A three-dimensional component layout design method supporting neighborhood reconstruction and scheme evolution

Abstract

The present invention discloses a three-dimensional component layout design method that supports neighborhood reconstruction and scheme evolution. First, different three-dimensional layout components and master information are loaded, and the construction direction of the three-dimensional component is determined by the principal component analysis method, and the three-dimensional layout problem is converted into a connected domain polygon outline layout and an initial solution is generated. Subsequently, two types of layout goals are set: one is to minimize the master layout length; the other is to maximize the space utilization rate, which can change the component layout frequency. The present invention adopts a two-stage evolutionary process. In the first stage, the initial solution is locally adjusted through random neighborhood transformation to explore the feasible solution space; in the second stage, the layout scheme is iteratively optimized based on the search agent technology, so as to evolve and obtain the global optimal solution. The present invention can realize the three-dimensional component layout design for different optimization targets, and generate a two-target, two-stage efficient evolutionary conceptual design scheme, thereby reducing raw material costs and improving manufacturing efficiency.

Description

Technical Field

[0001] The invention relates to a three-dimensional component layout design method, in particular to a three-dimensional component layout design method supporting neighborhood reconstruction and scheme evolution. Background Art

[0002] Part Layout Optimization (PLO) refers to the planning of the arrangement and layout of models in the conceptual design stage of modern manufacturing, so as to improve the utilization rate of raw materials and manufacturing efficiency. The nesting problem is usually limited by factors such as the shape and size of the master, which makes the algorithm complexity and solution space extremely complex. Evolutionary solution is imperative. The solution design aims to maximize the space utilization of the manufacturing platform, which can not only improve economic benefits and time efficiency, but also help to cope with high-complexity and demanding manufacturing scenarios. With the continuous improvement of extreme manufacturing requirements, PLO has become an effective means and key factor to improve manufacturing efficiency, precision and raw material utilization. It has broad application prospects in industrial fields such as CNC machine tools, sheet metal cutting, additive manufacturing, electronic circuit boards, semiconductor stereolithography, micro-nano and atomic manufacturing.

[0003] Some scholars have proposed various methods to solve PLO for different application scenarios, and explored their optimization strategies and practical applications. Researchers from the Grenoble National Institute of Technology in France (Chergui A, Hadj-Hamou K, Vignat F. Production scheduling and nesting in additive manufacturing [J]. Computers & Industrial Engineering, 2018, 126: 292-301.) reviewed the mathematical models of manufacturing planning, nesting and scheduling problems, and explained the importance of heuristic solutions in production planning and nesting. The US patent (Collomp J. Method of nesting three-dimensional print objects: US Patent 10,346,101 [P]. 2019-7-9.) describes a method for 3D nesting of formed objects, which determines the position of the object on the manufacturing surface according to its shape, size and height to minimize the surface area and group and nest highly similar objects. The US patent (Norman B C. Digital MES for production scheduling & nesting for additive manufacturing: US Patent Application 17 / 214,844 [P]. 2022-9-29.) optimizes 2D / 3D nesting and stacking arrangements based on production standards, and packages the optimized geometric data into a pallet file, which is finally transmitted to the manufacturing equipment to generate the corresponding physical object.

[0004] These methods explore the feasibility and advantages of nesting problems in different manufacturing scenarios and propose a variety of optimization solutions. However, nesting calculations are still affected by problems such as excessive safety collision detection overhead and slow calculations under high complexity, making it difficult to achieve large-scale three-dimensional component nesting layout conceptual design with problem reconstruction and solution evolution. Summary of the invention

[0005] In order to solve the problems existing in the background technology and improve the processing and forming efficiency problems of batch forming in the component manufacturing process, so as to further improve the production efficiency, the present invention aims to provide a three-dimensional component layout design method that supports neighborhood reconstruction and scheme evolution. The present invention is based on the evolution scheme of neighborhood transformation and search agent, and is a manufacturing platform layout optimization method with the goal of maximizing space utilization or minimizing motherboard length. The present invention can optimize the layout content by reconstructing the problem and evolving the scheme under different objective functions. Specifically, the present invention introduces a systematic two-stage process from the initial stage, through the intermediate stage to the termination stage. This two-stage optimization method enables the arrangement order of components and the length or space utilization of the motherboard to be optimally configured respectively, with flexibility and efficiency.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] 1. A 3D component layout design method supporting neighborhood reconstruction and scheme evolution

[0008] Step 1: According to the geometric feature information of the layout elements, several layout elements are pre-processed respectively to obtain the corresponding polygonal projection contours;

[0009] Step 2: Perform an initial layout according to the polygonal projection contours of all layout elements to obtain a feasible solution of the contour under the initial layout;

[0010] Step 3: Determine the layout optimization objectives and constraints according to different layout requirements. Based on the layout optimization objectives and constraints, perform random neighborhood transformation on the contour feasible solutions under the initial layout to obtain the contour feasible solution set S;

[0011] Step 4: Take the K contour feasible solutions with the best optimization target value in the current contour feasible solution set S as K search agents, where K is an integer greater than 1. Based on the K search agents, update the solutions of other contour feasible solutions in the current contour feasible solution set S, and then obtain an updated contour feasible solution set;

[0012] Step 5: Repeat step 4 to iteratively optimize the contour feasible solution set until the K search agents no longer change, and obtain the final contour feasible solution set. The contour feasible solution with the best optimization target value in the final contour feasible solution set is used for layout.

[0013] In the step 1, each arrangement element is preprocessed to obtain a corresponding polygonal projection profile, which specifically includes the following steps:

[0014] Step 11: After performing principal component analysis on the geometric feature information of each sample to be arranged, a component feature matrix is ​​obtained; then three eigenvectors are calculated based on the component feature matrix, which are recorded as the first eigenvector, the second eigenvector and the third eigenvector in order;

[0015] Step 12: Rotate the current layout element so that the first eigenvector of the current layout element is parallel to the z-axis direction;

[0016] Step 13: Rotate the three-dimensional element rotated in step 12 again around the second eigenvector so that the fit degree of the xOy plane of the current three-dimensional element is the highest, and record the construction direction at this time as the optimal construction direction;

[0017] Step 14: Project the current three-dimensional component in the optimal construction direction to the xOy plane and extract its projection contour, while reducing the number of contour vertices to a preset contour point number A to obtain the polygonal projection contour of the current layout component in the optimal construction direction in the xOy plane.

[0018] The step 2 is specifically as follows:

[0019] According to the width of the layout master, a layout order of layout elements is generated and the layout distance between the polygonal contours of two adjacent layout elements is set. Starting from the origin of the layout master, the polygonal contours of all layout elements are arranged in sequence, and the contour feasible solution is composed of the coordinates of the polygonal projection contour points corresponding to each layout element in the current layout order.

[0020] In step 3, the layout optimization goal is to keep the number of components to be arranged unchanged and to minimize the layout length of the master.

[0021] In step 3, the goal of layout optimization is to make the number of components to be arranged variable, with the goal of maximizing space utilization.

[0022] In step 3, the constraint conditions are specifically that the polygonal projection outlines of different layout elements do not overlap each other and the polygonal projection outlines of all layout elements cannot exceed the layout master.

[0023] The random neighborhood transformation includes exchanging neighborhoods, reversing neighborhoods, and rotating neighborhoods.

[0024] The random neighborhood transformation includes operations of exchanging neighborhoods, reversing neighborhoods, rotating neighborhoods, and inserting and deleting neighborhoods.

[0025] The step 4 is specifically as follows:

[0026] Step 4.1: Take the K contour feasible solutions with the best optimization target value in the current contour feasible solution set S as K search agents, and select a contour feasible solution other than the K search agents in the current contour feasible solution set S;

[0027] Step 4.2: Calculate the distance vector between the current contour feasible solution and the K search agents using the following formula:

[0028] D t = | C k ·X t - X |

[0029] Among them, X represents the position matrix of the feasible solution of the current contour, C k represents the kth distance adjustment factor, k=1,…,K; D t is the distance vector between the feasible solution of the current contour and the tth search agent; X t is the position matrix of the t-th search agent, t=1,…,K; | | is the absolute value of each element of the matrix;

[0030] Step 4.3: Based on the distance vector between the current contour feasible solution and the K search agents, calculate the K temporary position vectors corresponding to the current contour feasible solution using the following formula:

[0031] X k = | X t - A k ·D t |

[0032] A k = 2·a·r k - a

[0033] Among them, X k is the kth temporary position vector of the feasible solution of the current contour, A k is the kth position adjustment factor;

[0034] Step 4.4: Add the K temporary position vectors of the current contour feasible solution and divide by K to obtain the new position vector of the current contour feasible solution, and update the contour feasible solution set S;

[0035] Step 4.5: Select the next contour feasible solution other than the K search agents in the current contour feasible solution set S, repeat steps 4.2-4.4, calculate the corresponding new position vector, until all contour feasible solutions other than the K search agents in the current contour feasible solution set S are traversed and processed to obtain an updated contour feasible solution set S.

[0036] 2. A computer device

[0037] The device includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the three-dimensional component layout design method supporting neighborhood reconstruction and scheme evolution when executing the computer program.

