A two-dimensional arrangement method of irregular parts based on mutation-driven genetic algorithm

Abstract

The invention relates to a two-dimensional arrangement method of irregular parts based on a mutation-driven genetic algorithm. Firstly, a corresponding part shape diagram is obtained for the shape of the part, and the shape diagram is binarized and the size is adjusted. Considering the material loss in the processing process, the part image is expanded. The part position and angle information is recorded by coding, and mutation is performed to optimize the position relationship of adjacent parts. The optimization search includes three steps: using the variance criterion and the envelope area criterion to perform a preliminary search and optimization on the position relationship between two parts. On the basis of the first step optimization, the two parts are regarded as a whole, and the variance criterion and the envelope area criterion are continuously used to perform a second search and optimization. Based on the result of the second step, multiple parts are regarded as a whole again, and the distance between adjacent pattern columns is used as a criterion for final search and optimization to determine all the position relationships of the part arrangement. Finally, the parts in different columns are adjusted to be arranged horizontally, so as to complete the two-dimensional efficient arrangement of irregular parts.

Description

Technical field:

[0001] The present invention relates to the fields of computer science and engineering, in particular to the technical field related to a two-dimensional arrangement method of irregular parts, specifically a two-dimensional arrangement method of irregular parts based on a mutation-driven genetic algorithm. Background technology:

[0002] The 2D arrangement problem of irregular parts has a wide range of applications in manufacturing, logistics, and industrial production. These irregular parts often have complex shapes and contours, so their effective arrangement is not as intuitive as regular-shaped parts. In engineering and manufacturing applications such as sheet cutting, circuit board layout, integrated circuit design, and jigsaw puzzles, the arrangement problem of irregular parts needs to be solved.

[0003] At present, the methods for solving irregular parts arrangement problems mainly include heuristic algorithms, optimization algorithms, and meta-heuristic algorithms. These methods can solve the problem to a certain extent, but it is usually difficult to find the optimal solution within a reasonable time, especially when the number and complexity of irregular parts increase. In addition, different arrangement problems may require different algorithms and strategies, which limits the versatility and diversity of existing methods.

[0004] Therefore, a new and improved two-dimensional arrangement method for irregular parts is needed, which can more effectively solve the problem of irregular parts arrangement, improve the global search ability of the algorithm, reduce the convergence time, and have better versatility and adaptability.

[0005] Traditional solutions usually rely on complex mathematical models and heuristic rules. Although these methods are effective to a certain extent, they face a series of challenges. First, the irregular parts arrangement problem is a combinatorial optimization problem with a huge search space, which makes it very difficult to find the optimal solution. Second, existing methods often cannot handle cases with large-scale and highly complex parts because their computational costs are too high. In addition, as the diversity of irregular parts arrangement problems increases, the versatility of existing methods becomes limited, and different solutions need to be designed for each specific problem.

[0006] The purpose of the present invention is to provide a two-dimensional arrangement method of irregular parts without involving genetic algorithms. By introducing new algorithm strategies and optimization techniques, the limitations of existing methods are overcome, the problem of irregular parts arrangement can be solved more effectively, and the quality and efficiency of the arrangement results are improved.

[0007] In summary, the two-dimensional arrangement problem of irregular parts is a complex and important problem involving applications in multiple fields. Existing methods have some limitations and challenges in solving this problem, so a new and improved method is needed to more effectively solve the problem of irregular parts arrangement. The present invention provides a two-dimensional arrangement method of irregular parts that does not involve genetic algorithms. The method has better versatility and adaptability, and can find high-quality arrangement solutions in a shorter time, so it has broad application prospects in the fields of engineering, manufacturing and production. Summary of the invention:

[0008] The present invention provides a two-dimensional arrangement method of irregular parts based on a mutation-driven genetic algorithm, aiming to solve the challenges and limitations in the problem of irregular parts arrangement.

