Roof face brick efficient arrangement method based on intelligent algorithm

Abstract

The invention provides a roof face brick efficient arrangement method based on an intelligent algorithm. The roof face brick efficient arrangement method comprises the following steps that 1, warehouse separation problem decoupling and basic grid generation are carried out; 2, single-bin face brick parallel optimization based on an NSGA-II algorithm is carried out; and step 3, global coordination and optimal scheme output. The invention relates to the technical field of computer aided design (CAD) and artificial intelligence algorithms, and can solve the problem that in the prior art, large-scale complex roof face brick arrangement cannot achieve global optimum.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer-aided design (CAD) and artificial intelligence algorithms, and particularly relates to a high-efficiency roofing tile arrangement method based on an intelligent algorithm. BACKGROUND

[0002] In a construction project, the arrangement of roofing tiles is crucial to the waterproof performance, structural stability and overall aesthetics of the building. The arrangement of roofing tiles is a complex multi-objective optimization problem that needs to consider multiple objectives such as the reasonable arrangement of compartment joints, the overall alignment of tile joints, the minimization of broken tile quantity (economy), and the aesthetics of the arrangement.

[0003] Traditional methods mainly rely on manual scheme design and arrangement, which is not only time-consuming and labor-intensive, but also heavily dependent on the personal experience of the designer. It is often difficult for the designer to find a global optimal solution among multiple conflicting objectives (such as aesthetics and material loss).

[0004] In recent years, although some studies have attempted to introduce multi-objective optimization algorithms such as NSGA-II, direct application to complex roofing scenarios faces significant challenges. The complexity of the roofing geometry (such as slope, irregular boundaries) and the strong coupling between compartment joints and tile arrangement result in a dramatic increase in the dimensionality of the optimization problem. A roofing area of about 200 square meters (about 2000 tiles) has more than ten thousand dimensions, which makes the standard NSGA-II algorithm inefficient and difficult to converge within an acceptable time frame for engineering, and is prone to local optima.

[0005] Therefore, there is a need to provide a high-efficiency roofing tile arrangement method based on an intelligent algorithm, which can solve the problem that large-scale complex roofing tile arrangement cannot achieve global optimization in the prior art. SUMMARY

[0006] The purpose of the present application is to provide a high-efficiency roofing tile arrangement method based on an intelligent algorithm, which can solve the problem that large-scale complex roofing tile arrangement cannot achieve global optimization in the prior art.

[0007] To achieve the above purpose, the technical solution of the present application is as follows:

[0008] A high-efficiency roofing tile arrangement method based on an intelligent algorithm, comprising the following steps:

[0009] Step 1: Decoupling of compartment problem and generation of basic grid;

[0010] Step 2: Single-compartment tile parallel optimization based on NSGA-II algorithm;

[0011] Step 3: Global coordination and optimal scheme output.

[0012] The step 1 comprises the following sub-steps:

[0013] Step 1.1: Obtain the accurate geometric data of the roof to be laid out through CAD drawings, including the overall boundary V of the roof, the internal structure and the position of the preset fixed position of the warehouse joint;

[0014] Wherein, the roof boundary vertex coordinate set V = {(x1, y1), …, (x n , y n ), the fixed warehouse joint line segment set L = {(P start，1 , P end，1 ), …, (P start，m , P end，m )};

[0015] Step 1.2: Grid graph generation;

[0016] Step 1.3: Constraint and objective function definition;

[0017] Step 1.4: Dynamic programming to solve the optimal warehouse;

[0018] Step 1.5: Basic grid output.

[0019] In step 1.2, according to the size of the tiles used in the project, the roof area to be laid out is abstracted as a grid graph grid grap h; The horizontal grid line and the vertical grid line of the grid graph have a distance of delta x and delta y , which is determined by the length and width of the tile, representing all potential warehouse joint positions.

[0020] The step 1.3 comprises the following sub-steps:

[0021] Step 1.3.1: According to the building specifications and project requirements, set the hard constraint condition: the minimum allowable range W min and the maximum allowable range W max of single warehouse width;

[0022] Step 1.3.2: Define the optimization objective function of the dynamic programming stage, which aims to maximize the regularity of the warehouse shape and minimize the number of warehouses, expressed as score = W 规整度 *Socre 规整度 -W 数量 *amount;

[0023] Wherein, W 规整度 and W 数量 are the corresponding weight coefficients; Score 规整度The shape regularity score is calculated by the sum of the ratio of the area of each compartment i to the area of its minimum enclosing rectangle. The closer the ratio is to 1, the more regular the shape is.