[0038] The present invention has the following beneficial effects:

[0039] For the three-dimensional component layout design with different optimization objectives, when the method complexity and solution space are extremely complex, the present invention uses random neighborhood transformation to adjust and deeply evolve the layout solution, and generates a two-objective, two-stage efficient evolution conceptual design scheme, which meets the overall scheme requirements of the conceptual design stage of modern manufacturing, thereby significantly reducing raw material costs and improving manufacturing efficiency, and has high operability and efficient evolution effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Other features, objects and advantages of the present invention will become more apparent by reading the detailed description of the non-limiting implementation examples with reference to the following drawings:

[0041] Figure 1 It is a flow chart of the three-dimensional component layout design method supporting problem reconstruction and solution evolution of the present invention.

[0042] Figure 2 It is a three-dimensional element (28 teeth for an adult) according to an example of the arrangement scheme of the present invention.

[0043] Figure 3 The present invention uses principal component analysis to adjust the construction direction process of three-dimensional elements.

[0044] Figure 4 The present invention provides an initial layout and an intermediate layout with a layout distance of 1 targeting the minimum master length; wherein (a) is the initial layout with a layout distance of 1 targeting the minimum master length, and (b) is the intermediate layout with a layout distance of 1 targeting the minimum master length.

[0045] Figure 5 It is the terminal layout and final three-dimensional space layout of the present invention with a layout distance of 1 and a minimum master length as the target; wherein (a) is the terminal layout with a layout distance of 1 and a minimum master length as the target, and (b) is the final three-dimensional space layout with a layout distance of 1 and a minimum master length as the target.

[0046] Figure 6 It is a schematic diagram of the master length layout evolution with a layout distance of 1 and a minimum master length as a target according to the present invention.

[0047] Figure 7 These are the initial layout and intermediate layout with a layout distance of 1 aimed at maximum space utilization of the present invention; wherein (a) is the initial layout with a layout distance of 1 aimed at maximum space utilization, and (b) is the intermediate layout with a layout distance of 1 aimed at maximum space utilization.

[0048] Figure 8 It is the terminal arrangement layout and the final three-dimensional arrangement layout with the arrangement distance of 1 aimed at maximum space utilization of the present invention; wherein (a) is the terminal arrangement layout with the arrangement distance of 1 aimed at maximum space utilization, and (b) is the final three-dimensional arrangement layout with the arrangement distance of 1 aimed at maximum space utilization.

[0049] Fig. 9 It is a schematic diagram of the evolution of space utilization with a spacing of 1 and a maximum space utilization as the goal of the present invention.

[0050] Fig.10 These are the initial layout and the intermediate layout with a layout distance of 2 targeting the minimum master length of the present invention; wherein (a) is the initial layout with a layout distance of 2 targeting the minimum master length, and (b) is the intermediate layout with a layout distance of 2 targeting the minimum master length.

[0051] Fig.11 It is the terminal layout and final three-dimensional space layout of the present invention with a layout distance of 2 and the minimum master length as the target; wherein (a) is the terminal layout with a layout distance of 2 and the minimum master length as the target, and (b) is the final three-dimensional space layout with a layout distance of 2 and the minimum master length as the target.

[0052] Fig.12 It is a schematic diagram of the master length layout evolution with a layout distance of 2 and a minimum master length as a target according to the present invention.

[0053] Fig.13 These are the initial layout and the intermediate layout with a layout distance of 2 aimed at maximum space utilization of the present invention; wherein (a) is the initial layout with a layout distance of 2 aimed at maximum space utilization, and (b) is the intermediate layout with a layout distance of 2 aimed at maximum space utilization.

[0054] Fig.14 It is the terminal arrangement layout and the final three-dimensional arrangement layout with the arrangement distance of 2 aiming at the maximum space utilization of the present invention; wherein (a) is the terminal arrangement layout with the arrangement distance of 2 aiming at the maximum space utilization, and (b) is the final three-dimensional arrangement layout with the arrangement distance of 2 aiming at the maximum space utilization.

[0055] Fig.15 It is a schematic diagram of the evolution of space utilization with a spacing of 2 and a goal of maximum space utilization according to the present invention.

[0056] Fig.16 It is a comparison diagram of the layout design of different targets at different layout distances of the present invention. DETAILED DESCRIPTION

[0057] The present invention is further described in detail below with reference to the accompanying drawings and examples.

[0058] When dealing with complex three-dimensional layout problems, Figure 2 The 28-tooth model shown is used as an example to illustrate how to perform an efficient nesting optimization process. The description and mathematical number of the components are shown in Table 1:

[0059] Table 1 is the correspondence table between the numbers and names of the 28 tooth models

[0060]

[0061] The number of layout elements FDI is represented by n FDI , the projected contour area of ​​the component FDI is represented by A FDI (Unit: mm 2 ), the space occupied by the component FDI is represented by U FDI (Unit: %), the position of the contour centroid (AC) of the component FDI projection contour is represented by AC FDI (Coordinate unit: mm), the unit of the master length L is mm.

[0062] Example 1

[0063] Figure 1 It is an overall flow chart of the 3D component layout design method based on problem reconstruction and solution evolution. The process essentially involves the integration of multiple steps, aiming to minimize the master length and improve manufacturing efficiency. Each layout component is a 3D model, and the layout master is the platform.

[0064] Specifically, the following steps are included: Step 1: Preprocessing a number of layout elements respectively according to the geometric feature information of the layout elements to obtain the corresponding polygonal projection contours;

[0065] Step 11: After principal component analysis is performed on each geometric feature information to be arranged, the component feature matrix is ​​obtained; then three eigenvectors are calculated based on the component feature matrix. Specifically, the covariance matrix is ​​obtained from the component feature matrix and its transpose. After eigenvalue decomposition of the covariance matrix, the three eigenvectors of the component feature matrix can be obtained, which are recorded as the first eigenvector, the second eigenvector and the third eigenvector in order; these vectors describe the main distribution direction of the geometric features, such as Figure 3 shown.

[0066] Step 12: Rotate the current arrangement element so that the first eigenvector of the current arrangement element is parallel to the z-axis direction, and the projection area of ​​the three-dimensional element on the xOy plane is the smallest;

[0067] Step 13: Rotate the three-dimensional element rotated in step 12 again around the second eigenvector so that the fit degree of the xOy plane of the current three-dimensional element is the highest, and record the construction direction at this time as the optimal construction direction;

[0068] Step 14: Project the current three-dimensional component in the optimal construction direction to the xOy plane and use the rolling edge method to extract its projection contour. At the same time, use the RDP line simplification method to reduce the number of contour vertices to the preset contour point number A to obtain the polygonal projection contour of the current layout component in the xOy plane in the optimal construction direction.

[0069] Step 2: Perform an initial layout based on the polygonal projection contours of all tooth models to obtain a feasible solution for the contour under the initial layout; that is, an initial layout of three-dimensional components that supports problem reconstruction and solution evolution.

[0070] Step 2 is as follows:

[0071] According to the width of the platform, with the upper left corner of the platform as the origin (0,0), a tooth model arrangement order is randomly generated and the arrangement distance between the polygonal contours of two adjacent tooth models is set. Starting from the origin of the platform, the polygonal contours of all tooth models are arranged from top to bottom and from left to right. The contour feasible solution is composed of the coordinates of the polygonal projection contour points corresponding to each tooth model under the current arrangement order. The solution consists of A-dimensional column vectors, each column vector represents a polygonal contour, and the column vector elements are the coordinates of the contour vertices arranged in counterclockwise order. At this time, the maximum x coordinate of all contour vertices in the master is the horizontal arrangement length under this arrangement order.

[0072] The feasible solution of the contour with a spacing of 1 is as follows Figure 4 As shown in (a). Figure 4 In (a), the centroid of the star is located at AC. The total area occupied by all component models is 1450.3238, L=55.25, the total area of ​​the motherboard is A=2762.5, the space utilization rate of the motherboard is U=52.5004%, and the centroid of the motherboard is AC: (24.2366, 24.2876). The number of components in this layout target is 1 (i.e. n FDI =1).