[0009] A two-dimensional arrangement method for irregular parts based on mutation-driven genetic algorithm. The search process is mainly divided into three steps:

[0010] S1. Using the variance criterion and the envelope area criterion, a preliminary search and optimization is performed on the positional relationship between the two parts;

[0011] S2, based on the first step of optimization, the two parts are regarded as a whole, and the variance criterion and the envelope area criterion are continued to be used for the second search optimization;

[0012] S3. Based on the results of the second step, multiple parts are considered as a whole again, and the lateral distance criterion is used for final search optimization to determine all positional relationships of the parts arrangement.

[0013] In the first and second search steps, both the variance criterion and the envelope area criterion are used for search optimization, so a total of four results are obtained.

[0014] The corresponding envelope area criterion is divided into the following steps:

[0015] S1. Create a binary image of the same size as the original image, with all pixels set to black;

[0016] S2, perform horizontal analysis on the image pixels. For each row of the image matrix, the pixel analysis starts from the leftmost side and gradually extends to the right. Any black pixel encountered will be set to white at the corresponding position in the newly created binary image until the first white pixel is encountered. Repeat this process for each row, starting from the rightmost side and gradually extending to the left.

[0017] S3, then analyzing the image pixels vertically, using a similar method, analyzing pixels from top to bottom and from bottom to top; all black pixels encountered are set to white until the first white pixel is encountered;

[0018] S4, performing a bitwise OR operation on the image obtained by the horizontal analysis and the original image to obtain image I1, and performing a bitwise OR operation on the image obtained by the vertical analysis and the original image to obtain image I2;

[0019] S5, performing an “AND” operation on the binary images I1 and I2 to obtain a binary image I12;

[0020] S6, performing a bitwise NOT operation on the binary image I12 to obtain a binary image I12_R, and counting the number of white pixels N_I12_R in the image I12_R;

[0021] S7. Take N_I12_R as the search optimization target. The smaller the value, the better the result.

[0022] In the three search steps, after each genetic algorithm-based search, a local search is performed to improve the search efficiency and further optimize the search accuracy.

[0023] After the corresponding three search steps, the parts in different columns will be adjusted to a horizontal position, and the positional relationship between different parts will be recalculated.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] Through the above steps, the method of the present invention can achieve significant optimization results in the problem of irregular parts arrangement, which can not only improve the efficiency and quality of arrangement, but also meet the needs of different problems and has broad application prospects. Description of the drawings:

[0026] Figure 1 It is a two-dimensional arrangement method of irregular parts based on mutation-driven genetic algorithm;

[0027] Figure 2 Flowchart of the optimization process for mutation-driven genetic algorithm search;

[0028] Figure 3 Schematic diagram of the image cropping process;

[0029] Figure 4 Schematic diagram of the image expansion process;

[0030] Figure 5 For image expansion effect;

[0031] Figure 6 To encode information;

[0032] Figure 7 It is a schematic diagram of the size and location of parts;

[0033] Figure 8This is a schematic diagram of the parts combination in the first search optimization process;

[0034] Fig. 9 This is the principle diagram of the envelope area method calculation process;

[0035] Fig.10 This is a schematic diagram of parts combination in the second search optimization process;

[0036] Fig.11 This is a schematic diagram of the positional relationship obtained after the second search optimization;

[0037] Fig.12 A schematic diagram of the optimization target and its position relationship for the third search optimization;

[0038] Fig.13 It is a schematic diagram of local optimization;

[0039] Fig.14 It is a flow chart of the local optimization process;

[0040] Fig.15 This is the effect diagram of balancing different columns of parts after the third optimization;

[0041] Fig.16 This is the final layout effect diagram. Specific implementation method:

[0042] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0043] The method of the present invention achieves efficient irregular parts arrangement through a series of steps. Various aspects of the present invention are described in detail below.

[0044] (1) Part shape drawing acquisition and processing

[0045] First, the method of the present invention involves obtaining corresponding part shape drawings for the shape of irregular parts. These shape drawings can be obtained by image scanning, CAD system export or other methods. The obtained shape drawings need to be binarized to convert the image into a black and white binary image for subsequent processing. In addition, according to the actual size of the parts, corresponding adjustments are made to ensure that the size and shape of the parts can be accurately considered during the arrangement process.

