Based on the established workpiece priority determination mechanism, multi-parameter weighted scoring is used to intelligently sort the workpieces in the workpiece list to be sorted.

[0009] S3: Based on the shape and size of the stone, the defect boundary and the sorting order of the workpieces, an adaptive space allocation algorithm is executed for each workpiece so that the stone after each workpiece is arranged satisfies the stone boundary constraint, the defect avoidance constraint and the continuous cutting process constraint, until all workpieces are arranged or the remaining space is insufficient to accommodate any unarranged workpieces.

[0010] S4: Generate the final layout scheme, including workpiece coordinate data, cutting path planning, and material utilization analysis report.

[0011] Preferably, the defects in S1 are addressed by using a U-Net neural network and combining it with an adaptive threshold segmentation technique to divide the confidence map output by U-Net into transition regions based on the confidence level. A dynamic threshold is calculated using a sliding window, and the threshold segmentation results are logically fused with the high-confidence regions of U-Net for feature extraction and boundary determination.

[0012] Preferably, the multi-parameter weighted scoring in S2 considers the workpiece's area, aspect ratio, urgency of demand, and geometric relationship with the identified defective area, and performs comprehensive scoring and ranking through adaptive weights.

[0013] Preferably, the multi-parameter weighted scoring adopts the following comprehensive scoring function:

[0014] Score_i=w1·A_i+w2·(1 / |R_i-1|)+w3·P_i-w4·D_i

[0015] Where A_i is the workpiece area, R_i is the aspect ratio, P_i is the urgency of the requirement, D_i is the geometric relationship with the defect, and w1, w2, w3, and w4 are the area weight, aspect ratio weight, urgency weight, and geometric relationship weight with the defect weight, respectively. The area weight, aspect ratio weight, urgency weight, and geometric relationship weight with the defect are determined through the following dynamic calculation model, including the following steps:

[0016] (1) Obtain the temporary area weight w1_temp:

[0017] w1_temp = (max(A_i) / mean(A_i)) * (1 - CV_A), where max(A_i) is the maximum area in the current set of workpieces to be arranged, mean(A_i) is the average area of ​​the current set of workpieces to be arranged, CV_A is the coefficient of variation of the area of ​​the current set of workpieces to be arranged, CV_A = std_dev(A_i) / mean(A_i), where std_dev(A_i) is the standard deviation of the area;

[0018] (2) Obtain the temporary aspect ratio weight w2_temp:

[0019] w2_temp = mean(1 / (|R_i - 1| + ε)), where mean(1 / (|R_i - 1| + ε)) is the average value of 1 / |R_i - 1| in the current set of workpieces to be scheduled, and ε is a constant to prevent division by zero;

[0020] (3) Obtain the temporary urgency weight w3_temp:

[0021] w3_temp = sum(P_urgent) / sum(P_total), where sum(P_urgent) is the sum of P_i values ​​of all tasks with an urgency level higher than the threshold, and sum(P_total) is the sum of P_i values ​​of all tasks to be scheduled.

[0022] (4) Obtain the temporary weight w4_temp for avoidance difficulty:

[0023] w4_temp = N_critical / N_total, where N_critical is the number of workpieces in the current workpieces to be arranged whose minimum profile and minimum safe distance d_min_i from defects is lower than the preset safe threshold d_threshold, and N_total is the total number of workpieces to be arranged.

[0024] (5) Normalize the temporary weights for area, aspect ratio, urgency, and geometric relationship with defects to obtain the corresponding area weight w1, aspect ratio weight w2, urgency weight w3, and geometric relationship with defects weight w4:

[0025] Sum of temporary weights: Sum_temp = w1_temp + w2_temp + w3_temp + w4_temp, w1 = w1_temp / Sum_temp, w2 = w2_temp / Sum_temp.

[0026] w3=w3_temp / Sum_temp, w4=w4_temp / Sum_temp.

[0027] Preferably, S3 includes the following operations:

[0028] S3.1: Initialize unused spatial grids and establish a spatial search tree;

[0029] S3.2: Identify the current optimal placement area based on the dynamic boundary tracking method and evaluate the utilization value of the area;

[0030] S3.3: Calculate the optimal placement direction and position for the current workpiece to be arranged, while taking into account the geometric relationship of adjacent workpieces and the requirement for defect avoidance;

[0031] S3.4: Perform workpiece placement legality verification to ensure that the sheet metal boundary constraints, defect avoidance constraints, and continuous cutting process constraints are met;

[0032] S3.5: If the current workpiece cannot meet the placement conditions, the alternating search mechanism is activated to find the most suitable replacement workpiece for the currently unused space in the remaining workpiece set;

[0033] S3.6: When a single search fails to yield satisfactory results, a spatial repartitioning strategy is triggered to re-plan unused areas;

[0034] S3.7: Repeat S3.1 to S3.6 until all workpieces are arranged or there is insufficient space remaining to accommodate any unarranged workpieces.

[0035] Preferably, the dynamic boundary tracking method in S3.2 includes: starting from the unused spatial edge, tracking the path turning points to generate a closed polygon region, evaluating the region value through parameter weighting, and selecting the current optimal placement region.

[0036] Preferably, the continuous cutting process constraint verification in S3.4 includes: constructing a cutting path tree, analyzing each candidate placement scheme, ensuring that all cutting lines can be continuously introduced from the edge of the plate without interruption, and satisfying the kinematic constraints of the equipment.