[0073] The arrangement parameters of each component model are as follows:

[0074] A 27 =69.1933,U 27 =2.5047%,AC 27 :(5.3523,13.3434); A 26 =80.4419,U 26 =2.9119%,AC 26:(5.7076,23.6289);A 25 =43.5947,U 25 =1.5781%, AND 25 :(34.7069,19.6839);A 24 =37.822,U 24 =1.3691%, AND 24 :(42.787,35.0228);A 23 =44.7593,U 23 =1.6202%, AC 23 :(11.2487,44.5936);A 22 =37.0163,U 22 =1.34%, AND 22 :(36.899,39.6958);A 21 =53.2056,U 21 =1.926%, AC 21 :(23.9176,4.2284);A 11 =55.9188,U 11 =2.0242%, AC 11 :(9.353,4.4149);A 12 =36.9524,U 12 =1.3376%, AC 12 :(41.4096,46.0883);A 13 =50.6125,U 13 =1.8321%, AC 13 :(16.6728,9.4188);A 14 =39.2846,U 14 =1.4221%, AC 14 :(18.3707,19.8556);A 15 =45.6028,U 15 =1.6508%, AC 15 :(19.4358,41.488);A 16 =83.8578,U 16 =3.0356%, AC 16 :(12.9572,34.2397);A 17 =71.8803,U 17 =2.602%, AC 17 :(26.0758,14.3992);A 37 =78.3536,U 37=2.8363%, AC 37 :(29.0153,44.5136);A 36 =88.2018,U 36 =3.1928%, AC 36 :(49.8839,5.5592);A 35 =44.7595,U 35 =1.6203%, AND 35 :(4.6928,39.9384);A 34 =38.9986,U 34 =1.4117%, AC 34 :(27.6994,23.1855);A 33 =40.8653,U 33 =1.4793%, AND 33 :(21.0482,27.6042);A 32 =26.1724,U 32 =0.94742%, AND 32 :(12.4637,17.162);A 31 =25.6104,U 31 =0.92707%, AND 31 :(3.5865,46.8122);A 41 =26.784,U 41 =0.96956%, AND 41 :(3.7405,32.8732);A 42 =22.9443,U 42 =0.83056%, AND 42 :(13.5852,25.3935);A 43 =46.4415,U 43 =1.6811%, AC 43 :(25.0037,34.5673);A 44 =40.6625,U 44 =1.4719%, AC 44 :(31.8912,7.3349);A 45 =46.6267,U 45 =1.6878%, AND 45 :(41.887,24.7364);A 46 =92.0177,U 46 =3.331%, AC 46 :(40.5051,11.9494);A47 =81.5779,U 47 =2.953%, AC 47 :(33.9102,30.5559).

[0075] The feasible solution of the contour with a spacing of 2 is as follows Fig.10 As shown in (a). Fig.10 In (a), the star mark is the centroid position AC. The total occupied area of ​​all component models is 1450.3238, L=66, the total area of ​​the motherboard is A=3300, the space utilization rate of the motherboard is U=43.9492%, and the centroid position AC of the motherboard is (29.9549,24.8564). The number of components in this layout target is 1 (i.e. n FDI =1).

[0076] The arrangement parameters of each component model are as follows:

[0077] A 27 =69.0557,U 27 =2.0926%,AC 27 :(13.7781,39.5064); A 26 =80.5707,U 26 =2.4415%,AC 26 :(42.7606,43.6565); A 25 =43.6451, U 25 =1.3226%,AC 25 :(36.5181,9.76); A 24 =37.7517, U 24 =1.144%,AC 24 :(53.7356,12.8161); A 23 =44.7608, U 23 =1.3564%,AC 23 :(22.3966,44.8805); A 22 =37.1176, U 22 =1.1248%,AC 22 :(31.0888,16.8493); A 21 =53.2158,U 21 =1.6126%,AC 21 :(19.788,31.6518); A 11 =55.8628, U 11 =1.6928%,AC 11 :(44.9663,16.3915); A 12=36.9667,U 12 =1.1202%, AC 12 :(16.3804,13.0623);A 13 =50.6831,U 13 =1.5359%, AC 13 :(35.0199,35.2208);A 14 =39.303,U 14 =1.191%, AC 14 :(31.6261,44.4719);A 15 =45.5863,U 15 =1.3814%, AC 15 :(50.407,25.7162);A 16 =83.8682,U 16 =2.5415%, AC 16 :(46.1848,5.243);A 17 =71.9665,U 17 =2.1808%, AC 17 :(38.6621,25.2539);A 37 =78.3343,U 37 =2.3738%, AC 37 :(14.3405,22.0682);A 36 =88.3741,U 36 =2.678%, AC 36 :(25.5055,7.4868);A 35 =44.811,U 35 =1.3579%, AC 35 :(28.6371,27.2311);A 34 =39.0118,U 34 =1.1822%, AC 34 :(51.7549,37.5328);A 33 =40.9237,U 33 =1.2401%, AND 33 :(4.9909,45.0122);A 32 =26.172,U 32 =0.79309%, AND 32 :(23.1348,19.6705);A 31 =25.6091,U 31 =0.77603%, AND 31:(4.3463,19.0976); A 41 =26.8077, U 41 =0.81235%,AC 41 :(4.2612,36.6704); A 42 =22.917, U 42 =0.69446%, AC 42 :(26.7718,37.7226); A 43 =46.4371,U 43 =1.4072%,AC 43 :(4.9487,27.4862); A 44 =40.6622, U 44 =1.2322%,AC 44 :(44.2782,33.1602); A 45 =46.7059, U 45 =1.4153%,AC 45 :(14.7984,3.7529); A 46 =92.0594,U 46 =2.7897%,AC 46 :(60.3071,31.2252); A 47 =81.6675,U 47 =2.4748%,AC 47 :(6.4006,9.8538).

[0078] Step 3: Determine the layout optimization objectives and constraints according to different layout requirements. Based on the layout optimization objectives and constraints, perform random neighborhood transformation on the contour feasible solutions under the initial layout to obtain the contour feasible solution set S, satisfying S={s0, s1,…, s q},s q It represents the qth contour feasible solution, which contains the polygonal projection contour coordinates of all components under a layout (i.e., arrangement order). The polygonal projection contour coordinates of a component model form a position vector, that is, each contour feasible solution is a matrix composed of the position vectors of all component models; that is, the intermediate stage of three-dimensional component layout design that supports neighborhood reconstruction and scheme evolution.

[0079] The layout optimization goal is to keep the number of components to be arranged unchanged and to minimize the master layout length min L. The formula is:

[0080] f(s) = min L; L = max(x i +w i / 2), i∈1,2,...,n

[0081] Where, f(s) is the first objective function value, L is the master length, x i is the horizontal coordinate of the vertex of the polygonal projection contour of the i-th component model, w i is the width of the polygonal projection outline of the i-th component model, and n is the number of each type of components to be arranged, that is, the arrangement frequency.

[0082] The constraint conditions are specifically that the polygonal projection outlines of different component models do not overlap each other and the polygonal projection outlines of all component models cannot exceed the platform.

[0083] Random neighborhood transformations include swapping neighborhoods (i.e., randomly swapping the positions of two column vectors), reversing neighborhoods (i.e., randomly selecting a column vector and multiplying it by a rotation transformation matrix), and rotating neighborhoods (i.e., reversing the order of column vectors from the i-th to the j-th).

[0084] The feasible solution of the contour with a spacing of 1 is as follows Figure 4 (b) shows the total occupied area of ​​all component models is 1450.3238, L=49.25, the total area of ​​the motherboard is A=2462.5, the space utilization rate of the motherboard is U=58.8964%, and the centroid position AC of the motherboard is (22.8584,23.8088). The number of components in this layout target is 1 (i.e. n FDI =1).

[0085] The arrangement parameters of each component model are as follows:

[0086] A 27 =69.1932, U 27 =2.8099%,AC 27 :(5.3523,44.8434); A 26 =80.5396,U 26 =3.2706%,AC 26 :(21.4977,39.3194); A 25 =43.65, U 25 =1.7726%,AC 25 :(38.1833,45.85); A 24 =37.7249, U 24 =1.532%,AC 24 :(32.8025,40.3142); A 23 =44.7764, U 23 =1.8183%,AC 23 :(12.9406,13.3828); A 22 =36.9448, U 22=1.5003%, AND 22 :(4.0745,29.2968);A 21 =53.2921,U 21 =2.1641%, AC 21 :(32.0012,18.6222);A 11 =55.8233,U 11 =2.2669%, AC 11 :(4.7249,10.2912);A 12 =36.9543,U 12 =1.5007%, AND 12 :(14.3366,46.0888);A 13 =50.6293,U 13 =2.056%, AND 13 :(21.1492,29.806);A 14 =39.2907,U 14 =1.5956%, AND 14 :(27.5575,46.2226);A 15 =45.5012,U 15 =1.8478%, AC 15 :(29.7285,33.4868);A 16 =84.1062,U 16 =3.4155%, AC 16 :(5.8055,20.0834);A 17 =71.9811,U 17 =2.9231%, AC 17 :(44.3538,4.7908);A 37 =78.3944,U 37 =3.1835%, AC 37 :(11.3756,35.0605);A 36 =88.1909,U 36 =3.5814%, AC 36 :(23.8721,12.8503);A 35 =44.7909,U 35 =1.8189%, AC 35 :(9.5038,3.3697);A 34 =38.9335,U 34 =1.5811%, AND 34 :(17.5903,5.7492);A33 =40.8199,U 33 =1.6577%,AC 33 :(13.2756,26.1404); A 32 =26.2069, U 32 =1.0642%,AC 32 :(35.9246,2.3887); A 31 =25.6336, U 31 =1.041%, AC 31 :(38.7522,36.3759); A 41 =26.8586, U 41 =1.0907%,AC 41 :(3.0852,36.9491); A 42 =22.9725, U 42 =0.93289%, AC 42 :(25.1934,23.3763); A 43 =46.5748,U 43 =1.8914%,AC 43 :(33.3551,9.1674); A 44 =40.5827, U 44 =1.648%, AC 44 :(18.3956,20.4938); A 45 =46.7181,U 45 =1.8972%,AC 45 :(26.5289,3.4854); A 46 =92.1115,U 46 =3.7406%, AC 46 :(41.7814,14.9937); A 47 =81.4378,U 47 =3.3071%, AC 47 :(37.9834,27.9127).