[0046] (2) Expansion treatment considering material loss

[0047] In order to better simulate the material loss during the part processing, the method of the present invention performs expansion processing on the part image. This step expands the binary image of the part to enlarge the actual size of the part to take into account the material loss that may occur in actual processing.

[0048] (3) Encoding of part position and angle information

[0049] Next, the method of the present invention records the position and angle information of each part through coding. Coding is an important step that converts the geometric features of the parts into numerical data for subsequent optimization and arrangement. Each part is assigned a unique code including its position and angle information.

[0050] (4) Mutation-driven search optimization

[0051] The core part of the method of the present invention is a mutation-driven search optimization process, which is divided into three main steps to find the optimal part arrangement.

[0052] S1: Preliminary Search and Optimization In the first step, the variance criterion and the envelope area criterion are used to perform a preliminary search and optimization of the positional relationship between the two parts. This step helps determine the relative position between the parts and eliminate some unreasonable arrangements.

[0053] S2: Further search and optimization In the second step, based on the optimization in the first step, the two parts are regarded as a whole, and the variance criterion and envelope area criterion are continued to be used for the second search and optimization. This step helps to further optimize the position relationship of the parts to obtain a more compact and reasonable arrangement.

[0054] S3: Final search optimization In the third step, based on the results of the second step, multiple parts are considered as a whole again, and the lateral distance criterion is used to perform the final search optimization to determine all the positional relationships of the parts arrangement. The goal of this step is to find the final arrangement solution to minimize the gaps between parts and improve the efficiency of the arrangement.

[0055] (5) Local search optimization

[0056] After each search step, the image can be enlarged according to the required accuracy and local search optimization can be performed, which helps to improve the search efficiency and further optimize the quality of the arrangement.

[0057] (6) Final arrangement

[0058] Finally, the parts in different columns are adjusted to a horizontal position and arranged, thereby completing the efficient two-dimensional arrangement of irregular parts based on a mutation-driven genetic algorithm.

[0059] The envelope area criterion in the optimization target algorithm of the method of the present invention is mainly divided into the following steps:

[0060] S1. Create a binary image of the same size as the original image, with all pixels set to black;

[0061] S2. Perform horizontal analysis of the image pixels. For each row of the image matrix, the pixel analysis starts from the far left and gradually extends to the right. Any black pixel encountered will be set to white in the corresponding position of the newly created binary image until the first white pixel is encountered. Repeat this process for each row, starting from the far right and gradually extending to the left;

[0062] S3, then analyze the image pixels vertically, using a similar method to analyze pixels from top to bottom and from bottom to top. All black pixels encountered will be set to white until the first white pixel is encountered;

[0063] S4, performing a bitwise OR operation on the image obtained by the horizontal analysis and the original image to obtain image I1, and performing a bitwise OR operation on the image obtained by the vertical analysis and the original image to obtain image I2;

[0064] S5, performing a bitwise AND operation on the binary images I1 and I2 to obtain a binary image I12;

[0065] S6, performing a bitwise NOT operation on the binary image I12 to obtain a binary image I12_R, and counting the number of white pixels N_I12_R in the image I12_R;

[0066] S7. Take N_I12_R as the search optimization target. The smaller the value, the better the result.

[0067] Figure 1 This is the overall flow chart of the search optimization process. Figure 2 This is a flow chart of the search optimization process based on an improved genetic algorithm (mutation driven genetic algorithm).

[0068] (1) Image preprocessing

[0069] Binarize the acquired part image to obtain Figure 3 (a), the corresponding binary image is then cropped to completely remove the surrounding edges, as shown in Figure 3 As shown in (b), we get Figure 3 (c) shows the result, after which the image is scaled based on the actual size of the part and the actual size represented by each pixel.