[0037] Preferably, the alternating retrieval mechanism in S3.5 adopts a greedy heuristic algorithm, which locks the candidate workpiece that is most suitable for the current region by calculating the spatial matching degree score, and supports backtracking operations with a limited number of steps to avoid local optima.

[0038] Preferably, the optimal placement orientation determination in S3.3 includes four-way rotation evaluation at 0°, 90°, 180° and 270°. Under the condition that the workpiece is allowed to rotate, the optimal orientation is determined by calculating the comprehensive score of boundary fit and space utilization.

[0039] A stone defect area layout system based on multi-objective optimization includes:

[0040] The acquisition unit is used to acquire the external dimensions, defect boundaries, and list of workpieces to be arranged of the stone to be laid out;

[0041] The intelligent sorting unit is used to intelligently sort the workpieces in the workpiece list to be sorted based on the established workpiece priority determination mechanism and by using multi-parameter weighted scoring.

[0042] The space allocation unit is used to perform an adaptive space allocation algorithm on each workpiece according to the shape and size of the stone, the defect boundary and the sorting order of the workpieces, so that the stone after each workpiece is arranged satisfies the stone boundary constraint, the defect avoidance constraint and the continuous cutting process constraint, until all workpieces are arranged or the remaining space is insufficient to accommodate any unarranged workpieces.

[0043] The layout scheme generation unit is used to generate the final layout scheme, including workpiece coordinate data, cutting path planning, and material utilization analysis report.

[0044] This invention offers the following advantages: High-precision defect identification: Employing a deep learning model for defect identification overcomes the limitations of traditional image processing methods in handling complex textured backgrounds, significantly improving identification accuracy and reducing false recognition rate. Multi-objective comprehensive optimization: Integrating multiple objectives such as maximizing material utilization, optimizing processing efficiency, and strictly avoiding defects into a unified optimization framework, achieving a balance between different objectives through dynamic weight adjustment. Complete process adaptation: By constructing a cutting path tree and performing kinematic verification, the generated layout scheme ensures 100% compliance with actual processing requirements, avoiding the unexecutable problems caused by traditional algorithms ignoring process constraints. Adaptive spatial planning: Innovatively introducing dynamic boundary tracking and spatial repartitioning strategies effectively handles irregular available space caused by defect areas, improving space utilization efficiency. Intelligent interactive adjustment: The system supports human-machine collaborative optimization, allowing operators to fine-tune the algorithm-generated scheme based on experience, combining the advantages of artificial intelligence and human experience to achieve a more ideal layout effect. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0046] Figure 1 This is a flowchart illustrating the intelligent layout method for stone defect areas based on multi-objective optimization according to the present invention.

[0047] Figure 2 This is a structural block diagram of the intelligent layout system for stone defect areas based on multi-objective optimization according to the present invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of the present invention.

[0049] Example

[0050] The following are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the following embodiments. All technical solutions that fall within the scope of the present invention are within the scope of protection of the present invention.

[0051] Reference manual attached Figure 1 and Figure 2 A method for layout of stone defect areas based on multi-objective optimization includes the following steps:

[0052] S1: Obtain the external dimensions, defect boundaries, and list of workpieces to be arranged for the stone to be laid out;

[0053] The defect identification in S1 can use a U-Net neural network, combined with adaptive threshold segmentation technology to divide the confidence map output by U-Net into transition regions according to the confidence level, calculate the dynamic threshold with a sliding window, and logically fuse the threshold segmentation result with the high-confidence region of U-Net for feature extraction and boundary determination.

[0054] S2: Based on the established workpiece priority determination mechanism, multi-parameter weighted scoring is used to intelligently sort the workpieces in the workpiece list to be sorted.

[0055] The multi-parameter weighted scoring considers the workpiece's area, aspect ratio, urgency of demand, and geometric relationship with identified defect areas, and performs comprehensive scoring and ranking through adaptive weights. The following comprehensive scoring function is used:

[0056] Score_i=w1·A_i+w2·(1 / |R_i-1|)+w3·P_i-w4·D_i

[0057] Where A_i is the workpiece area, R_i is the aspect ratio, P_i is the urgency of the requirement, D_i is the geometric relationship with the defect, and w1, w2, w3 and w4 are the area weight, aspect ratio weight, urgency of the requirement weight and geometric relationship with the defect weight, respectively.

[0058] The area weight, aspect ratio weight, urgency weight, and geometric relationship weight with defects are determined through the following dynamic calculation model, including the following steps:

[0059] (1) Obtain the temporary area weight w1_temp:

[0060] w1_temp = (max(A_i) / mean(A_i)) * (1 - CV_A), where max(A_i) is the maximum area in the current set of workpieces to be arranged, mean(A_i) is the average area of ​​the current set of workpieces to be arranged, CV_A is the coefficient of variation of the area of ​​the current set of workpieces to be arranged, CV_A = std_dev(A_i) / mean(A_i), where std_dev(A_i) is the standard deviation of the area;

[0061] (2) Obtain the temporary aspect ratio weight w2_temp:

[0062] w2_temp = mean(1 / (|R_i - 1| + ε)), where mean(1 / (|R_i - 1| + ε)) is the average value of 1 / |R_i - 1| in the current set of workpieces to be scheduled, and ε is a constant to prevent division by zero;

[0063] (3) Obtain the temporary urgency weight w3_temp:

[0064] w3_temp = sum(P_urgent) / sum(P_total), where sum(P_urgent) is the sum of P_i values ​​of all tasks with an urgency level higher than the threshold, and sum(P_total) is the sum of P_i values ​​of all tasks to be scheduled.

