A search-based nesting method for arranging single-size circular parts on a rectangular plate.

Abstract

This invention discloses a search-based nesting method for arranging single-sized circular parts on a rectangular plate, relating to the field of optimized nesting. The method includes: Step 1, initializing the width W, length L, and radius R of the circular parts on the rectangular plate, and setting a maximum storage quantity K; Step 2, placing the first circular part on the rectangular plate to generate scheme S1, and saving the result to scheme set P1; Step 3, traversing the scheme set P... i In each existing scheme S ik Based on this, calculate all possible placement points for the next circular component; Step 4: Place S ik Step 5: Arrange the generated sampling points in descending order of utilization rate, and select the first two sampling locations; Step 6: Summarize all the new schemes generated in Step 4 into a new set S and arrange them in descending order; Step 7: Remove duplicates from S; Step 8: Select the first K schemes from S and add them to P. i+1 In the middle; Step 8, repeat steps 3 to 7 until the rectangular plate is filled; Step 9, output the optimal solution.

Description

Technical Field

[0001] This invention relates to the field of optimized layout, and more particularly to a search-based layout method for arranging single-sized circular parts on a rectangular plate. Background Technology

[0002] Circular blanks have wide applications in the machinery manufacturing industry. For example, they are used to cut and punch silicon steel sheets into circular pieces to manufacture the stator and rotor cores of motors; and to cut stainless steel coils into circular pieces to make pots, bowls, cups, basins, and kettles. In actual production, raw materials need to be processed using punching, shearing, and cutting methods to obtain circular blanks. As people pay increasing attention to resource and energy waste, minimizing waste has become a goal pursued by enterprises. A good layout scheme can not only reduce production costs, improve processing efficiency, and enhance enterprise competitiveness, but also save raw materials, making it an important part of green manufacturing. Research on layout problems has both economic benefits and theoretical value.

[0003] Statistics show that circular blanks typically account for about 60% of the total cost of the final product. Therefore, under the premise of meeting the processing requirements and leaving a certain processing allowance, when processing equipment with limited processing range to process single-size circular blanks on rectangular plates of fixed dimensions, it is necessary to first lay out the circular parts on the rectangular plates in order to obtain a higher plate utilization rate.

[0004] Existing layout methods include:

[0005] 1. Relying on experience for layout without certain rules leads to low material utilization, high manufacturing costs, serious waste of raw materials and corporate resources, and reduces the company's competitiveness.

[0006] 2. Use a linear arrangement for layout. Linear arrangement is the simplest and most common layout method, and its layout cycle is easy to find. During processing, simply repeat the processing of the first column or multiple columns. Figure 1 As shown. However, the utilization rate of the plate material in this layout method is also low, mainly due to the following reasons: 1) The area enclosed by the four adjacent circular pieces in a straight line is a quadrilateral, and the enclosed area is large; 2) The distances d1 and d2 between the circular pieces and the edges of the rectangular plate material are large.

[0007] Some new sorting methods have also emerged.

[0008] In their Chinese invention patent application "A Layout Method for Processing Circular Parts on Rolled Material" (application number: CN201910340227.3), Guo Weijian et al. addressed the problem of processing single-size circular parts from rectangular rolled materials (assuming a fixed width and unrestricted length) by utilizing an inclined layout method, effectively improving material utilization and reducing production costs. However, in actual production, most materials are rectangular sheets with fixed width and length, thus limiting the practicality of the aforementioned technical solution.

[0009] In their Chinese invention patent application "A Heuristic Layout Method for Circular Components on Rectangular Plates" (application number: CN202010344116.2), Wang Yingcong et al. proposed a method that determines the locations based on rules, and then randomly shifts forward or backward on an initial random sequence to generate a new arrangement order. This method comprehensively considers both the already arranged and unarranged spaces, improving the utilization rate of the plate, but it has a high degree of randomness, and the results of each calculation are different.

[0010] The circular nesting problem is a type of combinatorial optimization problem and is a classic NP-hard problem. Unless P = NP, there is no deterministic algorithm that can find an exact solution in polynomial time.