[0070] Considering that some materials will be removed during the processing of parts, a certain gap must be left between parts during the layout process. This gap plays a vital role because it accommodates the materials that will be removed during the cutting process. Here, the corresponding image is expanded, and the corresponding expansion principle is as follows:

[0071]

[0072] Here, "pg" indicates the size of the gap between components, and (a,b) indicates the coordinates of a pixel. If the precision used is 0.5mm, each pixel corresponds to 0.5mm. If the gap is defined as 4mm. The image expansion process is as follows Figure 4 shown. Figure 4 (a) The gray part is the part to be expanded, and Figure 4 (b) is the result after expansion. The effect of expanding the corresponding part image is as follows: Figure 5 shown.

[0073] (2) Coding

[0074] In the present invention, an improved genetic algorithm is used to determine the optimal spatial arrangement of two patterns. The positional attributes of the part drawing in the image are specified using three parameters: x-coordinate, y-coordinate, and rotation angle. Initially, this information is encoded in binary format. For each sample, the binary number contains a total of 50 bits. The first 12 bits represent the x-coordinate of the first part, followed by bits 13 to 24 representing the y-coordinate of the first part. The 25th bit represents the angular direction of the first component, where 0 represents 0° and 1 represents 180°. Similarly, the positional information of the second part is encoded using the remaining 25 bits. A visual representation of this encoding process is shown as follows Figure 6 shown.

[0075] (3) Variation

[0076] In the mutation operation, some randomly selected binary bits are changed from 0 to 1 or from 1 to 0. However, it may be difficult to determine the exact number of bits to be mutated. Therefore, the present invention introduces a random variable, denoted as Nr, whose value is in the interval [1,10]. In addition, another random variable r is taken to specify the specific bit to be changed during the mutation process. The mutation process can be concisely described by equation (2):

[0077]

[0078] Where BI represents the binary number used to encode information. The corresponding x coordinate x c and the y coordinate y c The value of must be within the defined range. This constraint can be expressed as follows:

[0079]

[0080] Considering that a 12-bit binary number has the ability to represent 2^12=4096 different combinations of information, the spatial properties of the two components can be represented using a 50-bit binary number as follows:

[0081]

[0082] In the formula, the variables can be assigned as follows: BI represents the 50-bit binary representation of each sample. Lx and Ly represent the size of the image along the X-axis and Y-axis, respectively. In addition, lx and ly refer to the size of the component along the X-axis and Y-axis, respectively, as Figure 7 shown.

[0083] (4) First step: search

[0084] The present invention introduces a simple overlap detection method based on the number of white pixels, as shown in formula (5):

[0085] N_com1=N1+N2(5)

[0086] Where N_com1 represents the cumulative count of white pixels in the merged image, while N1 and N2 represent the number of white pixels in I0_1 and I0_2, respectively.

[0087] The resulting merged image, denoted as I1, can be expressed by the following equation:

[0088] I1=I0_1 ∪I0_2 (6)

[0089] Figure 8 Schematic diagram of merging two images. Specifically, Figure 8 (c) shows that by merging Figure 8 The composite pattern formed by the individual patterns shown in (a) and (b) is used to describe the positional relationship dx1, dy2 between the individual patterns in the initial stage of the search process.

[0090] After determining the best pattern combination among all samples, all other codes in all samples will be modified to be consistent with the best solution. Subsequently, all samples are mutated, and if no better results are obtained in three consecutive iterations, the optimization process will be terminated and the best solution obtained before will be adopted.

[0091] In order to optimize the pattern, the present invention uses two criteria. The first criterion is called the variance method, and its expression is:

[0092]

[0093] Where "La" and "Wa" represent the mean values ​​of the coordinate values ​​of the white pixels along the horizontal and vertical axes, respectively. These values ​​can be expressed by the following formula:

[0094]

[0095]

[0096] Among them, "N white” represents the count of white pixels, and “I” is the image matrix of the corresponding image.