[0065] (4) Obtain the temporary weight w4_temp for avoidance difficulty:

[0066] w4_temp = N_critical / N_total, where N_critical is the number of workpieces in the current workpieces to be arranged whose minimum profile and minimum safe distance d_min_i from defects is lower than the preset safe threshold d_threshold, and N_total is the total number of workpieces to be arranged.

[0067] (5) Normalize the temporary weights for area, aspect ratio, urgency, and geometric relationship with defects to obtain the corresponding area weight w1, aspect ratio weight w2, urgency weight w3, and geometric relationship with defects weight w4:

[0068] Sum of temporary weights: Sum_temp = w1_temp + w2_temp + w3_temp + w4_temp, w1 = w1_temp / Sum_temp, w2 = w2_temp / Sum_temp.

[0069] w3=w3_temp / Sum_temp, w4=w4_temp / Sum_temp.

[0070] S3: Based on the shape and size of the stone, the defect boundary and the sorting order of the workpieces, an adaptive space allocation algorithm is executed for each workpiece so that the stone after each workpiece is arranged satisfies the stone boundary constraint, the defect avoidance constraint and the continuous cutting process constraint, until all workpieces are arranged or the remaining space is insufficient to accommodate any unarranged workpieces.

[0071] Specifically, the following operations are included:

[0072] S3.1: Initialize unused spatial grids and establish a spatial search tree;

[0073] S3.2: Identify the current optimal placement area based on the dynamic boundary tracking method and evaluate the utilization value of the area; wherein the dynamic boundary tracking method includes: starting from the edge of the unused space, tracking the path turning points to generate a closed polygonal area, evaluating the value of the area through parameter weighting, and selecting the current optimal placement area.

[0074] S3.3: Calculate the optimal placement direction and position for the current workpiece to be arranged, while considering the geometric relationship of adjacent workpieces and the need for defect avoidance; the optimal placement direction judgment includes four-way rotation evaluation of 0°, 90°, 180° and 270°. Under the condition that the workpiece rotation is allowed, the optimal orientation is determined by calculating the boundary fit and space utilization rate as a comprehensive score.

[0075] S3.4: Perform workpiece placement legality verification to ensure that the sheet metal boundary constraints, defect avoidance constraints, and continuous cutting process constraints are met; among which, the continuous cutting process constraint verification includes: constructing a cutting path tree, analyzing each candidate placement scheme, ensuring that all cutting lines can be continuously introduced from the edge of the sheet metal without interruption, and satisfying the kinematic constraints of the equipment.

[0076] S3.5: If the current workpiece cannot meet the placement conditions, the alternating retrieval mechanism is activated to find the most suitable replacement workpiece for the current unused space in the remaining workpiece set. The alternating retrieval mechanism adopts a greedy heuristic algorithm, which locks the candidate workpiece that is most suitable for the current region by calculating the space matching degree score, and supports backtracking operations of a finite number of steps to avoid local optima.

[0077] S3.6: When a single search fails to yield satisfactory results, a spatial repartitioning strategy is triggered to re-plan unused areas;

[0078] S3.7: Repeat S3.1 to S3.6 until all workpieces are arranged or there is insufficient space remaining to accommodate any unarranged workpieces.

[0079] S4: Generate the final layout scheme, including workpiece coordinate data, cutting path planning, and material utilization analysis report.

[0080] To further understand the present invention, an example will be used to illustrate its application below:

[0081] Example 1: Stone Defect Identification and Digital Characterization Based on Deep Learning

[0082] First, high-resolution images of the stone surface are captured using an industrial camera, with an image resolution of at least 300 DPI, to ensure that even minute defects are captured. A uniform lighting system is then employed to reduce shadows and glare.

[0083] To address the unique texture background of natural stone, we improved the standard U-Net neural network by adding an attention mechanism module and residual connections to enhance the detection capability of fine cracks and color differences. The training dataset contains 5000 labeled images, covering common types of stone defects. After 200 rounds of training, the model achieved a defect recognition accuracy of 95.3% on the test set. A defect probability map, or confidence map, is generated using the U-Net network. For ambiguous boundary regions with confidence scores of 0.3–0.7, dynamic local thresholding is used to correct the boundary pixel assignment, and this is logically fused with the U-Net probability map—retaining the direct output of high-confidence regions (>0.7), marking low-confidence regions (<0.3) as background, and performing pixel-level correction on transition regions using threshold segmentation results.

[0084] To address the potential boundary blurring issue that U-Net may produce in complex textured stone images, an adaptive thresholding segmentation technique is introduced for local dynamic threshold calculation:

[0085] Based on the defect probability map output by U-Net, a local optimal threshold is calculated for the transition region with a confidence level of 0.3–0.7 using a sliding window (30mm×30mm):

[0086] T(x,y)=μ(x,y)+k⋅σ(x,y)

[0087] in:

[0088] μ(x,y): Mean gray value of pixels within the window;

[0089] σ(x,y): Standard deviation of gray levels within the window;

[0090] k is dynamically adjusted according to the type of stone (granite: 0.15–0.25, marble: 0.25–0.35).