[0024] The step 1.4 comprises the following sub-steps:

[0025] Step 1.4.1: Define the dynamic programming state DP(x min , y min , x max , y max ) as the optimal compartmentalization scheme within the rectangular region defined by the coordinate points (x min , y min ) and (x max , y max );

[0026] Step 1.4.2: The state transition process starts with a basic judgment on the current rectangular region; if the rectangular region cannot be effectively cut again, it is considered as a compartment itself, and its shape regularity score Score 规整度 is calculated;

[0027] Subsequently, the DP algorithm enters the recursive cutting phase, traversing all eligible horizontal and vertical cutting lines; each cutting will decompose the current rectangular region into two sub-regions, and the DP algorithm recursively calls the dynamic programming function to obtain the optimal compartmentalization scheme for these sub-regions;

[0028] When merging the results of sub-regions, their shape regularity scores Score 规整度 and compartment amounts amount are accumulated, and the merits of the current cutting scheme are evaluated through the optimization objective function of step 1.3.2;

[0029] Step 1.4.3: The DP algorithm stores the scheme with the highest score in the DP table until the entire roof area is covered.

[0030] The step 1.5 comprises the following sub-steps:

[0031] Step 1.5.1: Find the complete cutting path that obtains the optimal score value by backtracking the DP table;

[0032] Step 1.5.2: Based on the complete cutting path, output the final compartmentalization scheme, i.e., a base grid base grid , which divides the entire roof into N independent, standard compartment units compartment unit .

[0033] The step 2 comprises the following sub-steps:

[0034] Step 2.1: Chromosome encoding;

[0035] Definition: individual represents a single layout scheme, i.e. individual chromosome; Real number coding is adopted, and the gene of the chromosome is a real number vector gene vector , is expressed as

[0036] Step 2.2: Single-bin optimization objective function construction;

[0037] Step 2.3: Parallel NSGA-II algorithm execution.

[0038] Wherein, x i and y i represent the relative coordinates of the i-th vertical cutting line and the j-th horizontal cutting line, respectively, and the value range is constrained by the horizontal width L H and the vertical width L V of the bin unit.

[0039] The step 2.2 includes the following steps:

[0040] Step 2.2.1: Minimize the broken brick rate objective function to quantify the economy;

[0041] For each layout scheme, the ratio of the total area of broken bricks generated by the bin unit to the total area of the bin unit is calculated, that is, The optimization objective is to minimize f 1,p ;

[0042] Wherein, f 1,p is the broken brick rate of the p-th bin unit, N 碎砖 is the number of broken bricks of the p-th bin unit, S 碎砖,i is the area of the i-th broken brick in the p-th bin unit, S 总面积 is the total area of the p-th bin unit;

[0043] Step 2.2.2: Maximize the edge broken brick concentration objective function to quantify the aesthetics;

[0044] For each layout scheme, the proportion of the area of broken bricks located in the edge area of the bin unit to the total area of broken bricks of the bin unit is calculated, that is, The optimization objective is to maximize f 3，p ;

[0045] Wherein, f 3，p is the edge broken brick concentration of the p-th bin unit (the maximum value is 1), N 碎砖 is the number of broken bricks of the p-th bin unit, M 边缘碎砖 is the number of broken bricks in the edge position of the p-th bin unit, S 边缘碎砖，j is the area of the j-th edge broken brick in the p-th bin unit, S碎砖,i The area of the i-th broken brick in the p-th sub-bin unit.

[0046] The step 3 comprises the following sub-steps:

[0047] Step 3.1: global coordination is performed by using NSGA-II algorithm;

[0048] Step 3.2: final scheme is selected by weighting;

[0049] Step 3.3: visualization report is generated.

[0050] In the step 3.1, the set of paving schemes is optimized by three global objective functions, i.e. minimizing the total broken brick area of the roof F1, maximizing the alignment rate of the brick joints across the bins F2, and maximizing the concentration degree of the broken bricks at the edges of the bin F3. After the iteration optimization by the NSGA-II algorithm, a final set of Pareto optimal solutions global pareto representing the paving of the entire roof is output.

[0051] The minimization of the total broken brick area of the roof is expressed as wherein N is the total number of the broken bricks in all the sub-bin units, S 碎砖，i is the area of the i-th broken brick;

[0052] The maximization of the alignment rate of the brick joints across the bins is expressed as wherein T 容忍 is the maximum acceptable alignment tolerance, d j,k is the alignment deviation of the k-th pair of brick joints on the j-th pair of boundaries, M is the number of the pairs of boundaries of the adjacent sub-bin units, and k j is the number of the brick joints needed to be aligned on each pair of boundaries.

