Stone defect area typesetting method and system based on multi-objective optimization

Abstract

The invention relates to and belongs to the field of artificial intelligence assisted stone processing, and provides a stone defect area typesetting method and system based on multi-objective optimization in order to solve the problem that stone plates with defects cannot be effectively processed in stone processing, and the method comprises the steps that a stone image is collected, and a defect area is accurately recognized through a deep learning model; establishing a feature space coordinate system, and carrying out vectorization representation on the defect region; performing priority ranking on the rectangular workpieces by adopting an improved self-adaptive grid search strategy; executing a space distribution algorithm combining depth-first search and a backtracking mechanism to determine the optimal position of the workpiece; it is ensured that the typesetting scheme completely meets the actual machining process requirement through continuous cutting path verification. According to the method, accurate avoidance of a defect area can be achieved, the material utilization rate is increased, the method is suitable for various complex cutting processes, and direct interfaces for visual simulation and numerical control machining are provided.

Description

Technical Field

[0001] The present invention relates to the field of intelligent manufacturing and computer-aided optimization technology, and in particular to a method and system for intelligent layout of stone defect areas based on multi-objective optimization, which is suitable for the efficient utilization of plates containing natural defects during the processing of natural stones such as marble and granite. Background Art

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

[0003] The current industry-wide approach relies on experienced technicians to manually plan layouts, a method characterized by subjectivity, low efficiency, and limited optimization. With the development of computer vision and optimization algorithms, some companies have begun adopting simple computer-aided layout systems, but these systems often suffer from the following deficiencies: low defect recognition accuracy and an inability to handle complex defects; layout algorithms lack in-depth consideration of actual processing techniques, resulting in solutions that are often difficult to directly apply to production; overly simplistic algorithm designs that fail to fully consider optimal space utilization, leading to material waste; and a lack of flexible adjustment mechanisms that prevent them from responding to dynamic changes in the layout process.

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

[0005] The purpose of the present invention is to solve the problems of inaccurate stone defect identification, insufficient layout optimization, and weak process adaptability in the prior art, and to provide an intelligent layout method and system for stone defect areas based on multi-objective optimization, so as to maximize the utilization rate of the plate while accurately avoiding defects, and ensure that the layout plan fully meets the actual processing requirements.

[0006] To achieve the above object, the present invention adopts the following technical solution: a stone defect area layout method based on multi-objective optimization, comprising the following steps: S1: Obtain the external dimensions, defect boundaries and list of workpieces to be arranged of the stone to be arranged; S2: Based on the established artifact priority determination mechanism, multi-parameter weighted scoring is used to intelligently sort the artifacts in the artifact list; S3: Based on the stone's dimensions, defect boundaries, and the workpiece sorting order, an adaptive space allocation algorithm is executed for each workpiece, so that the stone after each workpiece layout satisfies the 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; S4: Generate the final layout plan, including workpiece coordinate data, cutting path planning and material utilization analysis report.

[0007] Preferably, the defects in S1 are detected using a U-Net neural network, and the confidence map output by the U-Net is combined with adaptive threshold segmentation technology. The transition area is divided according to the confidence level, the dynamic threshold is calculated using a sliding window, and the threshold segmentation result is logically fused with the U-Net high confidence area to perform feature extraction and boundary determination.

[0008] Preferably, the multi-parameter weighted scoring in S2 takes into account the area, aspect ratio, urgency of the demand and the geometric relationship with the identified defective area of ​​the workpiece, and performs comprehensive scoring and ranking through adaptive weights.

[0009] Preferably, the multi-parameter weighted scoring adopts 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 demand urgency, D_i is the geometric relationship with the defect, w1, w2, w3, and w4 are the area weight, aspect ratio weight, demand urgency weight, and geometric relationship weight with the defect, respectively. The area weight, aspect ratio weight, demand urgency weight, and geometric relationship weight with the defect are determined by the following dynamic calculation model, including the following steps: (1) Get 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 of ​​the current set of workpieces to be sorted, mean(A_i) is the average area of ​​the current set of workpieces to be sorted, CV_A is the coefficient of variation of the area of ​​the current set of workpieces to be sorted, and CV_A = std_dev(A_i) / mean(A_i), where std_dev(A_i) is the standard deviation of the area; (2) Get 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 sorted, and ε is a constant to prevent division by zero; (3) Get the temporary urgency weight w3_temp: w3_temp = sum(P_urgent) / sum(P_total), where sum(P_urgent) is the sum of the P_i values ​​of all artifacts whose urgency is higher than the threshold, and sum(P_total) is the sum of the P_i values ​​of all artifacts to be queued. (4) Get the temporary weight of the avoidance difficulty w4_temp: w4_temp = N_critical / N_total, where N_critical is the number of workpieces currently to be sorted whose minimum safety distance d_min_i between the minimum contour and the defect is lower than the preset safety threshold d_threshold, and N_total is the total number of workpieces currently to be sorted; (5) Normalize the temporary weight of area, temporary weight of aspect ratio, temporary weight of demand urgency and temporary weight of geometric relationship with defect to obtain the corresponding area weight w1, aspect ratio weight w2, demand urgency weight w3 and geometric relationship 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.