[0091] For identified defect areas, the Douglas-Peucker algorithm is used to simplify the boundaries, converting complex contours into polygonal vector representations while preserving shape features. This representation method saves more storage space than raster representation and facilitates subsequent spatial calculations. The system supports manual correction, allowing operators to fine-tune defect boundaries according to actual conditions.

[0092] Example 2: Determining workpiece priority based on multi-parameter comprehensive scoring

[0093] This invention designs a flexible workpiece priority scoring mechanism, taking into account the following factors:

[0094] 1. Workpiece area (A_i): Workpieces with larger areas are given priority in placement to avoid difficulties in placing large-sized workpieces later;

[0095] 2. Aspect Ratio (R_i): Workpieces that are close to square (R_i close to 1) receive higher priority because extremely long and thin workpieces usually have more placement options;

[0096] 3. Urgency of demand (P_i): Production priority specified by the user, with a value range of 1-10;

[0097] 4. Geometric relationship with defects (D_i): Calculate the minimum distance between the possible contour of the workpiece and the defect area. The smaller the distance, the greater the difficulty of placement.

[0098] The comprehensive scoring function is:

[0099] Score_i=w1·A_i+w2·(1 / |R_i-1|)+w3·P_i-w4·D_i

[0100] in:

[0101] w1 to w4 are weighting coefficients, with default values ​​provided by the system (w1=0.5, w2=0.2, w3=0.2, w4=0.1).

[0102] It also allows users to adjust the weights according to specific production needs. The weighting coefficients w1 to w4 are determined through the following dynamic calculation model:

[0103] 1. w1_temp, w2_temp, w3_temp, and w4_temp are temporary weights that reflect the original "importance intensity" of each factor under the current workpiece set characteristics, but their sum (Sum_temp = w1_temp + w2_temp + w3_temp + w4_temp) is usually not equal to 1.

[0104] The selected temporary weight coefficients need to be normalized to ensure that the sum of the weight coefficients is 1 (∑w = 1):

[0105] Calculate the normalization factor:

[0106] (1)Sum_temp = w1_temp + w2_temp + w3_temp + w4_temp

[0107] (2)α=β=γ=δ=1 / Sum_temp

[0108] 2. Area weight (w1):

[0109] (1)w1_temp = (max(A_i) / mean(A_i)) * (1 - CV_A)

[0110] (2) w1=α * w1_temp

[0111] in:

[0112] α: Normalization factor for area weight (determined after calculation).

[0113] max(A_i): The maximum area in the current set of workpieces to be arranged.

[0114] mean(A_i): The average area of ​​the current set of workpieces to be arranged.

[0115] CV_A: Coefficient of Variation of the area of ​​the current set of workpieces to be arranged, CV_A = std_dev(A_i) / mean(A_i), where std_dev(A_i) is the standard deviation of the area.

[0116] When there are significantly large workpieces (max / mean large) and the workpiece sizes are relatively uniform (CV_A small), increase w1 to prioritize the arrangement of large workpieces.

[0117] 3. Aspect Ratio Weight (w2):

[0118] (1)w2_temp = mean(1 / (|R_i - 1| + ε))

[0119] (2) w2=β * w2_temp

[0120] in:

[0121] β: Normalization factor for aspect ratio weights (determined after calculation). mean(1 / (|R_i - 1| + ε)): Calculates the average value of 1 / |R_i - 1| in the current set of workpieces to be scheduled. ε is a small constant to prevent division by zero (e.g., ε = 0.01).

[0122] When the set of workpieces to be arranged is closer to a square as a whole (the average value of 1 / |R_i-1| is larger), increase w2 to take advantage of the layout of these regular workpieces.

[0123] 4. Urgency weight (w3):

[0124] (1) w3_temp = sum(P_urgent) / sum(P_total)

[0125] (2) w3 = γ * w3_temp

[0126] in:

[0127] γ: Normalization factor for urgency weight (determined after calculation).

[0128] sum(P_urgent): The sum of the P_i values ​​of all items whose urgency is higher than a certain threshold (e.g., P_i>= 7).

[0129] sum(P_total): The sum of the P_i values ​​of all workpieces to be scheduled.

[0130] When the total demand for high-urgent (P_urgent) jobs is high in the set of jobs to be scheduled, increase w3 to prioritize urgent orders.

[0131] 5. Avoidance Difficulty Weight (w4):

[0132] (1) w4_temp =N_critical / N_total

[0133] (2) w4 = δ * w4_temp

[0134] in:

[0135] δ: Normalization factor (determined after calculation).

[0136] N_critical: The number of workpieces currently scheduled whose minimum possible contour and minimum safe distance (d_min_i) from defects is lower than the preset safety threshold d_threshold.

[0137] N_total: The total number of workpieces currently awaiting scheduling.

[0138] When there are many workpieces (with large N_critical / N_total values) that are difficult or risky to place due to their proximity to defects, increase w4 to prioritize placing these "difficult" workpieces and avoid them having no suitable space available later.