[0097] The envelope area criterion is introduced here as another criterion for arranging the two patterns, which is divided into the following three steps:

[0098] Step 1: First create a black and white binary image

[0099] Create a binary image of the same size as the original image with all pixels set to black, such as Fig. 9 (a). Step 2: Horizontal pixel analysis of composite image

[0100] Composite images such as Fig. 9 As shown in (b), the pixels in each row are analyzed. Start from the leftmost position and gradually expand to the right. In the corresponding position of the newly generated binary image, any black pixel encountered will be converted to white until the first white pixel is encountered; thereafter, similar pixel analysis starts from the rightmost position and expands to the left. The result is shown in Fig. 9 (c) as shown.

[0101] Step 3: Vertical pixel analysis of composite image

[0102] Each column of pixels is analyzed, and the pixel analysis is performed from top to bottom and from bottom to top. Black pixels are converted to white until the first white pixel is encountered. The resulting image is as follows Fig. 9 (d) as shown.

[0103] After these steps, Fig. 9 Performing a bitwise OR operation on the binary images derived from (b) and (c) yields Fig. 9 (e). Similarly, Fig. 9 Applying bitwise OR operation on the binary images obtained in (b) and (d) yields Fig. 9 (f). Then, Fig. 9 The binary images generated by (e) and (f) are subjected to bitwise AND operation to obtain Fig. 9 (g). Finally, Fig. 9 (g) Perform bitwise NOT operation on the binary image to obtain Fig. 9 Results shown in (h).

[0104] exist Fig. 9 The number of white pixels in (h), denoted as N white , which forms the basis for the evaluation. The area formed by these white pixels is the area formed by the envelope area method.

[0105] (5) Second step search

[0106] In the second phase of relative position exploration, the merged results of the two patterns obtained from the initial phase analysis are used. Fig.10 Similar to the initial stage, the same two criteria are used to determine the appropriate relative position relationship dx2, dy2 of this merged pattern. These patterns ( Fig.10 The spatial position features of (a) and (b) are also represented by 50-bit binary numbers, consisting of white pixels, while the background pixels of the image are designated as black. The resulting synthesized image, denoted as I2, can be expressed as follows:

[0107] I2=I1_1∪I1_2 (10)

[0108] Fig.10 (c) shows the Fig.10 Results of merging the patterns presented in (a) and (b).

[0109] The results obtained by the envelope area method are as follows Fig.11 shown.

[0110] (6) Part 3 Search

[0111] So far, it is necessary to continue the search process for the third iteration. In the third step, the pattern combination obtained in the second search phase is established as a fixed pattern I2. The task of the third search is to determine the appropriate positional relationship between these patterns.

[0112] From the fixed position obtained in the second step of the search, the tilt angle θ can be determined using the following mathematical expression:

[0113] θ=arctan(dx2 / dy2) (11)

[0114] In the third search optimization process, the optimization goal is to minimize the distance between two adjacent columns of patterns, such as Fig.12 (a) shown.

[0115] Calculate the angle the pattern needs to rotate according to dx2 and dy2, such as Fig.12 (a). Based on Fig.12 (b), the corresponding distance can be determined by counting the columns in the image matrix that do not contain white pixels. This distance can be calculated using the following expression:

[0116] N0=∑(j=1 to n)[1-sign(c[j])] (12)

[0117] Among them, sign(k) is defined as: when k is equal to 0, sign(k) is equal to 0; when k is greater than 0, sign(k) is equal to 1. Here, the value of vector c is defined as follows:

[0118] c=[∑(i=1 to m)A[i][1], ∑(i=1 to m)A[i][2],…, ∑(i=1 to m)A[i][n]] (13)

[0119] By using genetic algorithm and fixed range optimization, the best pattern combination was obtained in the third iteration. The final result is shown in Fig.12 As shown in (c).