[0053] The maximization of the concentration degree of the broken bricks at the edges of the bin is expressed as wherein P is the total number of the sub-bin units, S 边缘碎砖，p is the area of the broken brick located at the edge region in the p-th sub-bin unit, S 总碎砖，p is the total area of the broken bricks in the p-th sub-bin unit.

[0054] The step 3.2 comprises the following sub-steps:

[0055] Step 3.2.1: weights w1, w2, w3 are respectively assigned to the three global objective functions F1, F2, F3, and the weight values are determined by experts according to the project emphasis.

[0056] Step 3.2.2: the final set of Pareto optimal solutions global paretofor each of the laying schemes, three global target function values thereof are normalized to obtain F1', F2', and F3', and then a comprehensive score W of each laying scheme is calculated according to a weighted sum formula W = w1xF1' + w2xF2' + w3xF3';

[0057] Step 3.2.3: selecting the scheme with the highest W as the final recommended scheme;

[0058] In step 3.3, based on the final recommended scheme in step 3.2, a final roofing tile laying plan is automatically generated in AutoCAD, and a detailed report file is also generated, wherein the report file includes a size statistical table of the tiles and the broken tiles, the area of the broken tiles, the tile joint alignment rate score and the edge broken tile concentration score.

[0059] Compared with the prior art, the present application has the following beneficial effects:

[0060] 1. The present application can significantly reduce the complexity of the roofing tile arrangement problem: by decoupling in stages, the global optimization problem with an exponential complexity O(2 N ) is reduced to N independent sub-problems with a linear complexity O(N), so that the global optimization calculation of a large-scale roofing (such as 1000 square meters), especially a complex roofing, becomes possible.

[0061] 2. The present application can greatly improve the calculation efficiency: compared with the traditional manual arrangement (3-5 days) and the direct use of the NSGA-II algorithm (8-15 hours), the calculation time of the present application can be shortened to 1-3 hours, greatly improving the design efficiency.

[0062] 3. The present application can effectively reduce the material cost: through optimization, the number of broken tiles of a 1000 square meter roofing can be reduced to 800-1200, which is significantly lower than the number of broken tiles (2500-3500) in the manual arrangement, and the material utilization rate is significantly improved.

[0063] 4. The present application can optimize the arrangement aesthetics: taking the tile joint alignment rate and the edge broken tile concentration as the core optimization targets, the final recommended scheme can realize the "best" aesthetics and alignment while ensuring the economy, and the effect is obviously better than that of the traditional method.

[0064] 5. The present application can provide diversified decision support: the method of the present application finally generates a final Pareto optimal solution set global pareto representing the entire roofing laying, and the decision maker can select the most suitable scheme according to the different emphases on the cost and aesthetics of the project, so as to realize the customized design. BRIEF DESCRIPTION OF DRAWINGS

[0065] The above and other objects, features and advantages of the present disclosure will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings, in which like reference characters refer to like parts throughout the figures, and in which:

[0066] Figure 1 is a flow chart of a high-efficiency roofing tile arrangement method based on an intelligent algorithm of the present application;

[0067] Figure 2 is a dynamic planning schematic diagram of a warehouse joint in a high-efficiency roofing tile arrangement method based on an intelligent algorithm of the present application;

[0068] Figure 3 is a schematic diagram of a detailed broken tile arrangement in a high-efficiency roofing tile arrangement method based on an intelligent algorithm of the present application. DETAILED DESCRIPTION

[0069] A high-efficiency roofing tile arrangement method based on an intelligent algorithm of the present application will be described in further detail below in conjunction with the accompanying drawings and specific embodiments. The advantages and features of the present application will be more apparent from the following description and claims. It should be noted that the drawings are very simplified and use non-precise proportions, only to facilitate and clarify the purpose of assisting the description of the embodiments of the present application.

[0070] Please refer to the accompanying drawings Figure 1 , a high-efficiency roofing tile arrangement method based on an intelligent algorithm, comprising the following steps:

[0071] Step 1: decoupling of warehouse problem and generation of basic grid.

[0072] Step 1 aims to decouple the complex problem of the entire roofing tile arrangement into N independent single warehouse arrangement problems, effectively simplifying the exponential computational complexity to linear complexity.