[0139] Example 3: Core Implementation of the Adaptive Space Allocation Algorithm

[0140] Initialization Phase. The system divides the stone slab surface into a grid (each grid typically has an area of ​​5mm × 5mm), marking grids covered by defects as disabled. A dynamic boundary tracking method is used to identify available space: starting from the lower left corner of the slab, the system travels along the edge of the slab and the boundaries of the arranged workpieces / defects, recording the coordinates of turning points to form a closed polygon representing an Available Space Region (ASR). A value score is calculated for each region.

[0141] V_region = w_area * Area_normalized + w_rect * Rectangularity - w_risk * DefectProximity

[0142] in:

[0143] The corresponding symbols are dynamic weight coefficients: w_area (area weight), w_rect (rectangularity weight), w_risk (risk weight); Area_normalized (normalized area); Rectangularity (rectangularity); DefectProximity (defect proximity).

[0144] 1. The dynamic weight coefficients w_area, w_rect, and w_risk sum to 1.

[0145] (1) w_area (area weight): controls the importance of the area size in the scoring. The larger the value, the more the system tends to prioritize larger areas. The default value is 0.6.

[0146] (2) w_rect (rectangularity weight): Controls the importance of the regularity of the region shape in the scoring. The larger the value, the more the system tends to prioritize regions that are close to rectangles. The default value is 0.3.

[0147] (3) w_risk (risk weight): The importance of the risk of the control area being close to the defect in the scoring. The larger the value, the more the system tends to avoid areas close to the defect. The default value is 0.1.

[0148] 2. Area_normalized: Actual area of ​​the target region (A_region) / Total area of ​​the board (A_board), reflecting the proportion of the area size.

[0149] 3. Rectangularity: A_region / A_mbr.

[0150] A_mbr is the area of ​​the minimum bounding rectangle (MBR) of the usable space formed by the profile of the board. The rectangularity value ranges from (0, 1], and the closer the value is to 1, the more regular the shape (closer to a rectangle).

[0151] Specific engineering implementation: (1) Contour extraction: Apply an edge detection algorithm (such as Canny) to the binary mask of the available space region. (2) Calculation of minimum bounding rectangle area A_mbr: Calculate the minimum bounding rectangle and its area of ​​the contour using the rotating caliper algorithm. (3) Calculation of actual area A_region: Count the number of effective grids in the available space region and multiply by the area of ​​a single grid (default is 5mm×5mm). (4) Calculation of rectangularity: Rectangularity = A_region / A_mbr.

[0152] Examples: (1) Perfect rectangular region: Rectangularity = 1.0; (2) Complex polygonal region: Rectangularity ≈ 0.6; (3) Circular region: Rectangularity ≈ 0.785 (π / 4);

[0153] 4. Defect Proximity: 1 - min(dist_edge) / D_board.

[0154] min(dist_edge) is the minimum Euclidean distance from the boundary of the available space region to the nearest defect edge; D_board = It is the diagonal length of the board material, used for normalization, where Represents the width of the board material. This represents the length of the board material. The defect proximity value ranges from [0, 1], with a larger value indicating closer proximity to the defect and a higher placement risk.

[0155] Specific engineering implementation: (1) Distance field construction: Perform Euclidean distance transformation (EDT) on the binary image of the defect to generate a field Dist_map of the distance from each pixel to the nearest defect edge. (2) Minimum distance query: Densely sample points on the contour of the available spatial region, query Dist_map to obtain the set of distance values, and take the minimum value min_dist = min(Dist_map(sample_points)). (3) Normalization calculation: DefectProximity = 1 - (min_dist / D_board).

[0156] Examples: (1) Available space overlaps with the defect: min_dist = 0, DefectProximity = 1.0; (2) Available space is 0.5 * D_board away from the defect: DefectProximity = 0.5; (3) Available space is far from the defect: min_dist ≈ D_board, DefectProximity ≈ 0;

[0157] The feasible placement phase involves searching for feasible placement locations for the current workpiece Part_i within its allowed rotational directions (0°, 90°, 180°, 270°) across each candidate available space region, and calculating a comprehensive placement score Score_placement for each feasible location.

[0158] Score_placement = λ_fit * EdgeFit + λ_util * SpaceUtilization - λ_waste * WastageRisk

[0159] in:

[0160] 1. Dynamic weighting coefficients: λ_fit, λ_util, λ_waste, the sum of which is always 1. Default configuration: λ_fit=0.4, λ_util=0.4, λ_waste=0.2.

[0161] (1) λ_fit (fit weight): controls the importance of edge fit in the scoring. The larger the value, the more the system tends to place the workpiece in a position that can fit closely to the existing boundary in order to optimize the cutting path length.

[0162] (2) λ_util (potential weight): controls the importance of space utilization potential in the scoring. The larger the value, the more the system tends to choose a position where the remaining space is more regular and more conducive to subsequent layout.

[0163] (3) λ_waste (waste risk weight): controls the importance of avoiding waste risk in the scoring. The larger the value, the more the system tends to avoid placement locations that may generate a large amount of unusable scrap.

[0164] 2. EdgeFit: L_contact / L_total.

[0165] L_contact is the effective contact length between the current workpiece Part_i contour and the currently cut boundaries of the sheet metal (including the sheet metal outer frame, the boundaries of already arranged workpieces, and the defect boundaries) under the condition of satisfying the maximum gap constraint Gap_max (default ≤ 1mm); L_total is the total perimeter of the current workpiece Part_i contour. The edge fit ranges from [0, 1], with a higher value indicating better fit and reducing the cutting path length.