[0011] Therefore, those skilled in the art are dedicated to developing a new layout method for arranging single-sized circular parts on rectangular plates, overcoming the aforementioned shortcomings in the prior art, and providing better layout results within a specified time. Summary of the Invention

[0012] In view of the above-mentioned deficiencies of the prior art, the technical problem to be solved by the present invention is how to provide an optimal layout method for processing single-size circular parts on rectangular plates, overcoming the problems of low material utilization, high manufacturing cost and serious waste of raw materials in the existing layout methods.

[0013] To address the aforementioned technical problems, this invention establishes a mathematical model for processing single-size circular parts on rectangular plates, and proposes a heuristic circular layout rule for arranging single-size circular parts on rectangular plates and a search-based layout method based on the layout rule. This constrains the length and width of the rectangular plates, which not only improves material utilization and reduces manufacturing costs, but is also applicable to rectangular plates of different sizes, making it highly practical.

[0014] Specifically, the present invention provides a search-based layout method for arranging single-sized circular parts on a rectangular plate, characterized in that the method includes the following steps:

[0015] Step 1: Initialize the width W and length L of the rectangular plate and the radius R of the circular part, and set the scheme set P. i Maximum storage capacity K;

[0016] Step 2: Place the first circular piece at the lower left corner of the rectangular plate to generate scheme S1, and save the result to the scheme set P1;

[0017] Step 3: Traverse the set of solutions P i In each existing scheme S ik Based on this, all possible placement points of the next circular component are calculated according to the layout rule algorithm;

[0018] Step 4: Submit the above scheme S ik The generated sampling points are arranged in descending order of the utilization rate of the used rectangular areas. The first two sampling positions are selected, and the circular component is placed in them to generate a new scheme. and

[0019] Step 5: Summarize all the new solutions generated in Step 4 into a new set. And sorted in descending order;

[0020] Step 6: Perform deduplication on the new set S, that is, if the position of each circle is the same in two layout schemes, delete one of them;

[0021] Step 7: Select the first K solutions from the new set S and add them to P. i+1 middle;

[0022] Step 8: Repeat steps 3 to 7 until there is no extra space in the rectangular plate to place the next circular piece;

[0023] Step 9: Output the optimal solution, i.e., the set of solutions P. i The first layout scheme S in i1 .

[0024] Furthermore, the sorting rule algorithm in step 3 is as follows: in the existing scheme S ik Based on this, let E be the set of sides formed by the roll edges of the rectangular sheet, and let C be the (i+1)th circular piece. i+1 Then C i+1 The following are the possible placement locations:

[0025] (1)C i+1 At least compared with the existing solution S ik The two circular parts are tangent to each other;

[0026] (2)C i+1 At least compared with the existing solution S ik It is tangent to one of the circular components and at least tangent to one edge of the edge set E;

[0027] (3)C i+1 It is tangent to at least two edges in the set of edges E;

[0028] Calculate C according to the rules in (1) to (3). i+1 All possible locations where it can be disposed of.

[0029] Furthermore, the roll edge of the rectangular sheet includes a left side, a right side, a top side, and a bottom side.

[0030] Furthermore, with the lower left corner of the rectangular plate as the origin, a Cartesian coordinate system is established with the length direction of the rectangular plate as the X-axis and the width direction as the Y-axis; let the center coordinates of the i-th circular component be (x... i y i Let M be the number of circles inserted into the rectangular plate, then the utilization rate of the rectangular area of ​​the rectangular plate is:

[0031]

[0032] Wherein, U represents the utilization rate of the rectangular area of ​​the rectangular plate.

[0033] Furthermore, the constraints of the mathematical model for the problem of nesting circular parts of a single size on a rectangular plate are as follows:

[0034]

[0035] Wherein, the center coordinates of the i-th circular component are (x... i y i The center coordinates of the j-th circular component are (x, y). j y j R is the radius of the circular component, W and L are the width and length of the rectangular plate, respectively, and M is the number of circles inserted into the rectangular plate.

[0036] Furthermore, the circular components must not overlap, and the circular components must not extend beyond the boundaries of the rectangular plate.