[0010] Preferably, the S3 includes the following operations: S3.1: Initialize unused spatial grids and build a spatial search tree; S3.2: Identify the current optimal placement area based on the dynamic boundary tracking method and evaluate the utilization value of the area; S3.3: Calculate the optimal placement direction and position for the current workpiece to be sorted, while considering the geometric relationship of adjacent workpieces and defect avoidance requirements; S3.4: Perform workpiece placement legality verification to ensure that plate boundary constraints, defect avoidance constraints, and continuous cutting process constraints are met; S3.5: If the current artifact cannot meet the placement conditions, the alternating search mechanism is activated to find the most suitable replacement artifact in the set of remaining artifacts for the currently unused space; S3.6: When a single search fails to obtain satisfactory results, the spatial repartitioning strategy is triggered to replan the unused areas; S3.7: Repeat S3.1 to S3.6 until all workpieces are arranged or there is insufficient space to accommodate any unarranged workpieces.

[0011] Preferably, the dynamic boundary tracking method in S3.2 includes: starting from the edge of the unused space, tracking the turning points of the path to generate a closed polygonal area, evaluating the value of the area through parameter weighting, and selecting the current optimal placement area.

[0012] 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 equipment kinematic constraints.

[0013] Preferably, the alternating search mechanism in S3.5 adopts a greedy heuristic algorithm, locks the candidate workpiece that best suits the current area by calculating the spatial matching score, and supports a limited number of backtracking operations to avoid local optimal solutions.

[0014] Preferably, the optimal placement direction judgment in S3.3 includes four-way rotation evaluation of 0°, 90°, 180° and 270°. When the workpiece is allowed to rotate, the optimal orientation is determined by calculating the comprehensive score of boundary fit and space utilization.

[0015] A stone defect area layout system based on multi-objective optimization, comprising: An acquisition unit is used to obtain the external dimensions, defect boundaries and a list of workpieces to be arranged of the stone to be arranged; An intelligent sorting unit, which is used to intelligently sort the artifacts in the to-be-sorted artifact list using a multi-parameter weighted score based on an established artifact priority determination mechanism; The space allocation unit is used to execute an adaptive space allocation algorithm for each workpiece according to the outer dimensions of the stone, the defect boundary and the sorting order of the workpieces, so that the stone after each workpiece layout 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 layout plan generation unit is used to generate the final layout plan, including workpiece coordinate data, cutting path planning and material utilization analysis report.

[0016] The present invention has the following beneficial effects: High-precision defect recognition: The deep learning model is used for defect recognition, which overcomes the problem that traditional image processing methods are difficult to deal with complex texture backgrounds, and the recognition accuracy is significantly improved and the misrecognition rate is significantly reduced. Multi-objective comprehensive optimization: Multiple goals such as maximizing material utilization, optimizing processing efficiency, and maximizing defect avoidance are incorporated into a unified optimization framework, and a balance between different goals is achieved through dynamic weight adjustment. Full process adaptation: By constructing a cutting path tree and kinematic verification, it is ensured that the generated typesetting scheme is 100% in line with the actual processing technology requirements, avoiding the problem of unexecutable schemes caused by traditional algorithms ignoring process constraints. Adaptive space planning: The innovative introduction of dynamic boundary tracking and space repartitioning strategies can effectively handle the irregular available space caused by defective areas and improve space utilization efficiency. Intelligent interactive adjustment: The system supports human-machine collaborative optimization. Operators can fine-tune the scheme generated by the algorithm based on experience, combining the advantages of artificial intelligence and human experience to achieve a more ideal typesetting effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For those skilled in the art, other relevant drawings can be obtained based on these drawings without creative work.

[0018] Figure 1 The figure is a flow chart of the intelligent typesetting method of stone defect areas based on multi-objective optimization of the present invention.