[0166] Specific engineering implementation: (1) Boundary distance field: Pre-calculate the Euclidean distance transformation (EDT) field Boundary_dist_map of the current plate layout (including all arranged elements); (2) Contact length calculation: Sample points on the contour after the current workpiece Part_i is placed. Calculate the total length of the contour segments that continuously satisfy Boundary_dist_map(point) ≤ Gap_max, i.e., L_contact; (3) Normalization: EdgeFit = L_contact / L_total.

[0167] Examples: (1) L-shaped nested placement: EdgeFit ≈ 0.8 (mainly due to the presence of non-contact edges); (2) Isolated placement: EdgeFit = 0.

[0168] 3. Space Utilization Potential:

[0169] (Σ (A_free_k * Rect_k)) / A_free_total.

[0170] The value ranges from (0, 1). A higher value indicates that after placing the current workpiece Part_i, the remaining free space will have a more regular shape (closer to a rectangle or a combination of rectangles), which is more conducive to the effective placement of subsequent workpieces and has greater space utilization potential.

[0171] A_free_total (Total Remaining Free Area): The total area of ​​all remaining free areas on the board after placing the current workpiece Part_i to be arranged.

[0172] A_free_k (subregion area): The area of ​​the kth independent remaining free connected region. The remaining free region is usually divided into k unconnected subregions by the current job to be scheduled, Part_i.

[0173] Rect_k (subregion rectangularity): The rectangularity of the kth remaining free subregion, calculated in the same way as ASR's ectangularity.

[0174] Rect_k = A_free_k / A_mbr_k

[0175] A_mbr_k (area of ​​minimum bounding rectangle of subregion): The area of ​​the minimum bounding rectangle (MBR) of the kth remaining free subregion outline.

[0176] Specific engineering implementation: (1) Extraction of free regions: After placing the current workpiece Part_i to be arranged, update the free mesh diagram, apply morphological opening operation to remove noise, extract and mark all connected free regions, and obtain k connected regions; (2) Evaluation of sub-regions: For each free connected region k, calculate its actual area A_free_k; calculate its minimum bounding rectangle area A_mbr_k. Calculate its rectangularity Rect_k = A_free_k / A_mbr_k. (3) Calculate the numerator: Σ (A_free_k *Rect_k) = A_free_1 * Rect_1 + A_free_2 * Rect_2 + ... + A_free_K * Rect_K. (4) Calculate the denominator: A_free_total = A_free_1 + A_free_2 + ... + A_free_K (i.e., the sum of all A_free_k) (5) Calculate SpaceUtilization: SpaceUtilization = (Σ (A_free_k * Rect_k)) / A_free_total.

[0177] Example: (1) Remaining single rectangular space: SpaceUtilization = 1.0; (2) Remaining multiple narrow slits: SpaceUtilization ≈ 0.3.

[0178] 4. Waste Risk: A_frag / A_free.

[0179] A_frag is the sum of the areas of all sub-regions with areas less than the fragment threshold A_min in the remaining free area after placement; A_free is the total area of the remaining free area. The value range is [0, 1), and the higher the value, the greater the risk of generating unusable scraps.

[0180] Specific engineering implementation: (1) Fragment detection: Identify areas that satisfy A_free_k < A_min in all remaining free connected regions. (2) Summation of fragment areas: A_frag = ΣA_free_k (where A_free_k < A_min). (3) Risk calculation: WastageRisk = A_frag / A_free. (4) Setting of the fragment threshold: A_min = k * A_part_avg. A_part_avg is the average area of the workpieces to be arranged; k is a proportionality coefficient (default k = 0.1, which can be adjusted according to the value of the plate).

[0181] Example: (1) Generating scraps accounting for 15% of the remaining area: WastageRisk = 0.15 (2) No effective fragments: WastageRisk = 0

[0182] Phase of verifying the legality of placement. It includes triple checks: Boundary check to ensure that the workpiece is completely within the plate; Overlap check to ensure that the workpiece does not intersect any defective areas; Cutting process verification to ensure that all cutting lines can reach the target position unobstructed from the edge of the plate by constructing a cutting path tree. It includes:

[0183] 1. Travel verification: Check whether the cutting path exceeds the physical travel of the equipment guide rail;

[0184] 2. Kinetic verification: Calculate the centripetal acceleration at the turning points of the path to ensure that it does not exceed the equipment allowable threshold. Generally, > 0.5G may cause tool deviation;

[0185] 3. Tool reachability verification: For workpieces with complex contours, verify whether the tool can cut in with a safe posture to avoid collision with the already cut workpieces.

[0186] Example: If the placement position of the workpiece causes the cutting path to make a sharp turn of 90°, and the minimum turning radius of the equipment is 50 mm, then the path needs to be re-planned or the orientation of the workpiece needs to be adjusted.

[0187] When the current workpiece cannot be placed, start the alternative retrieval mechanism: Calculate the matching degree between the remaining workpieces and the current space, and select the best-matching workpiece to try to place. The system supports three-step backtracking operations, that is, it can revoke the last three placement decisions and try alternative solutions to avoid local optimal solutions.