[0073] The said step 1 comprises the following steps:

[0074] Step 1.1: Obtain the accurate geometric data of the roofing to be arranged by CAD drawings, including the overall boundary V of the roofing, internal structures (such as chimneys, vents, etc.) and the positions of the preset fixed warehouse joints.

[0075] Wherein, the set of roofing boundary vertex coordinates V = {(x1, y1), …, (xN, yN)}, the set of fixed warehouse joint line segments L = {(P1, P2), …, (PN-1, PN)}. n n start，1 end，1 start，m end，m

[0076] Step 1.2: Grid map generation.​​​​​​

[0077] Specifically, according to the size of the tiles used in the project, the area to be paved is abstracted as a grid grap h. The horizontal and vertical grid lines of the grid have a spacing of delta x and delta y , respectively, determined by the length and width of the tiles, representing all potential locations of the compartmentalization joints.

[0078] Step 1.3: Constraint and objective function definition.

[0079] The step 1.3 includes the following sub-steps:

[0080] Step 1.3.1: According to the building codes and project requirements, set the hard constraint conditions, mainly the minimum allowable range W min and the maximum allowable range W max of the single compartment width (for example, W min = 4.5m, W max = 6m).

[0081] Step 1.3.2: Define the optimization objective function of the dynamic programming (DP) stage, which aims to maximize the regularity of the compartment shape and minimize the number of compartments, which can be represented as score = W 规整度 *Score 规整度 -W 数量 *amount.

[0082] Where W 规整度 and W 数量 are the corresponding weight coefficients; Score 规整度 is calculated by the sum of the ratio of the area of each compartment i to the area of its minimum circumscribed rectangle, and the closer the ratio is to 1, the more regular the shape is, which can be represented as

[0083] Please refer to the attached Figure 2 Step 1.4: Dynamic programming to solve the optimal compartment.

[0084] The step 1.4 includes the following sub-steps:

[0085] Step 1.4.1: Define the dynamic programming state DP(x min , y min , x max , y max ) as the optimal compartment scheme within the rectangular area defined by the coordinate points (x min , y min ) and (x max , y max ).

[0086] Step 1.4.2: The state transition process starts with a basic judgment on the current rectangular region; if the rectangular region cannot be effectively cut again (for example, the area is too small or most of it is outside the polygon), it is considered as a compartment itself, and its shape regularity score Score 规整度 is calculated. Subsequently, the DP algorithm enters the recursive cutting phase, traversing all eligible horizontal and vertical cutting lines. Each cut will decompose the current rectangular region into two sub-regions, and the DP algorithm recursively calls the dynamic programming (DP) function to obtain the optimal compartment scheme for these sub-regions. When merging the results of the sub-regions, their shape regularity scores Score 规整度 and the number of compartments amount are accumulated, and the merits of the current cutting scheme are evaluated through the optimization objective function of Step 1.3.2.

[0087] Step 1.4.3: The DP algorithm stores the scheme with the highest score in the DP table until the entire roof area is covered.

[0088] Step 1.5: Basic grid output.

[0089] The step 1.5 includes the following sub-steps:

[0090] Step 1.5.1: Find the complete cutting path that obtains the optimal score scor by backtracking the DP table.

[0091] Step 1.5.2: Based on the complete cutting path, output the final compartment scheme, i.e., a basic grid base grid , which divides the entire roof into N independent, standard compartment units compartment unit .

[0092] Step 2: Single-compartment tile parallel optimization based on NSGA-II algorithm.

[0093] Step 2 applies the NSGA-II algorithm in parallel for the internal tile arrangement optimization of each independent compartment unit compartment unit generated in Step 1, generating a set of Pareto optimal solutions for each compartment unit.

[0094] The step 2 includes the following sub-steps:

[0095] Step 2.1: Chromosome encoding.

[0096] Specifically, define a chromosome individual representing a single paving scheme (individual). Use real number encoding, and the gene of the chromosome is a real number vector gene vector , represented as

[0097] where x i and y i represent the relative coordinates of the i-th vertical cutting line and the j-th horizontal cutting line, respectively, whose value range is constrained by the horizontal width L H and vertical width L V of the compartment.

[0098] Step 2.2: Single-compartment optimization objective function construction.

[0099] The step 2.2 includes the following sub-steps:

[0100] Step 2.2.1: Minimizing the broken tile rate objective function to quantify economy.

[0101] For each paving scheme, the ratio of the total area of broken tiles produced by the compartment to the total area of the compartment, i.e. is calculated. The optimization objective is to minimize f 1，p .