[0019] Figure 2 This is a structural block diagram of the intelligent typesetting system for stone defect areas based on multi-objective optimization of the present invention. DETAILED DESCRIPTION

[0020] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work 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 drawings is not intended to limit the scope of the invention for which protection is sought, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0021] Example The following are only preferred embodiments of the present invention. The protection scope of the present invention is not limited to the following embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention.

[0022] Reference Manual Figure 1 and Figure 2 , a stone defect area layout method based on multi-objective optimization, comprising the following steps: S1: Obtain the external dimensions, defect boundaries and list of workpieces to be arranged of the stone to be arranged; The defect recognition in S1 can adopt the U-Net neural network, and combine the adaptive threshold segmentation technology to the confidence map output by the U-Net, divide the transition area according to the confidence, calculate the dynamic threshold with a sliding window, and logically fuse the threshold segmentation result with the U-Net high confidence area to perform feature extraction and boundary determination.

[0023] S2: Based on the established artifact priority determination mechanism, multi-parameter weighted scoring is used to intelligently sort the artifacts in the artifact list; The multi-parameter weighted scoring takes into account the workpiece area, aspect ratio, urgency of demand, and geometric relationship with the identified defect area, and uses adaptive weights to perform comprehensive scoring and ranking. The following comprehensive scoring function is used: 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 demand urgency, D_i is the geometric relationship with the defect, w1, w2, w3 and w4 are the area weight, aspect ratio weight, demand urgency weight and geometric relationship weight with the defect respectively.

[0024] The area weight, aspect ratio weight, demand urgency weight, and geometric relationship weight with the defect are determined by the following dynamic calculation model, including the following steps: (1) Get 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 of ​​the current set of workpieces to be sorted, mean(A_i) is the average area of ​​the current set of workpieces to be sorted, CV_A is the coefficient of variation of the area of ​​the current set of workpieces to be sorted, and CV_A = std_dev(A_i) / mean(A_i), where std_dev(A_i) is the standard deviation of the area; (2) Get 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 sorted, and ε is a constant to prevent division by zero; (3) Get the temporary urgency weight w3_temp: w3_temp = sum(P_urgent) / sum(P_total), where sum(P_urgent) is the sum of the P_i values ​​of all artifacts whose urgency is higher than the threshold, and sum(P_total) is the sum of the P_i values ​​of all artifacts to be queued. (4) Get the temporary weight of the avoidance difficulty w4_temp: w4_temp = N_critical / N_total, where N_critical is the number of workpieces currently to be sorted whose minimum safety distance d_min_i between the minimum contour and the defect is lower than the preset safety threshold d_threshold, and N_total is the total number of workpieces currently to be sorted; (5) Normalize the temporary weight of area, temporary weight of aspect ratio, temporary weight of demand urgency and temporary weight of geometric relationship with defect to obtain the corresponding area weight w1, aspect ratio weight w2, demand urgency weight w3 and geometric relationship 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.

[0025] S3: Based on the stone's dimensions, defect boundaries, and the workpiece sorting order, an adaptive space allocation algorithm is executed for each workpiece, so that the stone after each workpiece layout satisfies the 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; The specific operations include: S3.1: Initialize unused spatial grids and build a spatial search tree; S3.2: Identify the current optimal placement area based on the dynamic boundary tracking method and evaluate the utilization value of the area; the dynamic boundary tracking method includes: starting from the edge of the unused space, tracking the turning points of the path to generate a closed polygonal area, evaluating the regional value through parameter weighting, and selecting the current optimal placement area.

[0026] S3.3: Calculate the optimal placement orientation and position for the workpiece currently being sorted, taking into account the geometric relationships between adjacent workpieces and defect avoidance requirements. The optimal placement orientation includes a four-way rotation evaluation of 0°, 90°, 180°, and 270°. If workpiece rotation is permitted, the optimal orientation is determined by calculating a comprehensive score of boundary fit and space utilization. S3.4: Perform workpiece placement validation to ensure compliance with sheet boundary constraints, defect avoidance constraints, and continuous cutting process constraints. Continuous cutting process constraint validation includes constructing a cutting path tree and analyzing each candidate placement solution to ensure all cutting lines can be introduced continuously from the sheet edge without interruption and that the equipment kinematic constraints are met. S3.5: If the current artifact does not meet the placement conditions, the alternating retrieval mechanism is activated to find the replacement artifact that best fits the currently unused space in the remaining artifact set. The alternating retrieval mechanism uses a greedy heuristic algorithm to lock the candidate artifact that best fits the current area by calculating the spatial matching score, and supports a limited number of backtracking steps to avoid local optimal solutions.