[0087] The feasible solution of the contour with a spacing of 2 is as follows Fig.10 (b) shows the total occupied area of ​​1450.3238, L=60, the total area of ​​the motherboard A=3000, the space utilization rate of the motherboard U=48.3441%, and the centroid position AC of the motherboard is (27.7696,24.5515). The number of each component in this layout target is 1 (i.e. n FDI =1).

[0088] The specific number of emissions for each model is as follows:

[0089] A 27 =69.1091,U 27 =2.3036%, AC 27 :(44.7792,10.4);A 26 =80.4862,U 26 =2.6829%, AC 26 :(6.4796,43.6336);A 25 =43.65, U 25 =1.4553%, AC 25 :(10.8901,3.7102);A 24 =37.7606, U 24 =1.2587%, AC 24 :(26.0619,35.8714);A 23 =44.778, U 23 =1.4926%, AC 23 :(51.2793,28.8788);A 22 =37.0802, U 22 =1.236%, AC 22 :(4.897,26.8696);A 21 =53.2989,U 21 =1.7766%, AC 21 :(43.4735,44.7002);A 11 =55.9176,U 11 =1.8639%, AC 11 :(35.317,37.9767);A 12 =36.9915, U 12 =1.2331%, AC 12 :(4.5888,10.0565);A 13 =50.6595, U 13 =1.6887%, AC 13 :(13.045,32.7721);A 14 =39.2907,U 14 =1.3097%, AC 14 :(29.5575,45.4726);A 15 =45.4781,U 15 =1.5159%, AC 15 :(41.6484,30.8638);A 16=83.8964,U 16 =2.7965%, AC 16 :(13.9141,21.856);A 17 =72.1302,U 17 =2.4043%, AC 17 :(31.977,26.7672);A 37 =78.4019,U 37 =2.6134%, AC 37 :(21.356,5.0161);A 36 =88.2161,U 36 =2.9405%, AC 36 :(25.8408,17.1336);A 35 =44.769,U 35 =1.4923%, AC 35 :(45.1905,22.3527);A 34 =38.9953,U 34 =1.2998%, AND 34 :(21.5328,28.492);A 33 =40.8535,U 33 =1.3618%, AC 33 :(14.0888,11.89);A 32 =26.1751,U 32 =0.8725%, AND 32 :(39.1126,2.4829);A 31 =25.6091,U 31 =0.85364%, AND 31 :(4.3463,34.5976);A 41 =26.7884,U 41 =0.89295%, AND 41 :(4.5175,18.9013);A 42 =22.9786,U 42 =0.76595%, AND 42 :(48.2609,2.6938);A 43 =46.4346,U 43 =1.5478%, AC 43 :(36.7457,17.2833);A 44 =40.6627,U 44 =1.3554%, AND 44:(48.9256,37.5381); A 45 =46.703, U 45 =1.5568%,AC 45 :(31.8667,7.4302); A 46 =92.0562,U 46 =3.0685%,AC 46 :(18.5833,43.2171); A 47 =81.5568,U 47 =2.7186%,AC 47 :(54.437,17.0734).

[0090] Step 4: The three contour feasible solutions with the best optimization target values ​​in the current contour feasible solution set S are used as three search agents. Based on the three search agents, the solutions of other contour feasible solutions in the current contour feasible solution set S are updated to obtain an updated contour feasible solution set.

[0091] Step 4 is as follows:

[0092] Step 4.1: Take the three contour feasible solutions with the best optimization target values ​​in the current contour feasible solution set S as three search agents, and select a contour feasible solution other than the three search agents in the current contour feasible solution set S;

[0093] Step 4.2: Calculate the distance vector between the current contour feasible solution and the three search agents using the following formula:

[0094] D t = | C k ·X t - X |

[0095] Among them, X represents the position matrix of the feasible solution of the current contour, C k represents the kth distance adjustment factor, which is a random vector uniformly distributed in the range [0,2], k=1,2,3; D t is the distance vector between the feasible solution of the current contour and the tth search agent; X t is the position matrix of the t-th search agent, t=1,2,3; | | is the absolute value of each element in the matrix;

[0096] The details are as follows:

[0097] D α = | C1·X α - X |

[0098] D β = | C2·X β- X |

[0099] D γ = | C3·X γ - X |

[0100] Among them, X α , X β , X γ Represent the position vectors of the first, second and third search agents respectively, and the D α , D β , D γ is the distance vector between the current contour feasible solution and the first, second and third search agents.

[0101] Step 4.3: Based on the distance vectors between the current contour feasible solution and the three search agents, the three temporary position vectors corresponding to the current contour feasible solution are calculated using the following formula:

[0102] X k = | X t - A k ·D t |

[0103] A k = 2·a·r k - a

[0104] Among them, X k is the kth temporary position vector of the feasible solution of the current contour, A k is the kth position adjustment factor, which makes the first adjustment vector a decrease linearly from 2 to 0, and the second adjustment vector r i Uniformly distributed in the range [0,1], when A i When the value of is greater than 1, the new feasible solution will be far away from the search agent to prevent it from falling into the local optimal solution. i When it is less than 1, the feasible solution approximates the search agent to find the optimal solution in the neighboring area. The details are as follows:

[0105] The distance vector D between the feasible solution and the first, second and third search agents according to the current contour α , D β , D γ Calculate three new temporary position vectors X1, X2, X3:

[0106] X1= | X α – A1·D α |

[0107] X2= | X β – A2·D β |

[0108] X3= | Xγ – A3·D γ |

[0109] Step 4.4: Add the three temporary position vectors of the current contour feasible solution and divide by 3 to obtain the new position vector X of the current contour feasible solution. new , and update the contour feasible solution set S; that is

[0110] X new = (X1+ X2+ X3) / 3

[0111] Step 4.5: Select the next contour feasible solution except the three search agents in the current contour feasible solution set S, repeat steps 4.2-4.4, calculate the corresponding new position vector, until all contour feasible solutions except the three search agents in the current contour feasible solution set S are traversed and processed to obtain the updated contour feasible solution set S.

[0112] Step 5: Repeat step 4 to iteratively optimize the contour feasible solution set until the three search agents no longer change, and obtain the final contour feasible solution set, which is the final stage of the three-dimensional component layout design that supports neighborhood reconstruction and solution evolution. The layout is performed according to the contour feasible solution with the best optimization target value in the final contour feasible solution set, that is, the polygonal contour arrangement order and contour vertex coordinates represented by the final solution are used to display the arrangement results of the components on the motherboard from a three-dimensional perspective.

[0113] Figure 5 (a) is the final solution with a layout distance of 1 and the minimum motherboard length as the target. The total occupied area of ​​all component models is 1450.3238, L=45.75, the total motherboard area A=2287.5, the motherboard space utilization rate U=63.4021%, and the centroid position AC of the motherboard is (21.956,24.4505). The number of components in this layout target is 1 (i.e. n FDI =1).

[0114] The arrangement parameters of each component model are as follows:

[0115] A 27 =69.1933,U 27 =3.0248%, AC 27 :(5.3523,11.3434); A 26 =80.4344,U 26 =3.5163%,AC 26 :(11.3158,33.9641); A 25 =43.5879, U 25 =1.9055%,AC 25:(4.343,28.0375);A 24 =37.7491,U 24 =1.6502%, AND 24 :(4.6023,20.1232);A 23 =44.7937,U 23 =1.9582%, AND 23 :(31.566,3.6916);A 22 =37.0581,U 22 =1.620%, AC 22 :(37.0988,31.6308);A 21 =53.2921,U 21 =2.3297%, AC 21 :(22.7512,17.6222);A 11 =55.9188,U 11 =2.4445%, AC 11 :(41.353,4.4149);A 12 =37.0264,U 12 =1.6186%, AC 12 :(29.6456,29.9797);A 13 =50.6086,U 13 =2.2124%, AC 13 :(4.1974,45.0231);A 14 =39.3374,U 14 =1.7197%, AC 14 :(22.5346,27.1235);A 15 =45.489,U 15 =1.9886%, AND 15 :(14.8435,13.3999);A 16 =83.8053,U 16 =3.6636%, AC 16 :(22.5884,36.3725);A 17 =72.0665,U 17 =3.1504%, AC 17 :(32.6264,39.716);A 37 =78.3003,U 37 =3.423%, AC 37 :(13.9259,44.4749);A 36 =88.2772,U36 =3.8591%, AND 36 :(20.9628,5.3521);A 35 =44.824,U 35 =1.9595%, AND 35 :(37.1611,12.3351);A 34 =39.0007,U 34 =1.7049%, AC 34 :(28.5719,11.0566);A 33 =40.9106,U 33 =1.7884%, AND 33 :(41.793,40.8611);A 32 =26.2219,U 32 =1.1463%, AC 32 :(36.0373,46.918);A 31 =25.5867,U 31 =1.1185%, AC 31 :(40.4093,25.9126);A 41 =26.8586,U 41 =1.1741%, AC 41 :(3.0852,36.4491);A 42 =22.9521,U 42 =1.0034%, AND 42 :(3.0251,3.8073);A 43 =46.5404,U 43 =2.0346%, AC 43 :(10.9976,3.9213);A 44 =40.5954,U 44 =1.7747%, AND 44 :(41.988,18.5278);A 45 =46.662,U 45 =2.0399%, AND 45 :(24.2382,45.8048);A 46 =92.0601,U 46 =4.0245%, AC 46 :(13.6592,22.9284);A 47 =81.6516,U 47 =3.5695%, AC 47:(32.3822,21.0216).