[0037] Furthermore, a predetermined spacing d is left between the circular components; in this case, the radius R of the circular components is set to R+d / 2.

[0038] Furthermore, in step 7, if the number of schemes in the new set S is less than K, then directly let P... i+1 =S is sufficient.

[0039] Furthermore, the size of the maximum storage quantity K affects the quality of the sorting results: the larger K is, the better the sorting results, but the longer it takes.

[0040] Furthermore, the maximum storage quantity K has a value range of 10≤K≤20.

[0041] The present invention provides a search-based nesting method for arranging single-sized circular parts on a rectangular plate, which has at least the following technical effects:

[0042] 1. By establishing a mathematical model for single-size circular layout on rectangular panels, specific layout rules can be determined. Based on existing layout schemes, the specific coordinates for the next circular component can be determined. The utilization rate of the currently used panels can be calculated based on these coordinates, allowing for comparison of the quality of these coordinates. Then, K better coordinate points are selected for iterative updates, placing the circular components one by one until the rectangular panel can no longer accommodate the next circular component.

[0043] 2. When processing a single-sized circular part on a rectangular plate of fixed size, the search-based nesting method provided by this invention can obtain the same solution. Compared with existing technologies, it not only improves material utilization but also reduces manufacturing costs. It is applicable to rectangular plates of different sizes and has strong practicality. In actual production applications, simply inputting the radius of the circular part, the width and length of the rectangular plate, and the maximum storage quantity of the solution set into the computer will yield the optimal nesting solution in a short time. This method is convenient, fast, and highly automated, greatly improving production efficiency.

[0044] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the straight-line arrangement method in the prior art;

[0046] Figure 2 This is a schematic diagram showing the location of the next circular part searched according to the nesting rules.

[0047] Figure 3 This is a schematic diagram of the rectangular area where the board material has been consumed so far;

[0048] Figure 4 Let P be the set of solutions i An iterative diagram;

[0049] Figure 5 This is a flowchart illustrating a preferred embodiment of the method of the present invention;

[0050] Figure 6 for Figure 5 The diagram shows the test case results for the method shown. Detailed Implementation

[0051] The following description, with reference to the accompanying drawings, illustrates several preferred embodiments of the present invention to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0052] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, the thickness of some components has been appropriately exaggerated in the drawings.

[0053] This invention establishes a mathematical model for machining single-dimensional circular parts on rectangular plates. Due to the NP-hard nature of this problem, the technical solution provided by this invention proposes heuristic circular nesting rules and a search-based nesting method based on these rules.

[0054] Initialize the width W and length L of the rectangular plate and the radius R of the circular piece, and set the scheme set P. i The maximum storage quantity K is determined, and the lower left corner of the rectangular plate is set as the origin of the coordinate system. A Cartesian coordinate system is established with the length direction of the rectangular plate as the X-axis and the width direction as the Y-axis. Let the center coordinates of the i-th circular piece be (x... i y i Let M be the number of circles inserted into the rectangular panel. Then the utilization rate of the rectangular area of ​​the rectangular panel is:

[0055]

[0056] Where U represents the utilization rate of the rectangular area of ​​the rectangular plate.

[0057] The constraints of the mathematical model for the layout problem of machining single-dimensional circular parts on rectangular plates are as follows:

[0058]

[0059] Wherein, the center coordinates of the i-th circular component are (x... i y i The center coordinates of the j-th circular component are (x, y). j y j R is the radius of the circular component, W and L are the width and length of the rectangular plate, respectively, and M is the number of circles inserted into the rectangular plate.

[0060] By establishing a mathematical model for single-size circular layout on rectangular panels, specific layout rules can be determined. Based on existing layout schemes, the specific coordinates for the next circular component can be determined. The utilization rate of the currently used panels can be calculated based on these coordinates, allowing for a comparison of the quality of these coordinates. Then, K better coordinate points are selected for iterative updates, placing the circular components one by one until the rectangular panel can no longer accommodate the next circular component.