[0027] S3.6: When a single search fails to obtain satisfactory results, the spatial repartitioning strategy is triggered to replan the unused areas; S3.7: Repeat S3.1 to S3.6 until all workpieces are arranged or there is insufficient space to accommodate any unarranged workpieces.

[0028] S4: Generate the final layout plan, including workpiece coordinate data, cutting path planning and material utilization analysis report.

[0029] In order to further understand the present invention, the application of the present invention will be described below with reference to an example: Example 1: Stone defect recognition and digital representation based on deep learning First, an industrial camera is used to capture high-resolution images of the stone surface. The image resolution is no less than 300DPI to ensure that even the smallest defects are captured. A uniform lighting system is used to reduce shadows and reflections.

[0030] To address the unique textures and backgrounds of stone, we modified the standard U-Net neural network by adding an attention mechanism module and residual connections to enhance the detection of fine cracks and color variations. The training dataset contained 5,000 annotated images covering common stone defects. After 200 rounds of training, the model achieved 95.3% defect recognition accuracy on the test set. The U-Net network generated a defect probability map, also known as a confidence map. For fuzzy boundary regions with confidence levels of 0.3–0.7, dynamic local thresholding was used to correct the attribution of boundary pixels. This map was then logically fused with the U-Net probability map, retaining the direct output of high-confidence regions (>0.7) and marking low-confidence regions (<0.3) as background. Transition regions were then subjected to pixel-level correction using threshold segmentation results.

[0031] To address the boundary blurring problem that may occur in U-Net in complex texture stone images, the adaptive threshold segmentation technology is introduced to perform local dynamic threshold calculation: Based on the defect probability map output by U-Net, the local optimal threshold is calculated using a sliding window (30mm×30mm) for the transition region with a confidence level of 0.3–0.7: T(x,y)=μ(x,y)+k⋅σ(x,y) in: μ(x,y): mean grayscale value of pixels in the window; σ(x,y): standard deviation of grayscale within the window; k is dynamically adjusted according to the stone type (granite: 0.15–0.25, marble: 0.25–0.35); The Douglas-Peucker algorithm simplifies the boundaries of identified defect areas, converting complex contours into polygonal vector representations while preserving their shape characteristics. 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 based on actual conditions.

[0032] Example 2: Determining Workpiece Priority Based on Multi-Parameter Comprehensive Scoring This paper designs a flexible artifact priority scoring mechanism that comprehensively considers the following factors: 1. Workpiece area (A_i): Workpieces with larger areas are arranged first to avoid difficulties in placing large-sized workpieces in the later stage; 2. Aspect ratio (R_i): Workpieces that are close to square (R_i is close to 1) get higher priority because extremely slender workpieces usually have more placement options; 3. Demand urgency (P_i): Production priority specified by the user, ranging from 1 to 10; 4. Geometric relationship with the defect (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.

[0033] The comprehensive scoring function is: Score_i=w1·A_i+w2·(1 / |R_i-1|)+w3·P_i-w4·D_i in: w1 to w4 are weight coefficients, and the system provides default values ​​(w1=0.5, w2=0.2, w3=0.2, w4=0.1) At the same time, users can adjust according to specific production needs. The weight coefficients w1 to w4 are determined by the following dynamic calculation model: 1. w1_temp, w2_temp, w3_temp, and w4_temp are temporary weights that reflect the original "importance strength" of each factor under the characteristics of the current artifact set, but their sum (Sum_temp = w1_temp + w2_temp + w3_temp + w4_temp) is usually not equal to 1.

[0034] The selected temporary weight coefficients need to be normalized to ensure that the sum of the weight coefficients is 1 (∑w = 1): Calculate the normalization factor: (1)Sum_temp = w1_temp + w2_temp + w3_temp + w4_temp (2) α=β=γ=δ=1 / Sum_temp 2. Area weight (w1): (1)w1_temp = (max(A_i) / mean(A_i)) * (1 - CV_A) (2) w1 = α * w1_temp in: α: Normalization factor of area weight (determined after calculation).

[0035] max(A_i): The maximum area of ​​the current set of workpieces to be sorted.

[0036] mean(A_i): The average area of ​​the current set of workpieces to be sorted.

[0037] CV_A: Coefficient of Variation of the area of ​​the current set of workpieces to be sorted, CV_A = std_dev(A_i) / mean(A_i), where std_dev(A_i) is the standard deviation of the area.

[0038] When there are significant large workpieces (max / mean is large) and the workpiece sizes are relatively uniform (CV_A is small), increase w1 to prioritize large workpieces.