[0102] where f 1，p is the broken tile rate of the p-th compartment, N 碎砖 is the number of broken tiles of the p-th compartment, S 碎砖，i is the area of the i-th broken tile in the p-th compartment, S 总面积 is the total area of the p-th compartment.

[0103] Step 2.2.2: Maximizing the edge broken tile concentration objective function to quantify aesthetics.

[0104] For each paving scheme, the proportion of the area of broken tiles located in the edge region of the compartment to the total area of broken tiles of the compartment, i.e. is calculated. The optimization objective is to maximize f 3，p .

[0105] where f 3，p is the edge broken tile concentration of the p-th compartment (with a maximum value of 1), N 碎砖 is the number of broken tiles of the p-th compartment, M 边缘碎砖 is the number of broken tiles of the p-th compartment located in the edge region, S 边缘碎砖，j is the area of the j-th edge broken tile in the p-th compartment, S 碎砖,i is the area of the i-th broken tile in the p-th compartment.

[0106] Step 2.3: Parallel NSGA-II algorithm execution.

[0107] Specifically, for N compartments comp unitThe independent NSGA-II algorithm optimization process is started respectively. The NSGA-II algorithm selects through fast non-dominated sorting and crowded distance calculation, and combines crossover and mutation operators to iteratively evolve the population and search for optimal solutions. Finally, a Pareto optimal solution set pareto set is output for each sub-bin unit, which contains multiple excellent paving schemes with different balances between "economy" and "aesthetics" in the sub-bin unit.

[0108] The NSGA-II algorithm is a conventional calculation method in the field, and its setting of operation parameters and specific calculation process will not be described here.

[0109] Step 3: Global coordination and optimal scheme output.

[0110] The step 3 includes the following steps:

[0111] Step 3.1: Global coordination using the NSGA-II algorithm.

[0112] At this time, a global individual global individual is obtained, which is composed of a set of paving schemes combined from one paving scheme of each Pareto optimal solution set pareto set of each sub-bin unit. The set of paving schemes is optimized by three global objective functions, i.e., minimizing the total broken brick area of the roof F1, maximizing the alignment rate of the brick joints across the bins F2, and maximizing the concentration of broken bricks on the edges of the single bin F3. After iterative optimization by the NSGA-II algorithm, a final Pareto optimal solution set global pareto representing the entire roof paving is output.

[0113] Minimizing the total broken brick area of the roof can be expressed as where N is the total number of broken bricks in all sub-bin units, S 碎砖，i is the area of the i-th broken brick.

[0114] Maximizing the alignment rate of the brick joints across the bins can be expressed as where T 容忍 is the maximum acceptable alignment tolerance, d j，k is the alignment deviation of the k-th pair of brick joints on the j-th pair of boundaries, M is the number of adjacent sub-bin unit boundary pairs, and K j is the number of brick joints that need to be aligned on each pair of boundaries.

[0115] Maximizing the concentration of broken bricks on the edges of the single bin can be expressed as where P is the total number of sub-bin units, S 边缘碎砖，p is the area of the broken brick in the edge region of the p-th sub-bin unit, and S 总碎砖，p is the total area of the broken brick in the p-th sub-bin unit.

[0116] Step 3.2: Weighted selection of final scheme.

[0117] The step 3.2 includes the following sub-steps:

[0118] Step 3.2.1: Assign weights w1, w2, w3 to the three global objective functions F1, F2, F3 respectively, and the weight values are determined by experts according to the project focus (the sum of w1, w2, w3 is 1, for example, w1=0.3, w2=0.5, w3=0.2).

[0119] Step 3.2.2: For each paving scheme in the final Pareto optimal solution set global pareto , first normalize the three global objective function values to obtain F1', F2', F3', and then calculate the comprehensive score W of each paving scheme according to the weighted sum formula W=w1xF'1+w2xF'2+w3xF'3.

[0120] Step 3.2.3: Select the scheme with the highest W as the final recommended scheme.

[0121] Step 3.3: Visualization report generation.

[0122] Specifically, based on the final recommended scheme in step 3.2, the final paving map of the roof tile is automatically generated in AutoCAD, as shown in the accompanying Figure 3 , and a detailed report file is also generated, which includes the size statistics table of the tiles and broken tiles, the area of broken tiles, the tile joint alignment rate score, and the edge broken tile concentration score.

[0123] The present application decouples the complex global optimization problem through an innovative phased optimization framework, and combines the NSGA-II algorithm to quickly and automatically generate a set of Pareto optimal arrangement schemes that balance the amount of broken tiles, tile joint alignment, overall aesthetics and other multiple objectives, thereby significantly improving design efficiency, reducing material costs and optimizing the final visual effect, and realizing automatic, efficient and optimal arrangement of large-scale roof tiles.