[0061] The present invention provides a search-based layout method for arranging single-sized circular parts on a rectangular plate, comprising the following steps, such as... Figure 5 As shown:

[0062] Step 1: Initialize the width W and length L of the rectangular plate and the radius R of the circular part, and set the scheme set P. i Maximum storage capacity K;

[0063] Step 2: Place the first circular piece at the lower left corner of the rectangular plate to generate solution S1, and save the result to solution set P1;

[0064] Step 3: Traverse the set of solutions P i In each existing scheme S ik Based on this, the algorithm for the layout rule is used to calculate all possible placement points for the next circular component.

[0065] Step 4: Submit solution S ik The generated layout points are sorted in descending order of the utilization rate of the used rectangular areas. The first two layout positions are selected, and the circular parts are placed in them to generate a new layout. and

[0066] Step 5: Summarize all the new solutions generated in Step 4 into a new set. like Figure 4 As shown, and arranged in descending order;

[0067] Step 6: Perform deduplication on the new set S, that is, if the position of each circle is the same in two layout schemes, delete one of them;

[0068] Step 7: Select the first K solutions from the new set S and add them to P. i+1 If the number of schemes in the new set S is less than K, then directly let P... i+1 =S is sufficient;

[0069] Step 8: Repeat steps 3 to 7 until there is no extra space in the rectangular plate to place the next circular piece;

[0070] Step 9: Output the optimal solution, i.e., the solution set P. i The first layout scheme S ini1 .

[0071] The sorting rule algorithm in step 3 is as follows: Based on the existing scheme S... ik Based on this, let E be the set of edges formed by the roll edges (left, right, top, and bottom) of the rectangular sheet, and let C be the (i+1)th circular piece. i+1 Then C i+1 The following are the possible placement locations:

[0072] (1)C i+1 At least compared with existing scheme S ik The two circular parts are tangent to each other;

[0073] (2)C i+1 At least compared with existing scheme S ik It is tangent to one of the circular components in the set and is tangent to at least one edge of the edge set E;

[0074] (3)C i+1 It is tangent to at least two edges in edge set E;

[0075] Calculate C according to the rules in (1) to (3). i+1 All possible locations where it can be disposed of.

[0076] like Figure 2 As shown, given the existing set S2, according to the rules, there are 6 possible locations for C3 (p1, p2, p3, p4, p5, p6).

[0077] For all the locations where sampling can be carried out, an evaluation function is defined to select sampling points.

[0078] Assuming the next circular part is placed at one of these locations, the utilization rate of the used sheet metal area can be calculated. The sheet metal area utilization rate is calculated for all locations, and then the part is placed at the location with the highest utilization rate.

[0079] like Figure 3 As shown, if the third circular piece is placed at p1, the utilization rate of the used sheet material area is the area of ​​the three circles divided by the area of ​​rectangle Rect1, resulting in U1≈58.9%. If the third circular piece is placed at p3, the utilization rate of the used sheet material area is the area of ​​the three circles divided by the area of ​​rectangle Rect2, resulting in U3≈78.5%. Clearly, U3 is greater than U1, so placing the third circle at position p3 is better.

[0080] In the above embodiments of the present invention, the spacing between circular parts is not considered. However, in actual production, a spacing d between circular parts is sometimes required. Even with a spacing d, the optimal nesting method described in this invention is still applicable to situations where there is a spacing between circular parts; simply set the radius R of the circular parts to R+D / 2 in step 1.

[0081] The maximum storage quantity K affects the quality of the sorting results: the larger K is, the better the sorting results, but the longer it takes. The value of K ranges from 10 to 20.

[0082] Compared to existing technologies, the proposed method for searching and nesting single-size circular parts on rectangular plates not only improves material utilization but also reduces manufacturing costs. It is applicable to rectangular plates of different sizes and is highly practical. In actual production applications, simply inputting the radius of the circular part, the width and length of the rectangular plate, and the maximum storage capacity of the solution set into the computer will yield the optimal nesting solution in a short time. This method is convenient, fast, and highly automated, significantly improving production efficiency. A nesting example is provided below.