[0039] 3. Aspect ratio weight (w2): (1)w2_temp = mean(1 / (|R_i - 1| + ε)) (2) w2 = β * w2_temp in: β: Normalization factor for aspect ratio weighting (determined after calculation). mean(1 / (|R_i - 1| +ε)): Calculates the mean of 1 / |R_i - 1| for the current set of workpieces to be sorted. ε is a small constant to prevent division by zero (e.g., ε = 0.01).

[0040] 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), w2 is increased to give priority to the layout advantages of these regular workpieces.

[0041] 4. Urgency weight (w3): (1) w3_temp = sum(P_urgent) / sum(P_total) (2) w3 = γ * w3_temp in: γ: Normalization factor of urgency weight (determined after calculation).

[0042] sum(P_urgent): The sum of the P_i values ​​of all artifacts whose urgency is higher than a certain threshold (such as P_i>= 7).

[0043] sum(P_total): The sum of the P_i values ​​of all workpieces to be queued.

[0044] When the total demand for high-urgency (P_urgent) workpieces in the set of workpieces to be scheduled accounts for a high proportion, w3 is increased to give priority to meeting urgent orders.

[0045] 5. Avoidance Difficulty Weight (w4): (1) w4_temp =N_critical / N_total (2) w4 = δ * w4_temp in: δ: normalization factor (determined after calculation).

[0046] N_critical: The number of workpieces in the current queue whose minimum possible contour and the minimum safety distance (d_min_i) of the defect are lower than the preset safety threshold d_threshold.

[0047] N_total: The total number of workpieces currently waiting to be arranged.

[0048] When there are many workpieces (N_critical / N_total is large) that are difficult or risky to place due to being close to defects, increase w4 to prioritize placing these "difficult" workpieces to avoid them having no suitable space available in the later stage.

[0049] Example 3: Core Implementation of Adaptive Space Allocation Algorithm Initialization phase. The system divides the stone slab surface into grids (the area of ​​a single grid is usually 5mm×5mm), and grids covered by defects are marked as disabled. A dynamic boundary tracking method is used to identify available space: starting from the lower left corner of the slab, moving along the edge of the slab and the boundary of the arranged workpieces / defects, recording the coordinates of the turning points to form a closed polygon representing an available space region (Available Space Region, ASR). A value score is calculated for each region: V_region = w_area * Area_normalized + w_rect * Rectangularity - w_risk * DefectProximity in: 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).

[0050] 1. Dynamic weight coefficients w_area, w_rect, w_risk, the sum of which is 1.

[0051] (1) w_area (area weight): controls the importance of area size in scoring. The larger the value, the more the system tends to prioritize large areas. The default value is 0.6.

[0052] (2) w_rect (rectangularity weight): controls the importance of region shape regularity in scoring. The larger the value, the more the system tends to prioritize regions that are close to rectangular. The default value is 0.3.

[0053] (3) w_risk (risk weight): This controls the importance of the risk of the 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.

[0054] 2. Area_normalized (normalized area): actual area of ​​the target region (A_region) / total area of ​​the board (A_board), reflecting the area size ratio.

[0055] 3. Rectangularity: A_region / A_mbr.

[0056] A_mbr is the area of ​​the minimum bounding rectangle (MBR) of the usable space formed by the plate's outline. Rectangularity ranges from (0 to 1), with values ​​closer to 1 indicating a more regular shape (closer to a rectangle).

[0057] Specific project implementation: (1) Contour extraction: Apply an edge detection algorithm (such as Canny) to the binary mask of the available space region. (2) Minimum bounding rectangle area A_mbr calculation: Use the rotating caliper algorithm to calculate the minimum bounding rectangle of the contour and its area. (3) Calculation of the actual area of ​​the region A_region: Count the number of valid grids in the available space region and multiply by the area of ​​a single grid (the default is 5mm×5mm). (4) Rectangularity calculation: Rectangularity = A_region / A_mbr.

[0058] Examples: (1) Perfect rectangular area: Rectangularity = 1.0; (2) Complex polygonal area: Rectangularity ≈ 0.6; (3) Circular area: Rectangularity ≈ 0.785 (π / 4); 4. DefectProximity: 1 - min(dist_edge) / D_board.

[0059] min(dist_edge) is the minimum Euclidean distance from the boundary of the available space area to the nearest defect edge; D_board = is the diagonal length of the plate, used for normalization, where Represents the width of the plate, Represents the length of the plate. The value range of defect proximity is [0, 1]. A larger value indicates a closer proximity to the defect and a higher placement risk.