[0116] Figure 5 (b) is the final three-dimensional space layout with a layout distance of 1 and a minimum master length as the target. Figure 6 This is a monotonically decreasing graph of the master length evolution with the minimum master length as the target and the layout distance of 1. The maximum value is 5.525000e+01, the minimum value is 4.575000e+01, the sum is 49414.0000, the average value is 49.4140, the standard deviation is 1.4274, the variance is 2.0375, and the second-order central moment is 2.0355. Regarding the adjacent evolution difference, the maximum is 0. Regarding the absolute value of the slope, the maximum is 77.2666 and the minimum is 0.

[0117] Fig.11 (a) is the final layout design with a layout distance of 2 and the minimum motherboard length as the goal. The total occupied area of ​​all component models is 1450.3238, L=55.5, the total motherboard area A=2775, the motherboard space utilization rate U=52.2639%, and the centroid position AC of the motherboard is (27.7344,24.2602). The number of components in this layout goal is 1 (i.e. n FDI =1).

[0118] The arrangement parameters of each component model are as follows:

[0119] A 27 =69.1184,U 27 =2.4908%,AC 27 :(17.6229,23.1594); A 26 =80.5472,U 26 =2.9026%,AC 26 :(16.4173,34.1005); A 25 =43.6724, U 25 =1.5738%,AC 25 :(34.7032,29.9719); A 24 =37.8414, U 24 =1.3637%,AC 24 :(50.1544,26.4454); A 23 =44.7251, U 23 =1.6117%,AC 23 :(5.277,37.7308); A 22 =37.0017, U 22 =1.3334%,AC 22:(12.7513,13.849);A 21 =53.294,U 21 =1.9205%, AND 21 :(31.1478,20.2156);A 11 =55.7609,U 11 =2.0094%, AND 11 :(5.3788,7.845);A 12 =36.9543,U 12 =1.3317%, AC 12 :(50.8366,4.8388);A 13 =50.6594,U 13 =1.8256%, AC 13 :(41.545,3.7721);A 14 =39.3908,U 14 =1.4195%, AC 14 :(50.9728,38.3675);A 15 =45.5269,U 15 =1.6406%, AC 15 :(43.6634,33.4596);A 16 =83.9488,U 16 =3.0252%, AND 16 :(40.8366,43.5876);A 17 =72.0569,U 17 =2.5966%, AC 17 :(19.4867,5.6614);A 37 =78.2158,U 37 =2.8186%, AC 37 :(29.8371,39.2014);A 36 =88.3593,U 36 =3.1841%, AC 36 :(49.4957,15.42);A 35 =44.813,U 35 =1.6149%, AC 35 :(41.2931,23.0605);A 34 =38.962,U 34 =1.404%, AC 34 :(39.0625,14.9955);A 33 =40.8669,U 33=1.4727%,AC 33 :(23.3079,14.8341); A 32 =26.1753, U 32 =0.94325%, AC 32 :(4.6186,46.2312); A 31 =25.6018, U 31 =0.92259%,AC 31 :(50.6247,46.2371); A 41 =26.8316, U 41 =0.9669%, AC 41 :(11.7333,43.2603); A 42 =22.9879, U 42 =0.82839%,AC 42 :(11.1539,2.8922); A 43 =46.4931,U 43 =1.6754%,AC 43 :(26.5997,28.8469); A 44 =40.6105, U 44 =1.4634%,AC 44 :(5.0895,17.4485); A 45 =46.6919,U 45 =1.6826%,AC 45 :(20.2598,44.4494); A 46 =92.1463,U 46 =3.3206%,AC 46 :(31.1434,7.533); A 47 =81.7815,U 47 =2.9471%, AC 47 :(6.5707,27.8444).

[0120] The maximum value is 6.495652e-01, the minimum value is 5.826953e-01, the total is 616.9064, the average value is 0.6169, the standard deviation is 0.0116, the variance is 0.0001, and the second-order central moment is 0.0001. Regarding the adjacent evolution difference, the maximum is 0.0020. Regarding the absolute value of the slope, the maximum is 17.4411 and the minimum is 0.0074.

[0121] Fig.11 (b) is the final three-dimensional space layout with a layout distance of 2 and the minimum master length as the target. Fig.12 This is a monotonically decreasing graph of the master length evolution with a sample distance of 2 and the minimum master length as the target. The maximum value is 6.495652e-01, the minimum value is 5.826953e-01, the total is 616.9064, the average value is 0.6169, the standard deviation is 0.0116, the variance is 0.0001, and the second-order central moment is 0.0001. Regarding the adjacent evolution difference, the maximum is 0.0020. Regarding the absolute value of the slope, the maximum is 17.4411 and the minimum is 0.0074. Figure 6 and Fig.12 It can be seen from the comparison that as the spacing between samples increases, the required master length increases monotonically.

[0122] Example 2

[0123] When dealing with complex three-dimensional layout problems, Figure 2 The 28-component model shown is used as an example to illustrate how to perform an efficient nesting optimization process. The process essentially involves the integration of multiple steps to maximize raw material utilization and improve manufacturing efficiency. Each nesting component is a three-dimensional model and the layout master is the platform.

[0124] The present invention proposes a three-dimensional component layout design method supporting neighborhood reconstruction and scheme evolution, the method comprising the following steps:

[0125] Step 1: According to the geometric feature information of the component model, several component models are preprocessed respectively to obtain the corresponding polygonal projection contours;

[0126] In step 1, each component model is preprocessed to obtain the corresponding polygonal projection contour, which specifically includes the following steps:

[0127] Step 1.1: Extract geometric feature information from the metafile of each component model, perform principal component analysis (PCA) on each geometric feature information to be arranged, and obtain a component feature matrix; then calculate and obtain three eigenvectors based on the component feature matrix, which are recorded as the first eigenvector, the second eigenvector, and the third eigenvector in order to determine the main distribution direction of the geometric features;

[0128] In step 1.1, three eigenvectors are calculated based on the component characteristic matrix, specifically:

[0129] The covariance matrix C is calculated using the following formula: 3×3 :

[0130] C 3×3 = A 3×N A T N×3 / N

[0131] Among them, A 3×N is the component feature matrix, A T N×3 is the transpose of the component feature matrix, N is the number of geometric features, and T is the transpose.

[0132] Then, the covariance matrix C is decomposed into three eigenvectors.

[0133] Step 1.2: Rotate the current component model so that the first eigenvector of the current component model is parallel to the z-axis direction. At this time, the projection area of ​​the three-dimensional component on the xOy plane is the smallest, as shown in Figure 3 As shown;

[0134] Step 1.3: Rotate the three-dimensional element rotated in step 12 again around the second eigenvector so that the xOy plane of the current three-dimensional element has the highest fit, and record the construction direction at this time as the optimal construction direction, that is, the construction direction that fits the xOy plane as much as possible when the projection area is small;

[0135] Step 1.4: Project the current three-dimensional component in the optimal construction direction to the xOy plane and use the rolling edge method to extract its projection contour. At the same time, use the RDP (Ramer-Douglas-Peucker) line simplification method to reduce the number of contour vertices to the preset contour point number A, so that the number of polygonal projection contour vertices of each component model is the same, and the polygonal projection contour of the current component model in the optimal construction direction in the xOy plane is obtained.

[0136] Step 2: Perform an initial layout based on the polygonal projection contours of all component models to obtain a feasible solution for the contour under the initial layout; that is, an initial layout of three-dimensional components that supports neighborhood reconstruction and solution evolution.

[0137] Step 2 is as follows:

[0138] According to the width of the platform, with the upper left corner of the platform as the origin (0,0), generate a component model arrangement order and set the arrangement distance between the polygonal contours of two adjacent component models. Starting from the origin of the platform, from top to bottom and from left to right, the polygonal contours of all component models are arranged in sequence. The contour feasible solution is composed of the coordinates of the polygonal projection contour points corresponding to each component model in the current arrangement order. The solution consists of A-dimensional column vectors, each column vector represents a polygonal contour, and the column vector elements are the coordinates of the contour vertices arranged in counterclockwise order. At this time, the maximum x coordinate of all contour vertices in the master is the layout length under this arrangement order.