[0124] Embodiment 1: The present application is applied to the paving design of roof tiles of a certain building project, and the specific operation steps are as follows:

[0125] S1. In the project roof deepening design stage, open the project roof CAD file Roof.dwg, draw the initial horizontal and vertical partition joints with line segments, and check whether the roof and structures on the roof are drawn using closed polylines.

[0126] S2. Click the function button and set the key parameters in the pop-up page according to the specifications: the brick size is 300mm×300mm, and the single compartment width is constrained to 3000mm~5000mm.

[0127] S3. Select the roof polyline as the roof boundary floor, and select the horizontal and vertical compartment joints as the initial compartment joint origins. h origin v Select the polyline of the roof structure as the boundary of the roof obstacle.

[0128] S4. To balance the regularity of the warehouse shape and the number of warehouses, set the regularity weight Wregularity to 0.7 and the quantity weight Wamoun to 0.3.

[0129] S5. Compartment Optimization. The program abstracts the entire roof area into a fine grid based on a 300mm step size. graph Its grid lines represent all potential compartment seam cutting locations.

[0130] S6. The dynamic programming (DP) algorithm is initiated, using the minimum bounding rectangle of the roof as the initial region, according to the formula score = W 规整度 *Score 规整度 -W 数量 *amount recursively evaluates all possible horizontal and vertical cuts. Each cut ensures that the width of the resulting sub-compartments is between 3000mm and 5000mm.

[0131] S7. After traversing all possibilities, the algorithm backtracks the complete cutting path with the optimal score value stored in the DP table, and finally outputs a complete compartmentation scheme, i.e., the base grid. grid This base grid In this embodiment, the complex roof is divided into 64 independent, compliant compartmentalized units.

[0132] S8. Single-Compartment Parallel Optimization. Set the operating parameters of the NSGA-II algorithm in the single-compartment optimization stage: population size is set to 100 (each compartment optimization includes 100 independent layout schemes as the population), and the number of iterations is num. generations Set to 200, crossover probability probability Set to 0.9, mutation probability probability Set to 0.1, crossover operator operator Simulated binary crossover (SBX) and mutation operator are used. operator Employ polynomial mutation.

[0133] S9. The system starts independent NSGA-II algorithm optimization processes for each of the 64 sub-bay units, enabling parallel computing.

[0134] S10. In each process, an initial population consisting of 100 individual chromosome individual is randomly generated, with each individual's gene being a real number vector gene vector representing an initial tile cutting scheme within the sub-bay unit.

[0135] S11. In the 200-generation evolutionary process, the NSGA-II algorithm evaluates, selects, crosses, and mutates the population based on two optimization objectives: minimizing the broken tile rate f 1，p of the pth sub-bay unit, and maximizing the edge broken tile concentration f 3，p of the pth sub-bay unit.

[0136] S12. After optimization, each process outputs a Pareto optimal solution set for the sub-bay unit. A total of 64 Pareto optimal solution sets pareto set are obtained, each containing dozens of excellent paving schemes that strike a balance between "economy" and "aesthetics" within the sub-bay unit. set

[0137] S13. Global coordination optimization. The running parameters of the NSGA-II algorithm in the global optimization phase are set, and the iteration number can be appropriately reduced for fast search in the better solution space. The population size population is set to 100 (each global individual global individual is composed of 64 paving schemes from different Pareto optimal solution sets), the iteration number num generations is set to 150, and other parameters remain the same as S8.

[0138] S14. An initial global population containing 100 global individuals is created by randomly combining schemes from the 64 Pareto optimal solution sets.

[0139] S15. The NSGA-II algorithm is run to optimize with three global objectives: minimizing the total broken tile area F1, maximizing the cross-bay joint alignment rate F2, and maximizing the edge broken tile concentration F3.

[0140] S16. After 150 generations of evolution, the algorithm outputs a final global Pareto optimal solution set global pareto , where each solution is a complete and coordinated roof paving scheme.

[0141] ​S17. According to the high requirements of the overall visual effect of the traffic hub commercial project, set W = w1 x F'1 + w2 x F'2 + w3 x F'3, wherein the weights are w1 (broken brick area) = 0.3, w2 (brick joint alignment) = 0.5, and w3 (edge concentration) = 0.2.