[0083] like Figure 6 As shown, the rectangular plate has a width W = 500 and a length L = 500. The radius of the circle to be processed is R = 20, and the maximum storage capacity of the solution set is K = 20. Using a straight-line arrangement, 144 circular parts can be processed. Figure 6 (Left, material utilization rate is 72.38%), 166 circular parts can be processed using the method described in this invention. Figure 6 On the right, the material utilization rate is 83.44%, which is an increase of 11.06%.

[0084] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A search-based nesting method for arranging circular parts of a single size on a rectangular plate, characterized in that, The method includes the following steps: Step 1: Initialize the width of the rectangular plate. ,length and the radius of the circular part and set up a set of schemes. Maximum storage capacity ; Step 2: Place the first circular component at the lower left corner of the rectangular plate to generate the design. And save the results to the solution set. middle; Step 3: Traverse the set of solutions In each existing solution Based on this, let the set of sides formed by the roll edges of the rectangular sheet be denoted as . And record the first The circular component is ,but The following are the possible placement locations: (1) At least compared with the existing solutions The two circular parts are tangent to each other. (2) At least compared with the existing solutions One of the circular pieces is tangent to and at least tangent to the set of edges. Tangent to one of the edges, (3) At least with the set of edges The two sides in the middle are tangent. Calculate according to the rules in (1) to (3) All possible locations for discharge; Step 4: Apply the proposed solution The generated sampling points are arranged in descending order of the utilization rate of the used rectangular areas. The first two sampling positions are selected, and the circular component is placed in them to generate a new scheme. and ; Step 5: Summarize all the new solutions generated in Step 4 into a new set. And sorted in descending order; Step 6: For the new set Perform deduplication: if two layout schemes have the same position for every circle, delete one of them. Step 7: Select the new set The front of the middle Add one plan to middle; Step 8: Repeat steps 3 to 7 until there is no extra space on the rectangular plate to place the next circular piece; Step 9: Output the optimal solution, i.e., the set of solutions. The first layout scheme .

2. The search-based layout method for arranging single-sized circular parts on a rectangular plate as described in claim 1, characterized in that, The roll edges of the rectangular sheet include the left, right, top, and bottom edges.

3. The search-based layout method for arranging single-sized circular parts on a rectangular plate as described in claim 1, characterized in that, The lower left corner of the rectangular plate is the origin of the coordinate system, and the length direction of the rectangular plate is the coordinate system. Axial and width directions are Establish a Cartesian coordinate system based on the x-axis; let the x-axis be the first x-axis. The center coordinates of the circular component are: ,set up To determine the number of circles to be inserted into the rectangular plate, the utilization rate of the rectangular area of ​​the rectangular plate is: in, The utilization rate of the rectangular area of ​​the rectangular plate.

4. The search-based layout method for arranging single-sized circular parts on a rectangular plate as described in claim 3, characterized in that, The constraints of the mathematical model for the problem of arranging circular parts of a single size on a rectangular plate are as follows: Among them, the The center coordinates of the circular component are: , No. The center coordinates of the circular component are: , The radius of the circular component is... and These represent the width and length of the rectangular plate, respectively. The number of circles to be inserted into the rectangular plate.

5. The search-based layout method for arranging single-sized circular parts on a rectangular plate as described in claim 3, characterized in that, The circular components must not overlap, and the circular components must not extend beyond the boundaries of the rectangular plate.

6. The search-based layout method for arranging single-sized circular parts on a rectangular plate as described in claim 3, characterized in that, A predetermined spacing d is left between the circular components; in this case, the radius R of the circular components is set to R+d / 2.

7. The search-based layout method for arranging single-sized circular parts on a rectangular plate as described in claim 1, characterized in that, In step 7, if the new set If the number of solutions is less than K, then directly let That's all.

8. The search-based layout method for arranging single-sized circular parts on a rectangular plate as described in claim 1, characterized in that, The maximum storage quantity The size affects the quality of the sorting results: The larger the value, the better the sorting results, but the longer it takes.

9. The search-based layout method for arranging single-sized circular parts on a rectangular plate as described in claim 1, characterized in that, The maximum storage quantity The range of values ​​is .

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