[0060] Specific project implementation: (1) Distance field construction: Perform Euclidean distance transform (EDT) on the binary defect image to generate a Dist_map field representing the distance from each pixel to the nearest defect edge. (2) Minimum distance query: Densely sample points along the contour of the available spatial area, query the Dist_map to obtain a set of distance values, and take the minimum value min_dist = min(Dist_map(sample_points)). (3) Normalized calculation: DefectProximity = 1 - (min_dist / D_board).

[0061] Examples: (1) The free space overlaps the defect: min_dist = 0, DefectProximity = 1.0; (2) The free space is 0.5 * D_board away from the defect: DefectProximity = 0.5; (3) The free space is far from the defect: min_dist ≈ D_board, DefectProximity ≈ 0; Search for feasible placement positions. For the current workpiece Part_i, search for feasible placement positions in each candidate available space area under its allowed rotation directions (0°, 90°, 180°, 270°), and calculate the comprehensive placement score Score_placement for each feasible position: Score_placement = λ_fit * EdgeFit + λ_util * SpaceUtilization - λ_waste * WastageRisk in: 1. Dynamic weight coefficients: λ_fit, λ_util, λ_waste. The sum of the three weight coefficients is always 1. The default configuration is λ_fit=0.4, λ_util=0.4, λ_waste=0.2.

[0062] (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 fits closely to the existing boundary to optimize the cutting path length.

[0063] (2) λ_util (potential weight): controls the importance of space utilization potential in the scoring. The larger the value, the more likely the system is to choose a location with more regular remaining space after placement and more conducive to subsequent typesetting.

[0064] (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 placements that may produce a large amount of unusable scrap.

[0065] 2. EdgeFit (edge ​​fit): L_contact / L_total.

[0066] L_contact is the effective contact length between the contour of the workpiece Part_i to be sorted and the currently cut boundary of the sheet (including the sheet's outer frame, the boundary of the sorted workpiece, and the defect boundary), while satisfying the maximum gap constraint Gap_max (default ≤1mm). L_total is the total perimeter of the contour of the workpiece Part_i to be sorted. Edge fit ranges from [0 to 1]. Higher values ​​indicate better fit, which reduces the cutting path length.

[0067] Specific engineering implementation: (1) Boundary distance field: Pre-calculate the Euclidean distance transform (EDT) field Boundary_dist_map of the current plate layout (including all arranged elements); (2) Contact length calculation: Sample points on the contour of the current workpiece Part_i after placement. Count 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.

[0068] Examples: (1) L-nested placement: EdgeFit ≈ 0.8 (mainly due to the existence of non-contact edges); (2) Isolated placement: EdgeFit = 0.

[0069] 3. Space Utilization (Space Utilization Potential): (Σ (A_free_k * Rect_k)) / A_free_total.

[0070] The value range is (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 combined rectangle), which is more conducive to the effective placement of subsequent workpieces and has greater space utilization potential.

[0071] A_free_total (total remaining free area): the total area of ​​all remaining free areas on the plate after placing the current workpiece Part_i.

[0072] A_free_k (sub-region area): The area of ​​the kth independent remaining free connected region. The remaining free region is usually divided into k disconnected sub-regions by the current workpiece Part_i.

[0073] Rect_k (sub-region rectangularity): The rectangularity of the kth remaining free sub-region, calculated in the same way as ASR's ectangularity: Rect_k = A_free_k / A_mbr_k A_mbr_k (area of ​​the minimum bounding rectangle of a sub-region): The area of ​​the minimum bounding rectangle (MBR) of the outline of the kth remaining free sub-region.

[0074] Specific engineering implementation: (1) Free area extraction: After placing the current workpiece Part_i, update the free grid map, apply morphological opening operation to remove noise, extract and mark all connected free areas, and obtain k connected domains; (2) Sub-region evaluation: For each free connected domain k, calculate its actual area A_free_k; calculate its minimum enclosing 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.

[0075] Example: (1) A single rectangular space remains: SpaceUtilization = 1.0; (2) Multiple narrow gaps remain: SpaceUtilization ≈ 0.3.

[0076] 4. Waste risk: A_frag / A_free.

[0077] A_frag is the sum of the areas of all subregions in the remaining free area after placement that are smaller than the fragmentation threshold A_min; A_free is the total area of ​​the remaining free area. The value range is [0, 1), with higher values ​​indicating a greater risk of generating unusable scrap.