[0142] S18. The program normalizes F1, F2, and F3 in each scheme into F1', F2', and F3' according to the formula in S17, calculates the comprehensive score W of each paving scheme in the global Pareto optimal solution set, and selects the scheme with the highest score as the final recommended scheme in this embodiment.

[0143] S19. According to the final recommended scheme, the program automatically generates a final AutoCAD roof tile paving drawing final_drawing.dwg and a detailed PDF report file report_file.pdf. The roof tile paving drawing final_drawing.dwg clearly shows the optimized arrangement of broken tiles, achieving a high degree of unity of aesthetics and economy. The report file report_file.pdf contains accurate size tile statistical data and performance index scores, providing a reliable basis for subsequent construction.

[0144] The above description is only a description of the preferred embodiments of the present application, and is not any limitation on the scope of the present application. Any modification or change made by a person of ordinary skill in the art based on the above disclosure is within the protection scope of the claims.

Claims

1. A method for efficient arrangement of roofing tiles based on intelligent algorithm, characterized in that, The method comprises the following steps: Step 1: decoupling of the bin problem and generation of a basic grid; Step 2: single-bin optimization based on the NSGA-II algorithm; Step 3: global coordination and output of the optimal solution.

2. The intelligent algorithm based efficient arrangement of roofing tiles method as claimed in claim 1, wherein, The step 1 comprises the following sub-steps: Step 1.1: obtaining accurate geometric data of the to-be-paved roof through CAD drawings, including the overall boundary V of the roof, internal structures, and the positions of the preset fixed-position bin joints; Wherein, the roof boundary vertex coordinate set V = {(x1, y1), (x2, y2), …, (xn, yn)}, the fixed sub-warehouse joint line segment set L = {(P1, P2), (P3, P4), …, (P2n-1, P2n)}. n n start，1 end，1 start，m end，m ​​​​​​ Step 1.2: generation of a grid map; Step 1.3: definition of constraints and objective functions; Step 1.4: solving the optimal binning by dynamic programming; Step 1.5: output of the basic grid.

3. The intelligent algorithm based efficient arrangement of roofing tiles method as claimed in claim 2, wherein, In step 1.2, according to the size of the tiles used in the project, the area to be paved is abstracted into a grid grap h; the horizontal grid lines and the vertical grid lines of the grid have a spacing of delta x and delta y , which is determined by the length and width of the tiles, and represents all potential locations of the dividing joints.

4. The intelligent algorithm based efficient arrangement of roofing tiles method as claimed in claim 2, wherein, The step 1.3 comprises the following sub-steps: Step 1.3.1: Set hard constraints according to building code and project requirements: minimum allowed range of single bin width W min and maximum allowed range of single bin width W max ; Step 1.3.2: Define the optimization objective function for the dynamic programming phase, which aims to maximize the regularity of the bin shapes while minimizing the number of bins, denoted as score = W 规整度 *Score 规整度 -W 数量 *amount; wherein W 规整度 and W 数量 are corresponding weight coefficients; Score 规整度 is calculated by the sum of the ratio of the area of each bin i to the area of its minimum circumscribed rectangle, the closer the ratio is to 1, the more regular the shape is, and is represented as 5. The intelligent algorithm based efficient arrangement of roofing tiles method as claimed in claim 2, wherein, The step 1.4 comprises the following sub-steps: Step 1.4.1 : Define the dynamic programming state DP(x min , y min , x max , y max ) as the optimal binning scheme within the rectangular region defined by the coordinate points (x min , y min ) and (x max , y max ); Step 1.4.2: The state transition process begins with a basic judgment on the current rectangular region; if the rectangular region cannot be effectively cut again, it is regarded as a sub-warehouse itself, and the shape regularity score Score is calculated 规整度 ; Subsequently, the DP algorithm enters the recursive cutting stage, and traverses all the horizontal and vertical cutting lines that meet the conditions; Each cutting will decompose the current rectangular region into two sub-regions, and the DP algorithm recursively calls the dynamic programming function to obtain the optimal binning solution of the sub-regions; In merging the results of the sub-regions, their shape regularity scores Score 规整度 and the number of bins amount, and evaluating the current cutting scheme by the optimization objective function of step 1.3.

2. Step 1.4.3: the DP algorithm stores the solution with the highest score in the DP table until the entire roof area is covered.

6. The intelligent algorithm based efficient arrangement of roofing tiles method as claimed in claim 2, wherein, The step 1.5 comprises the following sub-steps: Step 1.5.1: finding the complete cutting path that obtains the optimal score value by backtracking the DP table; Step 1.5.2: output the final compartmenting scheme, i.e. a base grid base, based on the complete cutting path grid , which divides the entire roof into N independent, code-compliant compartmenting units comp unit .