[0139] The feasible solution of the contour with a spacing of 1 is as follows Figure 7As shown in (a). The total occupied area of ​​all component models is 1456.7382, the total area of ​​the motherboard is A=2500, the space utilization rate of the motherboard is U=58.2695%, and the centroid position AC of the motherboard is (24.3222, 25.2356). The specific layout parameters of each component model are as follows:

[0140] n 27 =1,A 27 =69.126, U 27 =2.765%,AC 27 :(27.7931,15.9524);n 25 =2,A 25 =87.2215,U 25 =3.4889%, AC 25 :(4.093,10.2875),(42.9622,32.8778);n 24 =1,A 24 =37.7606, U 24 =1.5104%,AC 24 :(44.3119,12.6214);n 21 =2,A 21 =106.5663,U 21 =4.2627%,AC 21 :(10.5417,4.5866), (24.8445,42.9281);n 12 =2,A 12 =73.9037, U 12 =2.9561%,AC 12 :(3.7629,40.2388), (33.1596,8.8383);n 13 =1,A 13 =50.6989, U 13 =2.028%, AC 13 :(33.2892,46.1145);n 16 =1,A 16 =83.971,U 16 =3.3588%,AC 16 :(36.4125,26.2797);n 17 =3, A 17 =215.9966, U 17 =8.6399%,AC 17 :(20.0758,22.6492), (32.6562,36.4957), (41.5195,4.7219); n 37=3,A 37 =235.0548,U 37 =9.4022%, AC 37 :(11.8743,15.1477),(22.1105,32.9914),(24.8757,5.3308);n 33 =2,A 33 =81.8343,U 33 =3.2734%, AC 33 :(3.9909,25.7622),(37.293,17.1111);n 32 =2,A 32 =52.4114,U 32 =2.0965%, AND 32 :(3.4484,47.166),(27.8942,26.2393);n 31 =2,A 31 =51.1769,U 31 =2.0471%, AC 31 :(3.3365,33.0622),(17.6218,8.7825);n 41 =1,A 41 =26.8368,U 41 =1.0735%, AND 41 :(3.4349,18.5693);n 42 =3,A 42 =68.9209,U 42 =2.7568%, AC 42 :(43.5488,20.8705),(44.4242,47.2447),(46.2665,26.6378);n 43 =1,A 43 =46.493,U 43 =1.8597%, AND 43 :(40.5997,40.8469);n 44 =1,A 44 =40.564,U 44 =1.6226%, AC 44 :(12.2926,27.6238);n 45 =1,A 45 =46.6938,U 45 =1.8678%, AND 45 :(16.7935,46.0968);n 47 =1,A47 =81.5006,U 47 =3.26%, AC 47 :(12.2233,37.1194).

[0141] The feasible solution of the contour with a spacing of 2 is as follows Fig.13 As shown in (a). The total occupied area is 1133.4528, the total area of ​​the motherboard is A=2500, the space utilization rate of the motherboard is U=45.3381%, and the centroid position AC of the motherboard is (23.9275, 24.7574). The arrangement parameters of each component model are as follows:

[0142] n 25 =4, A 25 =174.7243, U 25 =6.989%, AC 25 :(5.7961,34.7232), (17.796,45.2232), (23.2636,12.6843), (25.9666,40.5041); n 23 =2,A 23 =89.5396,U 23 =3.5816%,AC 23 :(11.841,27.6147),(30.3966,31.3805);n 21 =1,A 21 =53.292, U 21 =2.1317%,AC 21 :(32.7512,8.8722);n 11 =1,A 11 =55.7609,U 11 =2.2304%,AC 11 :(5.3788,44.345);n 14 =1,A 14 =39.3057, U 14 =1.5722%,AC 14 :(46.6506,12.1759);n 35 =3, A 35 =134.3544,U 35 =5.3742%, AC 35 :(5.4773,8.5656), (19.6612,34.2973), (41.2604,3.6218); n 34 =1,A 34 =38.9989, U 34 =1.56%,AC34 :(13.3225,13.6915);n 33 =1,A 33 =40.9222,U 33 =1.6369%,AC 33 :(17.8145,5.2252);n 31 =2,A 31 =51.2167, U 31 =2.0487%,AC 31 :(3.7419,27.0106), (27.2989,19.8904); n 41 =1,A 41 =26.8313, U 41 =1.0733%,AC 41 :(26.2178,2.9831);n 42 =5,A 42 =114.8122,U 42 =4.5925%, AC 42 :(10.1872,2.9468), (12.1812,38.8986), (23.1812,26.8986), (33.2035,23.3545), (43.7619,45.9425) n 43 =3, A 43 =139.4774,U 43 =5.5791%,AC 43 :(4.9487,17.9862), (18.117,20.6987), (33.4882,44.7906); n 45 =2,A 45 =93.4329, U 45 =3.7373%, AC 45 :(39.2984,17.2529), (41.2432,26.4378); n 47 =1,A 47 =81.6033,U 47 =3.2641%, AC 47 :(39.9769,36.7712);

[0143] Step 3: Determine the layout optimization objectives and constraints according to different layout requirements. Based on the layout optimization objectives and constraints, perform random neighborhood transformation on the contour feasible solutions under the initial layout to obtain the contour feasible solution set S, S = {s0, s1, ..., s q},s qIt represents the qth contour feasible solution, which contains the polygonal projection contour coordinates of all component models under a layout (i.e., arrangement order). The polygonal projection contour coordinates of a component model form a position vector, that is, each contour feasible solution is a matrix composed of the position vectors of all component models; that is, the intermediate stage of three-dimensional component layout design that supports neighborhood reconstruction and scheme evolution.

[0144] The goal of layout optimization is to maximize space utilization with a variable number of components to be arranged. The formula is:

[0145] f(s) = min (1 / U), U = (∑ n i=1 A i ) / A platform

[0146] Among them, f(s) is the second objective function value, U is the space utilization, A i is the area of ​​the polygonal projection outline of the i-th component model, A platform is the area of ​​the master plate, and n is the number of each type of components to be arranged.

[0147] In step 3, the constraint conditions are specifically that the polygonal projection outlines of different component models do not overlap each other and the polygonal projection outlines of all component models cannot exceed the platform.

[0148] Random neighborhood transformation includes operations of exchanging neighborhoods, reversing neighborhoods, rotating neighborhoods, and inserting and deleting neighborhoods (i.e., randomly deleting a column vector and preferentially inserting the column vector represented by the contour with the largest area into this position).

[0149] The feasible solution of the contour with a spacing of 1 is as follows Figure 7 (b) shows the total occupied area of ​​1541.9253, the total area of ​​the motherboard A = 2500, the space utilization rate of the motherboard U = 61.677%, and the centroid position AC of the motherboard is (24.286, 25.2648). The arrangement parameters of each component model are as follows:

[0150] n 27 =1,A 27 =69.1931,U 27 =2.7677%,AC 27 :(5.1023,33.8434);n 26 =1,A 26 =80.4865,U 26 =3.2195%,AC 26 :(36.5575,22.7593);n 24 =1,A 24 =37.7045, U 24=1.5082%, AC 24 :(40.2262,38.7975);n 23 =1,A 23 =44.7719,U 23 =1.7909%, AND 23 :(42.2471,30.2383);n 22 =1,A 22 =37.0482,U 22 =1.4819%, AC 22 :(19.0729,46.2997);n 12 =1,A 12 =36.9512,U 12 =1.478%, AC 12 :(3.7629,18.9888);n 13 =1,A 13 =50.6413,U 13 =2.0257%, AND 13 :(25.2067,39.574);n 16 =2,A 16 =167.645,U 16 =6.7058%, AC 16 :(15.1018,38.1105),(17.1793,16.0167);n 37 =1,A 37 =78.2431,U 37 =3.1297%, AC 37 :(33.2252,44.3357);n 35 =1,A 35 =44.7463,U 35 =1.7899%, AND 35 :(45.274,18.1176);n 34 =1,A 34 =39.0072,U 34 =1.5603%, AND 34 :(25.187,21.0203);n 41 =2,A 41 =53.6303,U 41 =2.1452%, AC 41 :(41.6413,46.8877),(46.9519,42.1933);n 42 =2,A 42 =45.9182,U 42=1.8367%,AC 42 :(2.7751,26.3073), (47.1281,24.8596); n 43 =1,A 43 =46.5091,U 43 =1.8604%,AC 43 :(3.9938,10.3094);n 45 =1,A 45 =46.7326, U 45 =1.8693%,AC 45 :(32.8982,3.799);n 46 =1,A 46 =92.203, U 46 =3.6881%, AC 46 :(41.7566,9.0238);n 47 =7, A 47 =571.2711,U 47 =22.8508%,AC 47 :(5.2688,44.4236),(11.4486,25.0843),(12.2233,5.6193),(21.6482,29.7179),(23.0026,6.8576),(31.2663,13.2722),(32.7338,32.7326).