[0120] (7) Local Search Optimization

[0121] However, it is usually challenging to obtain the best results using genetic algorithms in a short time. In order to improve efficiency, the present invention proposes an optimization method within a fixed range to explore the possibility of obtaining better results. The optimization method can be described as follows:

[0122] I2 ij ={I2:translate(i,j),-i0≤i≤i0,-j0≤j≤j0} (14)

[0123] In fixed range optimization, such as Fig.13 As shown, the pattern will be translated (2i+1)·(2j+1) times. After each translation, the standard value will be calculated. Then a comparison will be made to determine whether there is a better value in the calculated results. If a better value is found, the pattern will be translated to the improved position and the search method will be repeated according to the new position. This search process will continue until no better position is found within the fixed range. The corresponding process is as follows Fig.14 In the previous three-step search optimization process, local search optimization is required after the optimization using genetic algorithm is completed.

[0124] (8) Angle adjustment

[0125] Based on the three search steps completed, the spatial relationship between the patterns has been determined for the layout process. In the last step, the pattern needs to be rotated by minimizing the vertical displacement dy3 to achieve a horizontal layout. The angle β of the required rotation can be calculated using the following formula:

[0126] β=arctan(dy3 / dx3) (15)

[0127] The final rotated image is as follows Fig.15 As shown. Note that in the first and second search processes, two criteria are used, namely the variance criterion and the envelope area criterion. Therefore, a total of four different results will be obtained. At this time, you only need to select the solution with the largest number of arrangement patterns. Finally, according to the obtained spatial positions dx1, dy1, dx2, dy2, dx3, dy3 and the rotation angle β, the final pattern arrangement result is as follows Fig.16。

Claims

1. A two-dimensional arrangement method of irregular parts based on mutation-driven genetic algorithm, characterized by: The search process is mainly divided into three steps: S1. Using the variance criterion and the envelope area criterion, a preliminary search and optimization is performed on the positional relationship between the two parts; S2, based on the first step of optimization, the two parts are regarded as a whole, and the variance criterion and the envelope area criterion are continued to be used for the second search optimization; S3. Based on the results of the second step, the multiple parts are considered as a whole again, and the lateral distance criterion is used to perform the final search optimization to determine all the positional relationships of the parts arrangement; The first criterion, called the variance method, is expressed as: (7) in," La "and" Wa " represents the mean of the coordinate values ​​of the white pixels along the horizontal and vertical axes respectively; these values ​​are expressed by the following formulas: (8) (9) in," N white ” represents the count of white pixels, and “I” is the image matrix of the corresponding image; The corresponding envelope area criterion is divided into the following steps: S1. Create a binary image of the same size as the original image, with all pixels set to black; S2, perform horizontal analysis on the image pixels. For each row of the image matrix, the pixel analysis starts from the leftmost side and gradually extends to the right. Any black pixel encountered will be set to white at the corresponding position in the newly created binary image until the first white pixel is encountered. Repeat this process for each row, starting from the rightmost side and gradually extending to the left. S3, then analyzing the image pixels vertically, using a similar method, analyzing pixels from top to bottom and from bottom to top; all black pixels encountered are set to white until the first white pixel is encountered; S4, performing a bitwise OR operation on the image obtained by the horizontal analysis and the original image to obtain image I1, and performing a bitwise OR operation on the image obtained by the vertical analysis and the original image to obtain image I2; S5, performing an "AND" operation on the binary images I1 and I2 to obtain a binary image I12; S6, performing a bitwise NOT operation on the binary image I12 to obtain a binary image I12_R, and counting the number of white pixels N_I12_R in the image I12_R; S7. Take N_I12_R as the search optimization target. The smaller the value, the better the result.

2. According to claim 1, a method for two-dimensional arrangement of irregular parts based on mutation-driven genetic algorithm is characterized by: In the first and second search steps, both the variance criterion and the envelope area criterion are used for search optimization, so a total of four results are obtained.

3. The method for two-dimensional arrangement of irregular parts based on mutation-driven genetic algorithm according to claim 1, characterized in that: In the three search steps, after each genetic algorithm-based search, a local search is performed to improve the search efficiency and further optimize the search accuracy.

4. The method for two-dimensional arrangement of irregular parts based on mutation-driven genetic algorithm according to claim 1, characterized in that After the corresponding three search steps, the parts in different columns will be adjusted to a horizontal position, and the positional relationship between different parts will be recalculated.

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