7. The intelligent algorithm based efficient arrangement of roofing tiles as claimed in claim 1 wherein, The step 2 comprises the following sub-steps: Step 2.1: chromosome coding; Definition: Chromosome represents a single solution, i.e. individual; the genes of the chromosome are represented as a real number vector vector , i.e. |x1, x2,..., x a |; y1, y2,..., y b |; Step 2.2: construction of a single-bin optimization objective function; Step 2.3: execution of the parallel NSGA-II algorithm. wherein x i and y i represent the relative coordinates of the i-th vertical cutting line and the j-th horizontal cutting line, respectively, whose values are constrained by the horizontal width L H and the vertical width L V of the binning unit.

8. The intelligent algorithm based efficient arrangement of roofing tiles method as claimed in claim 7, wherein, The step 2.2 comprises the following sub-steps: Step 2.2.1: minimizing the broken tile rate objective function to quantify the economy; For each paving scheme, the ratio of the total area of broken bricks produced by the binning unit to the total area of the binning unit is calculated, i.e. The optimization objective is to minimize f 1，p ; wherein f 1，p is the broken brick rate of the pth sub-warehouse unit, N 碎砖 is the number of broken bricks of the pth sub-warehouse unit, S 碎砖，i is the area of the ith broken brick in the pth sub-warehouse unit, S 总面积 is the total area of the pth sub-warehouse unit; Step 2.2.2: maximizing the edge broken tile concentration objective function to quantify the aesthetics; For each paving scheme, the proportion of the total area of broken tiles in the sub-warehouse unit that is located in the edge region of the sub-warehouse unit is calculated, i.e. The optimization objective is to maximize f 3，p ; wherein f 3，p is the edge tile concentration (maximum value 1) of the pth sub-bin unit, N 碎砖 is the number of tiles in the pth sub-bin unit, M 边缘碎砖 is the number of tiles in the pth sub-bin unit, M 边缘碎砖，j is the area of the jth edge tile in the pth sub-bin unit, S 碎砖，i is the area of the ith tile in the pth sub-bin unit.

9. The intelligent algorithm based efficient arrangement of roofing tiles method as claimed in claim 1, wherein, The step 3 comprises the following sub-steps: Step 3.1: global coordination using the NSGA-II algorithm; Step 3.2: weighted selection of the final solution; Step 3.3: generation of a visual report.

10. The intelligent algorithm based efficient arrangement of roofing tiles method as claimed in claim 9, wherein, In step 3.1, the set of paving schemes is optimized by three global objective functions, i.e., minimizing the total broken brick area of the roof F1, maximizing the alignment rate of the brick joints across the warehouse F2, and maximizing the concentration of broken bricks on the edges of a single warehouse F3. Through the iterative optimization of the NSGA-II algorithm, a final set of Pareto optimal solutions representing the entire roof paving is output global pareto ; Minimizing the total broken tile area of the roof is expressed as where N is the total number of broken tiles in all of the sub-bins, S 碎砖，i is the area of the i-th broken tile. Maximizing the cross-bin joint alignment rate can be expressed as where T 容忍 is the maximum alignment tolerance acceptable, d j，k is the alignment deviation of the kth pair of joints on the jth pair of boundaries, M is the number of adjacent bin unit boundary pairs, K j is the number of joints that need to be aligned on each pair of boundaries; Maximizing the concentration of edge bricks in a bin is represented as where P is the total number of binning units, S 边缘碎砖，p is the area of edge bricks in the pth binning unit, S 总碎砖，p is the total area of edge bricks in the pth binning unit. The step 3.2 comprises the following sub-steps: Step 3.2.1: assigning weights w1, w2, and w3 to the three global objective functions F1, F2, and F3, respectively, and determining the weight values according to the project focus by experts; Step 3.2.2: for each paving solution in the global Pareto optimal solution set globalpareto of the entire roof paving, first normalizing the three global objective function values to obtain F1', F2', and F3', and then calculating the comprehensive score W of each paving solution according to the weighted sum formula W = w1xF1' + w2xF2' + w3xF3'; Step 3.2.3: selecting the solution with the highest W as the final recommended solution; In the step 3.3, based on the final recommended solution in step 3.2, a final roof tile paving map is automatically generated in AutoCAD, and a detailed report file is also generated, the contents of the report file including a size statistics table of the tiles and broken tiles, a broken tile area, a tile joint alignment rate score, and an edge broken tile concentration score.

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