[0151] The feasible solution of the contour with a spacing of 2 is as follows Fig.13 (b) shows the total occupied area of ​​1244.5864, the total area of ​​the motherboard A = 2500, the space utilization rate of the motherboard U = 49.7835%, and the centroid position AC of the motherboard is (24.5074, 24.3488). The arrangement parameters of each component model are as follows:

[0152] n 24 =1,A 24 =37.6848, U 24 =1.5074%,AC 24 :(4.9545,25.9271);n 22 =1,A 22 =37.0729, U 22 =1.4829%,AC 22 :(41.273,45.6161);n 11 =2,A 11 =111.6498,U 11 =4.466%, AC 11:(5.3788,5.345),(15.2296,8.0626);n 12 =2,A 12 =73.9571,U 12 =2.9583%, AND 12 :(12.432,28.811),(24.6741,39.8853);n 15 =2,A 15 =91.1136,U 15 =3.6445%, AC 15 :(21.0403,31.5786),(43.9578,32.7523);n 17 =2,A 17 =143.9644,U 17 =5.7586%, AC 17 :(14.0327,39.6703),(43.4208,16.1322);n 37 =1,A 37 =78.3343,U 37 =3.1334%, AC 37 :(32.3405,16.0682);n 34 =1,A 34 =39.0024,U 34 =1.5601%, AND 34 :(31.1514,32.9619);n 33 =1,A 33 =40.8748,U 33 =1.635%, AC 33 :(26.3184,24.3136);n 32 =3,A 32 =78.5682,U 32 =3.1427%, AC 32 :(36.6856,38.5112),(45.6126,39.9829),(46.5373,25.168);n 31 =1,A 31 =25.5854,U 31 =1.0234%, AND 31 :(19.5168,46.2292);n 42 =2,A 42 =45.9346,U 42 =1.8374%, AC 42:(14.1078,20.9327), (44.6967,2.9651); n 43 =3, A 43 =139.5109,U 43 =5.5804%,AC 43 :(21.117,16.1987), (37.117,25.6987), (37.2457,6.7833); n 44 =2,A 44 =81.2724,U 44 =3.2509%,AC 44 :(5.0895,34.9485), (32.2183,45.1119);n 45 =1,A 45 =46.7304, U 45 =1.8692%,AC 45 :(4.8156,44.4164);n 46 =1,A 46 =92.2003,U 46 =3.688%, AC 46 :(26.1842,5.4107);n 47 =1,A 47 =81.7815,U 47 =3.2713%, AC 47 :(6.5707,16.3444).

[0153] Step 4: The three contour feasible solutions with the best optimization target values ​​in the current contour feasible solution set S are used as three search agents. Based on the three search agents, the solutions of other contour feasible solutions in the current contour feasible solution set S are updated to obtain an updated contour feasible solution set.

[0154] Step 4 is as follows:

[0155] Step 4.1: Take the three contour feasible solutions with the best optimization target values ​​in the current contour feasible solution set S as three search agents, and select a contour feasible solution other than the three search agents in the current contour feasible solution set S;

[0156] Step 4.2: Calculate the distance vector between the current contour feasible solution and the three search agents using the following formula:

[0157] D t = | C k ·X t - X |

[0158] Among them, X represents the position matrix of the feasible solution of the current contour, C k represents the kth distance adjustment factor, which is a random vector uniformly distributed in the range [0,2], k=1,2,3; D t is the distance vector between the feasible solution of the current contour and the tth search agent; X t is the position matrix of the t-th search agent, t=1,2,3; | | is the absolute value of each element of the matrix;

[0159] The details are as follows:

[0160] D α = | C1·X α - X |

[0161] D β = | C2·X β - X |

[0162] D γ = | C3·X γ - X |

[0163] Among them, X α , X β , X γ Represent the position vectors of the first, second and third search agents respectively, and the D α , D β , D γ is the distance vector between the current contour feasible solution and the first, second and third search agents.

[0164] Step 4.3: Based on the distance vectors between the current contour feasible solution and the three search agents, the three temporary position vectors corresponding to the current contour feasible solution are calculated using the following formula:

[0165] X k = | X t - A k ·D t |

[0166] A k = 2·a·r k - a

[0167] Among them, X k is the kth temporary position vector of the feasible solution of the current contour, A k is the kth position adjustment factor, which makes the first adjustment vector a decrease linearly from 2 to 0, and the second adjustment vector r i Uniformly distributed in the range [0,1], when A i When the value of is greater than 1, the new feasible solution will be far away from the search agent to prevent it from falling into the local optimal solution. iWhen it is less than 1, the feasible solution approximates the search agent to find the optimal solution in the neighboring area. The details are as follows:

[0168] The distance vector D between the feasible solution and the first, second and third search agents according to the current contour α , D β , D γ Calculate three new temporary position vectors X1, X2, X3:

[0169] X1= | X α – A1·D α |

[0170] X2= | X β – A2·D β |

[0171] X3= | X γ – A3·D γ |

[0172] Step 4.4: Add the three temporary position vectors of the current contour feasible solution and divide by 3 to obtain the new position vector X of the current contour feasible solution. new , and update the contour feasible solution set S; that is

[0173] X new = (X1+ X2+ X3) / 3

[0174] Step 4.5: Select the next contour feasible solution except the three search agents in the current contour feasible solution set S, repeat steps 4.2-4.4, calculate the corresponding new position vector, until all contour feasible solutions except the three search agents in the current contour feasible solution set S are traversed and processed to obtain the updated contour feasible solution set S.

[0175] Step 5: Repeat step 4 to iteratively optimize the contour feasible solution set until the three search agents no longer change, and obtain the final contour feasible solution set, which is the final stage of the three-dimensional component layout design that supports neighborhood reconstruction and solution evolution. The layout is performed according to the contour feasible solution with the best optimization target value in the final contour feasible solution set, that is, the polygonal contour arrangement order and contour vertex coordinates represented by the final solution are used to display the arrangement results of the components on the motherboard from a three-dimensional perspective.

[0176] Figure 8 (a) is the final layout design with a layout distance of 1. The total occupied area is 1623.913, the total area of ​​the motherboard is A=2500, the space utilization rate of the motherboard is U=64.9565%, and the centroid position AC of the motherboard is (24.517, 24.7316). The layout parameters of each component model are as follows:

[0177] n 26 =1,A 26 =80.387,U 26 =3.2155%, AC 26 :(14.7685,38.8091);n 25 =2,A 25 =87.3423,U 25 =3.4937%, AC 25 :(34.0552,39.3121),(44.625,3.4922);n 24 =1,A 24 =37.7387,U 24 =1.5095%, AND 24 :(46.4307,11.4763);n 23 =1,A 23 =44.7929,U 23 =1.7917%, AC 23 :(20.5882,46.1366);n 22 =2,A 22 =74.0555,U 22 =2.9622%, AC 22 :(26.3739,12.1461),(40.3929,15.2702);n 21 =1,A 21 =53.3468,U 21 =2.1339%, AC 21 :(36.9699,22.7443);n 11 =1,A 11 =55.7651,U 11 =2.2306%, AC 11 :(17.6812,29.4207);n 12 =2,A 12 =74.0742,U 12 =2.963%, AC 12 :(38.1112,31.5942),(46.3589,20.0624);n 13 =1,A 13 =50.6749,U 13 =2.027%, AC 13 :(20.6693,6.0397);n 14 =1,A 14 =39.4205,U 14 =1.5768%, AC14 :(28.8237,46.1709);n 16 =2,A 16 =168.055,U 16 =6.7222%, AC 16 :(5.5555,15.5834),(43.0866,41.0876);n 37 =1,A 37 =78.3002,U 37 =3.132%, AC 37 :(5.0698,44.5349);n 36 =1,A 36 =88.4156,U 36 =3.5366%, AC 36 :(35.1134,7.3922);n 34 =1,A 34 =39.0219,U 34 =1.5609%, AC 34 :(45.0876,27.3927);n 32 =2,A 32 =52.3507,U 32 =2.094%, AC 32 :(27.2552,3.202),(32.0665,29.5701);n 31 =1,A 31 =25.5615,U 31 =1.0225%, AND 31 :(3.4239,24.7273);n 41 =1,A 41 =26.8072,U 41 =1.0723%, AND 41 :(36.4465,47.0783);n 42 =3,A 42 =68.8869,U 42 =2.7555%, AC 42 :(2.8961,2.8456),(32.0149,16.4911),(47.0165,33.8878);n 44 =1,A 44 =40.5681,U 44 =1.6227%, AC 44 :(11.1326,23.7359);n 46 =3,A 46=275.9596, U 46 =11.0384%,AC 46 :(11.0546,5.9805), (17.0023,16.2988), (26.0212,23.1655) n 47 =2,A 47 =163.281,U 47 =6.5312%,AC 47 :(5.2688,33.4236),(25.658,36.3937);

[0178] Figure 8 (b) is the final three-dimensional spatial arrangement with a pattern distance of 1 and the goal of maximum space utilization. Fig. 9 This is a monotonically increasing graph of the evolution of space utilization with the maximum space utilization as the target when the spacing is 1. The maximum value is 66, the minimum value is 5.550000e+01, the sum is 59887.5000, the average value is 59.8875, the standard deviation is 1.5743, the variance is 2.4786, and the second-order central moment is 2.4761. Regarding the adjacent evolution difference, the maximum is 0. Regarding the absolute value of the slope, the maximum is 52.4309 and the minimum is 0.