[0078] Specific engineering implementation: (1) Fragment detection: Identify areas in all remaining free connected regions that satisfy A_free_k < A_min. (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 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 sheet).

[0079] Example: (1) Generating scrap accounting for 15% of the remaining area: WastageRisk = 0.15 (2) No effective fragments: WastageRisk = 0 Phase of verifying the legality of placement. It includes triple checks: Boundary check to ensure that the workpiece is completely within the sheet; 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 sheet by constructing a cutting path tree. It includes: 1. Stroke verification: Check whether the cutting path exceeds the physical stroke of the equipment guide rail; 2. Dynamics verification: Calculate the centripetal acceleration at the turning points of the path to ensure that it does not exceed the equipment - allowed threshold. Generally, > 0.5G may cause tool deviation; 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.

[0080] 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.

[0081] When the current workpiece cannot be placed, start the alternating 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.

[0082] Example 4: System architecture and interaction design The system adopts a modular design, with each module exchanging data via standardized interfaces. The image acquisition and defect recognition module is implemented using the deep learning framework TensorFlow and supports GPU acceleration. The data modeling and management module uses a hybrid architecture combining a relational database with a NoSQL database, balancing structured data management with unstructured geometric data storage. The core typesetting algorithm module is implemented in C++ and integrates the OpenMP parallel computing framework for high-performance computing. The visualization and output module uses WebGL technology, providing cross-platform 3D visualization capabilities.

[0083] The system provides a user-friendly interface, allowing operators to intuitively view stone materials, defects, and layout results via the touchscreen. Gestures are supported, allowing zooming in, out, and rotating the view for easy inspection of details. Manual fine-tuning allows operators to make minor adjustments to the algorithm-generated solution based on their experience. The system automatically verifies whether manual adjustments violate constraints, ensuring that the adjusted solution remains feasible.

[0084] Example 5: Practical application effect verification This invention has been tested in a six-month practical application at a large stone processing company. Comparing the results of traditional manual typesetting with the automated typesetting system, the system achieved significant results when processing 100 defective stone slabs: material utilization increased by an average of 11.3%, the defect avoidance success rate reached 100%, and typesetting planning time was reduced from an average of 45 minutes per slab to 3 minutes. The generated cutting plans all met the process requirements of the production equipment and could be used directly in production without manual adjustments. Reference Manual Figure 2 , a stone defect area layout system based on multi-objective optimization, including: An acquisition unit is used to obtain the external dimensions, defect boundaries and a list of workpieces to be arranged of the stone to be arranged; An intelligent sorting unit, which is used to intelligently sort the artifacts in the to-be-sorted artifact list using a multi-parameter weighted score based on an established artifact priority determination mechanism; The space allocation unit is used to execute an adaptive space allocation algorithm for each workpiece according to the outer dimensions of the stone, the defect boundary and the sorting order of the workpieces, so that the stone after each workpiece layout 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 layout plan generation unit is used to generate the final layout plan, including workpiece coordinate data, cutting path planning and material utilization analysis report.

[0085] The above embodiments are intended only to illustrate the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. They are not intended to limit the scope of protection of the present invention. Any equivalent changes or modifications made in accordance with the spirit of the present invention are intended to be covered by the scope of protection of the present invention.

Claims

1. A stone defect area layout method based on multi-objective optimization, characterized in that: The following steps are involved: S1: Obtain the external dimensions, defect boundaries and list of workpieces to be arranged of the stone to be arranged; S2: Based on the established artifact priority determination mechanism, multi-parameter weighted scoring is used to intelligently sort the artifacts in the artifact list; S3: Based on the stone's dimensions, defect boundaries, and the workpiece sorting order, an adaptive space allocation algorithm is executed for each workpiece, so that the stone after each workpiece layout satisfies the 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; S4: Generate the final layout plan, including workpiece coordinate data, cutting path planning and material utilization analysis report.

2. The method for layout of stone defect areas based on multi-objective optimization according to claim 1, characterized in that: The defects in S1 are detected using the U-Net neural network and combined with the adaptive threshold segmentation technology to divide the transition area according to the confidence map output by the U-Net. The dynamic threshold is calculated using a sliding window, and the threshold segmentation result is logically fused with the U-Net high confidence area to perform feature extraction and boundary determination.

3. The method for layout of stone defect areas based on multi-objective optimization according to claim 1, characterized in that: The multi-parameter weighted scoring in S2 takes into account the area, aspect ratio, urgency of the demand, and geometric relationship of the workpiece with the identified defect area, and performs comprehensive scoring and ranking through adaptive weights.