[0188] Example 4: System architecture and interaction design

[0189] The system of this invention adopts a modular design, with each module exchanging data through standardized interfaces. The image acquisition and defect recognition module is implemented based on the deep learning framework TensorFlow and supports GPU acceleration; the data modeling and management module adopts a hybrid architecture combining relational databases and NoSQL databases, balancing structured data management and unstructured geometric data storage; the core typesetting algorithm module is implemented in C++ and combined with the OpenMP parallel computing framework to achieve high-performance computing; the visualization and output module is based on WebGL technology, providing cross-platform 3D visualization capabilities.

[0190] The system offers a user-friendly interface, allowing operators to intuitively view stone materials, defects, and layout results via touchscreen. Gesture controls are supported, enabling zooming in, zooming out, and rotating views for easy inspection of details. Manual fine-tuning is provided, allowing operators to make localized adjustments to the algorithm-generated scheme based on experience. The system automatically verifies whether manual adjustments violate constraints, ensuring that the adjusted scheme remains feasible.

[0191] Example 5: Verification of Practical Application Effect

[0192] This invention has undergone a 6-month practical application test at a large stone processing enterprise. Comparing the results of traditional manual layout with the automatic layout of this system, the system achieved significant results when processing 100 defective stone slabs: material utilization increased by an average of 11.3%, defect avoidance success rate reached 100%, layout planning time was reduced from an average of 45 minutes per slab to 3 minutes, and the generated cutting schemes all met the process requirements of the production equipment and could be directly used in production without manual adjustment.

[0193] Reference manual attached Figure 2 A stone defect area layout system based on multi-objective optimization includes:

[0194] The acquisition unit is used to acquire the external dimensions, defect boundaries, and list of workpieces to be arranged of the stone to be laid out;

[0195] The intelligent sorting unit is used to intelligently sort the workpieces in the workpiece list to be sorted based on the established workpiece priority determination mechanism and by using multi-parameter weighted scoring.

[0196] The space allocation unit is used to perform an adaptive space allocation algorithm on each workpiece according to the shape and size of the stone, the defect boundary and the sorting order of the workpieces, so that the stone after each workpiece is arranged satisfies the stone boundary constraint, the defect avoidance constraint and the continuous cutting process constraint, until all workpieces are arranged or the remaining space is insufficient to accommodate any unarranged workpieces.

[0197] The layout scheme generation unit is used to generate the final layout scheme, including workpiece coordinate data, cutting path planning, and material utilization analysis report.

[0198] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for layout of stone defect areas based on multi-objective optimization, characterized in that, Includes the following steps: S1: Obtain the external dimensions, defect boundaries, and list of workpieces to be arranged for the stone to be laid out; S2: Based on the established workpiece priority determination mechanism, the workpieces in the workpiece list to be sorted are intelligently sorted by multi-parameter weighted scoring. The multi-parameter weighted scoring in S2 considers the workpiece area, aspect ratio, urgency of demand and geometric relationship with the identified defect area, and performs comprehensive scoring and sorting through adaptive weights. S3: Based on the stone's shape and dimensions, defect boundaries, and the workpiece's sorting order, an adaptive space allocation algorithm is executed for each workpiece, ensuring that the stone after each workpiece layout satisfies stone boundary constraints, defect avoidance constraints, and continuous cutting process constraints, until all workpieces are arranged or the remaining space is insufficient to accommodate any unarranged workpieces; S3 includes the following operations: S3.1: Initialize unused spatial grids and establish a spatial search tree; S3.2: Identify the current optimal placement area based on the dynamic boundary tracking method, evaluate the utilization value of the area, the dynamic boundary tracking method includes: starting from the edge of the unused space, tracking the path turning points to generate a closed polygon area, evaluating the value of the area through parameter weighting, and selecting the current optimal placement area; S3.3: Calculate the optimal placement direction and position for the current workpiece to be arranged, while taking into account the geometric relationship of adjacent workpieces and the requirement for defect avoidance; S3.4: Perform workpiece placement legality verification to ensure that the sheet metal boundary constraints, defect avoidance constraints, and continuous cutting process constraints are met. Continuous cutting process constraint verification includes: constructing a cutting path tree, analyzing each candidate placement scheme, ensuring that all cutting lines can be continuously introduced from the edge of the sheet metal without interruption, and meeting the kinematic constraints of the equipment. S3.5: If the current workpiece cannot meet the placement conditions, the alternating retrieval mechanism is started to find the most suitable replacement workpiece for the current unused space in the remaining workpiece set. The alternating retrieval mechanism adopts a greedy heuristic algorithm, locks the candidate workpiece most suitable for the current area by calculating the space matching degree score, and supports backtracking operations of a limited number of steps to avoid local optima. S3.6: When a single search fails to yield satisfactory results, a spatial repartitioning strategy is triggered to re-plan unused areas; S3.7: Repeat S3.1 to S3.6 until all workpieces are arranged or there is insufficient space remaining to accommodate any unarranged workpieces; S4: Generate the final layout scheme, including workpiece coordinate data, cutting path planning, and material utilization analysis report.

2. The stone defect area layout method based on multi-objective optimization according to claim 1, characterized in that, The defect in S1 uses a U-Net neural network and an adaptive threshold segmentation technique to divide the confidence map output by U-Net into transition regions based on the confidence level. A dynamic threshold is calculated using a sliding window, and the threshold segmentation result is logically fused with the high-confidence region of U-Net for feature extraction and boundary determination.