[0179] Fig.14 (a) is the final layout design with a layout distance of 2 and the goal of maximum space utilization. The total occupied area is 1341.352, the total area of ​​the motherboard is A=2500, U=53.6541%, and AC is (24.907, 24.3148). The layout parameters of each component model are as follows:

[0180] n 26 =2,A 26 =160.9703,U 26 =6.4388%,AC 26 :(33.5153,43.2768), (36.4589,17.5831); n 25 =1,A 25 =43.6883, U 25 =1.7475%,AC 25 :(5.796,28.2232); n 23 =1,A 23 =44.6879, U 23 =1.7875%,AC 23 :(24.0232,36.5476);n 22 =1,A 22 =36.9925, U 22 =1.4797%,AC22 :(43.6345,45.536);n 21 =1,A 21 =53.2496,U 21 =2.13%, AND 21 :(24.7556,4.2112);n 11 =2,A 11 =111.6451,U 11 =4.4658%, AC 11 :(24.9612,19.3443),(45.9163,11.2368);n 14 =1,A 14 =39.2853,U 14 =1.5714%, AC 14 :(4.9407,36.7876);n 15 =1,A 15 =45.5964,U 15 =1.8239%, AC 15 :(22.9578,45.2523);n 16 =1,A 16 =84.0346,U 16 =3.3614%, AC 16 :(6.6369,5.6851);n 17 =1,A 17 =71.9495,U 17 =2.878%, AC 17 :(13.5947,41.6946);n 36 =1,A 36 =88.3595,U 36 =3.5344%, AC 36 :(42.9957,34.42);n 31 =1,A 31 =25.5854,U 31 =1.0234%, AND 31 :(29.0168,11.2292);n 41 =1,A 41 =26.8453,U 41 =1.0738%, AND 41 :(4.5705,45.4574);n 42 =1,A 42 =22.9731,U 42 =0.91892%, AND 42:(15.8673,20.515);n 43 =1,A 43 =46.5021,U 43 =1.8601%,AC 43 :(44.9882,23.2906);n 46 =3, A 46 =276.3402, U 46 =11.0536%,AC 46 :(6.8412,17.7198), (31.7722,28.9235), (36.7566,5.2738); n 47 =2,A 47 =163.2313,U 47 =6.5293%,AC 47 :(16.0397,30.092),(17.4769,11.2712);

[0181] Fig.14 (b) is the final three-dimensional spatial arrangement with a pattern distance of 2 and the goal of maximum space utilization. Fig.15 This is a monotonically increasing graph of the spatial utilization rate of the sample arrangement with a sample distance of 2 and the maximum spatial utilization rate as the target. The maximum value is 5.365408e-01, the minimum value is 4.533811e-01, the total is 497.2772, the average value is 0.4973, the standard deviation is 0.0126, the variance is 0.0002, and the second-order central moment is 0.0002. Regarding the adjacent evolution difference, the maximum is 0.0095. Regarding the absolute value of the slope, the maximum is 47.0936 and the minimum is 0.0106. Fig. 9 and Fig.15 It can be seen from the comparison that with the increase of the spacing between samples, the area utilization rate shows a monotonically decreasing trend.

[0182] Fig.16It is a comparison of the layout design of different targets under different layout distances of the present invention. As can be seen from the figure, when the layout distance increases, under different optimization targets, the ratio of the component area of ​​the final layout to the motherboard area will decrease accordingly. Among them, when the optimization is carried out with the minimum motherboard layout length as the target, the maximum area utilization rate under different layout distances is 63.4021%, the minimum is 26.8844%, the total is 252.7497%, the average is 42.1249%, the standard deviation is 13.5264%, the variance is 1.8296%, the second-order central moment is 1.5247%, the maximum gradient is 11.1382% (the first and the second); the minimum gradient is 4.4312% (the third and the fourth). When optimizing with the minimum space utilization as the goal, the maximum area utilization under different arrangement distances is 64.9565%, the minimum is 28.0290%, the total is 260.5075%, the average is 43.4179%, the standard deviation is 13.6888%, the variance is 1.8738%, and the second-order central moment is 1.5615%. The maximum gradient is 11.3024% (the first and second); the minimum gradient is 4.0667% (the fourth and fifth). By comparison, it can be seen that changing the arrangement frequency can improve the space utilization.

[0183] Under the circumstances of extremely complex method complexity and solution space, the overall plan of the conceptual design stage of modern manufacturing is obtained, the arrangement state of the final solution is displayed in three-dimensional space, and its effectiveness under actual manufacturing conditions is evaluated. The three-dimensional component arrangement layout can be fine-tuned according to indicators such as the accuracy capability of the actual manufacturing platform.

[0184] The above specific implementation modes are used to explain the present invention rather than to limit the present invention. Any modification and change made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A three-dimensional component layout design method supporting neighborhood reconstruction and scheme evolution, characterized in that: The following steps are involved: Step 1: According to the geometric feature information of the layout elements, several layout elements are pre-processed respectively to obtain the corresponding polygonal projection contours; Step 2: Perform an initial layout according to the polygonal projection contours of all layout elements to obtain a feasible solution of the contour under the initial layout; Step 3: Determine the layout optimization objectives and constraints according to different layout requirements. Based on the layout optimization objectives and constraints, perform random neighborhood transformation on the contour feasible solutions under the initial layout to obtain the contour feasible solution set S; Step 4: Take the K contour feasible solutions with the best optimization target value in the current contour feasible solution set S as K search agents, where K is an integer greater than 1. Based on the K search agents, update the solutions of other contour feasible solutions in the current contour feasible solution set S, and then obtain an updated contour feasible solution set; Step 5: Repeat step 4 to iteratively optimize the contour feasible solution set until the K search agents no longer change, and obtain the final contour feasible solution set. Perform layout according to the contour feasible solution with the best optimization target value in the final contour feasible solution set; The step 4 is specifically as follows: Step 4.1: Take the K contour feasible solutions with the best optimization target value in the current contour feasible solution set S as K search agents, and select a contour feasible solution other than the K search agents in the current contour feasible solution set S; Step 4.2: Calculate the distance vector between the current contour feasible solution and the K search agents using the following formula: D t = | C k ·X t - X | Among them, X represents the position matrix of the feasible solution of the current contour, C k represents the kth distance adjustment factor, k=1,…,K; D t is the distance vector between the feasible solution of the current contour and the tth search agent; X t is the position matrix of the t-th search agent, t=1,…,K; | | is the absolute value of each element of the matrix; Step 4.3: Based on the distance vector between the current contour feasible solution and the K search agents, calculate the K temporary position vectors corresponding to the current contour feasible solution using the following formula: X k = | X t - A k ·D t | A k = 2·a·r k - a Among them, X k is the kth temporary position vector of the feasible solution of the current contour, A k is the kth position adjustment factor; a is the first adjustment vector; r k is the second adjustment vector; Step 4.4: Add the K temporary position vectors of the current contour feasible solution and divide by K to obtain the new position vector of the current contour feasible solution, and update the contour feasible solution set S; Step 4.5: Select the next contour feasible solution other than the K search agents in the current contour feasible solution set S, repeat steps 4.2-4.4, calculate the corresponding new position vector, until all contour feasible solutions other than the K search agents in the current contour feasible solution set S are traversed and processed to obtain an updated contour feasible solution set S.

2. A three-dimensional component layout design method supporting neighborhood reconstruction and scheme evolution according to claim 1, characterized in that: In the step 1, each arrangement element is preprocessed to obtain a corresponding polygonal projection profile, which specifically includes the following steps: Step 11: After performing principal component analysis on the geometric feature information of each sample to be arranged, a component feature matrix is ​​obtained; then three eigenvectors are calculated based on the component feature matrix, which are recorded as the first eigenvector, the second eigenvector and the third eigenvector in order; Step 12: Rotate the current layout element so that the first eigenvector of the current layout element is parallel to the z-axis direction; Step 13: Rotate the three-dimensional element rotated in step 12 again around the second eigenvector so that the fit degree of the xOy plane of the current three-dimensional element is the highest, and record the construction direction at this time as the optimal construction direction; Step 14: Project the current three-dimensional component in the optimal construction direction to the xOy plane and extract its projection contour, while reducing the number of contour vertices to a preset contour point number A to obtain the polygonal projection contour of the current layout component in the optimal construction direction in the xOy plane.

3. A three-dimensional component layout design method supporting neighborhood reconstruction and scheme evolution according to claim 1, characterized in that: The step 2 is specifically as follows: According to the width of the layout master, a layout order of layout elements is generated and the layout distance between the polygonal contours of two adjacent layout elements is set. Starting from the origin of the layout master, the polygonal contours of all layout elements are arranged in sequence, and the contour feasible solution is composed of the coordinates of the polygonal projection contour points corresponding to each layout element in the current layout order.

4. A three-dimensional component layout design method supporting neighborhood reconstruction and scheme evolution according to claim 1, characterized in that: In step 3, the layout optimization goal is to keep the number of components to be arranged unchanged and to minimize the layout length of the master.

5. The three-dimensional component layout design method supporting neighborhood reconstruction and scheme evolution according to claim 1, characterized in that: In step 3, the goal of layout optimization is to make the number of components to be arranged variable, with the goal of maximizing space utilization.

6. A three-dimensional component layout design method supporting neighborhood reconstruction and scheme evolution according to claim 1, characterized in that: In step 3, the constraint conditions are specifically that the polygonal projection outlines of different layout elements do not overlap each other and the polygonal projection outlines of all layout elements cannot exceed the layout master.

7. A three-dimensional component layout design method supporting neighborhood reconstruction and scheme evolution according to claim 4, characterized in that: In step 3, the random neighborhood transformation includes exchanging the neighborhood, reversing the neighborhood, and rotating the neighborhood.

8. A three-dimensional component layout design method supporting neighborhood reconstruction and scheme evolution according to claim 5, characterized in that: In step 3, the random neighborhood transformation includes operations of exchanging neighborhoods, reversing neighborhoods, rotating neighborhoods, and inserting and deleting neighborhoods.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the three-dimensional component layout design method supporting neighborhood reconstruction and scheme evolution as described in any one of claims 1 to 8 are implemented.

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