4. The method for layout of stone defect areas based on multi-objective optimization according to claim 3, characterized in that: The multi-parameter weighted scoring adopts 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 demand urgency, D_i is the geometric relationship with the defect, w1, w2, w3 and w4 are the area weight, aspect ratio weight, demand urgency weight and geometric relationship weight with the defect respectively; The area weight, aspect ratio weight, demand urgency weight, and geometric relationship weight with the defect are determined by the following dynamic calculation model, including the following steps: (1) Get 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 of ​​the current set of workpieces to be sorted, mean(A_i) is the average area of ​​the current set of workpieces to be sorted, CV_A is the coefficient of variation of the area of ​​the current set of workpieces to be sorted, and CV_A = std_dev(A_i) / mean(A_i), where std_dev(A_i) is the standard deviation of the area; (2) Get 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 sorted, and ε is a constant to prevent division by zero; (3) Get the temporary urgency weight w3_temp: w3_temp = sum(P_urgent) / sum(P_total), where sum(P_urgent) is the sum of the P_i values ​​of all artifacts with an urgency higher than the threshold, and sum(P_total) is the sum of the P_i values ​​of all artifacts to be queued. (4) Get the temporary weight of the avoidance difficulty w4_temp: w4_temp = N_critical / N_total, where N_critical is the number of workpieces currently to be sorted whose minimum safety distance d_min_i between the minimum contour and the defect is lower than the preset safety threshold d_threshold, and N_total is the total number of workpieces currently to be sorted; (5) Normalize the temporary weight of area, temporary weight of aspect ratio, temporary weight of demand urgency and temporary weight of geometric relationship with defect to obtain the corresponding area weight w1, aspect ratio weight w2, demand urgency weight w3 and geometric relationship 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.

5. The method for layout of stone defect areas based on multi-objective optimization according to claim 1, characterized in that: The S3 includes the following operations: S3.1: Initialize unused spatial grids and build a spatial search tree; S3.2: Identify the current optimal placement area based on the dynamic boundary tracking method and evaluate the utilization value of the area; S3.3: Calculate the optimal placement direction and position for the current workpiece to be sorted, while considering the geometric relationship of adjacent workpieces and defect avoidance requirements; S3.4: Perform workpiece placement legality verification to ensure that plate boundary constraints, defect avoidance constraints, and continuous cutting process constraints are met; S3.5: If the current artifact cannot meet the placement conditions, the alternating search mechanism is activated to find the most suitable replacement artifact in the set of remaining artifacts for the currently unused space; S3.6: When a single search fails to obtain satisfactory results, the spatial repartitioning strategy is triggered to replan the unused areas; S3.7: Repeat S3.1 to S3.6 until all workpieces are arranged or there is insufficient space to accommodate any unarranged workpieces.

6. The method for layout of stone defect areas based on multi-objective optimization according to claim 5, characterized in that: The dynamic boundary tracking method in S3.2 includes: starting from the edge of the unused space, tracking the turning points of the path to generate a closed polygonal area, evaluating the value of the area through parameter weighting, and selecting the current optimal placement area.

7. The method for layout of stone defect areas based on multi-objective optimization according to claim 5, characterized in that: 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 equipment kinematic constraints.

8. The method for layout of stone defect areas based on multi-objective optimization according to claim 5, characterized in that: The alternating retrieval mechanism in S3.5 adopts a greedy heuristic algorithm to lock the candidate artifact that best suits the current area by calculating the spatial matching score, and supports a limited number of backtracking operations to avoid local optimal solutions.

9. The method for layout of stone defect areas based on multi-objective optimization according to claim 5, characterized in that: The optimal placement direction judgment in S3.3 includes four-way rotation evaluation of 0°, 90°, 180° and 270°. When the workpiece is allowed to rotate, the optimal orientation is determined by calculating the comprehensive score of boundary fit and space utilization.

10. A stone defect area layout system based on multi-objective optimization, characterized in that: include: An acquisition unit is used to obtain the external dimensions, defect boundaries and a list of workpieces to be arranged of the stone to be arranged; An intelligent sorting unit, which is used to intelligently sort the artifacts in the to-be-sorted artifact list using a multi-parameter weighted score based on an established artifact priority determination mechanism; The space allocation unit is used to execute an adaptive space allocation algorithm for each workpiece according to the outer dimensions of the stone, the defect boundary and the sorting order of the workpieces, so that the stone after each workpiece layout 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 layout plan generation unit is used to generate the final layout plan, including workpiece coordinate data, cutting path planning and material utilization analysis report.

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