3. The stone defect area layout method based on multi-objective optimization according to claim 1, characterized in that, The multi-parameter weighted scoring uses the following comprehensive scoring function: Score_i=w1·A_i+w2·(1 / |R_i-1|)+w3·P_i-w4·D_i Where A_i is the workpiece area, R_i is the aspect ratio, P_i is the urgency of the requirement, D_i is the geometric relationship with the defect, and w1, w2, w3 and w4 are the area weight, aspect ratio weight, urgency of the requirement weight and geometric relationship with the defect weight, respectively. The area weight, aspect ratio weight, urgency weight, and geometric relationship weight with defects are determined through the following dynamic calculation model, including the following steps: (1) Obtain the temporary area weight w1_temp: w1_temp = (max(A_i) / mean(A_i)) * (1 - CV_A), where max(A_i) is the maximum area in the current set of workpieces to be arranged, mean(A_i) is the average area of ​​the current set of workpieces to be arranged, CV_A is the coefficient of variation of the area of ​​the current set of workpieces to be arranged, CV_A = std_dev(A_i) / mean(A_i), where std_dev(A_i) is the standard deviation of the area; (2) Obtain the temporary aspect ratio weight w2_temp: w2_temp = mean(1 / (|R_i - 1| + ε)), where mean(1 / (|R_i - 1| + ε)) is the average value of 1 / |R_i - 1| in the current set of workpieces to be scheduled, and ε is a constant to prevent division by zero; (3) Obtain the temporary urgency weight w3_temp: w3_temp = sum(P_urgent) / sum(P_total), where sum(P_urgent) is the sum of P_i values ​​of all tasks with an urgency level higher than the threshold, and sum(P_total) is the sum of P_i values ​​of all tasks to be scheduled. (4) Obtain the temporary weight w4_temp for avoidance difficulty: w4_temp = N_critical / N_total, where N_critical is the number of workpieces in the current workpieces to be arranged whose minimum profile and minimum safe distance d_min_i from defects is lower than the preset safe threshold d_threshold, and N_total is the total number of workpieces to be arranged. (5) Normalize the temporary weights for area, aspect ratio, urgency, and geometric relationship with defects to obtain the corresponding area weight w1, aspect ratio weight w2, urgency weight w3, and geometric relationship with defects weight w4: Sum of temporary weights: Sum_temp = w1_temp + w2_temp + w3_temp + w4_temp, w1 = w1_temp / Sum_temp, w2 = w2_temp / Sum_temp. w3=w3_temp / Sum_temp, w4=w4_temp / Sum_temp.

4. The stone defect area layout method based on multi-objective optimization according to claim 1, characterized in that, The optimal placement orientation determination in S3.3 includes four-way rotation evaluation at 0°, 90°, 180° and 270°. Under the condition that the workpiece is allowed to rotate, the optimal orientation is determined by calculating the comprehensive score of boundary fit and space utilization.

5. A stone defect area layout system based on multi-objective optimization, characterized in that, include: The acquisition unit is used to acquire the external dimensions, defect boundaries, and list of workpieces to be arranged of the stone to be laid out; The intelligent sorting unit is used to intelligently sort the workpieces in the workpiece list based on the established workpiece priority determination mechanism and adopts multi-parameter weighted scoring. The multi-parameter weighted scoring considers the workpiece area, aspect ratio, urgency of demand, and geometric relationship with the identified defect area, and performs comprehensive scoring and sorting through adaptive weights. The space allocation unit is used to perform an adaptive space allocation algorithm on each workpiece according to the shape and size of the stone, the defect boundary and the sorting order of the workpieces, so that the stone after each workpiece is arranged satisfies the stone boundary constraint, the defect avoidance constraint and the continuous cutting process constraint, until all workpieces are arranged or the remaining space is insufficient to accommodate any unarranged workpieces. The adaptive space allocation algorithm includes the following operations: initializing unused space grids and establishing a space search tree; The optimal placement area is identified based on a dynamic boundary tracking method, which evaluates the utilization value of the area. This method includes: starting from the edge of unused space, tracing path turning points to generate closed polygonal regions; evaluating the region's value through parameter weighting to select the optimal placement area; calculating the optimal placement direction and position for the current workpiece to be arranged, while considering the geometric relationships of adjacent workpieces and defect avoidance requirements; performing workpiece placement legality verification to ensure compliance with plate boundary constraints, defect avoidance constraints, and continuous cutting process constraints. Continuous cutting process constraint verification includes: constructing a cutting path tree, analyzing each candidate placement scheme to ensure all cutting lines can be continuously introduced from the plate edge without interruption and satisfying equipment kinematic constraints; if the current workpiece cannot meet the placement conditions, an alternating search mechanism is initiated to find the most suitable alternative workpiece for the current unused space from the remaining workpiece set. The alternating search mechanism uses a greedy heuristic algorithm, calculating a spatial matching score to lock the most suitable candidate workpiece for the current region, and supports finite-step backtracking operations to avoid local optima; when a single search fails to obtain satisfactory results, a spatial repartitioning strategy is triggered to replan the unused area; repeating the above steps until all workpieces are arranged or the remaining space is insufficient to accommodate any unarranged workpieces. The layout scheme generation unit is used to generate the final layout scheme, including workpiece coordinate data, cutting path planning, and material utilization analysis report.

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