Method for designing three-dimensional space nestable layout scheme based on hybrid element heuristic evolution

Abstract

This invention discloses a method for designing nested layout schemes in 3D space based on hybrid meta-heuristic evolution. The method includes the following steps: First, constructing an enclosing structure that completely encompasses the 3D space container, setting a safe distance for interference prevention of 3D components, and generating an initial 3D nesting conceptual design layout; next, constructing a set of meta-heuristic operator strategies, generating a group of meta-heuristic operators using the Markov chain Monte Carlo algorithm, and mixing four types of meta-heuristic operators; during the evolution process, solving for a better group of meta-heuristic operators, and using it to update the current 3D prototype layout scheme to obtain a 3D layout based on hybrid meta-heuristic evolution. The method disclosed in this invention can solve the layout problem in irregular 3D space, and also supports nested layouts of 3D components, making full use of the available space inside the components, overcoming the difficulty of existing methods in handling the arrangement of island-shaped containers or components, and significantly improving the utilization rate and layout efficiency of 3D space.

Description

Technical Field

[0001] This invention relates to a three-dimensional component layout design method, and more particularly to a three-dimensional spatial nestable layout scheme design method based on hybrid element heuristic evolution. Background Technology

[0002] Layout design, which can be understood as the process of generating and visualizing layout schemes, involves proposing systematic, innovative, feasible, and phased solutions based on overall requirements analysis and technical feasibility. It forms the foundation for subsequent detailed design and has significant applications in industrial fields such as smart factories, additive manufacturing, micro / nano manufacturing, stereolithography, atomic manufacturing, aerospace, warehousing and logistics, and conceptual design. Spatial nesting layouts within complex geometrically irregular regions exhibit high computational complexity. This involves both assembling or placing components within interference-free safety distance constraints and overcoming multiple contradictions between space utilization, assembly efficiency, and computational speed. Against this backdrop, using hybrid heuristic evolutionary methods to solve the problem of nestable 3D component layouts in irregular spatial regions has become an important technological approach. Existing literature explores this topic from multiple perspectives.

[0003] Firstly, the optimization and scheduling of manufacturing planning and nesting algorithms, as the core of the 3D component layout problem, have received widespread attention. Bennell et al. from the University of Leeds, UK, explored the problem of irregular shape cutting and loading, which is widely used in industries such as clothing manufacturing, metal cutting, and furniture making (Bennell JA, Oliveira J F. The geometry ofnesting problems: A tutorial[J]. European journal of operational research,2008, 184(2): 397-415.). US Patent (Sadovnik I. Method and systems for nestingobjects: US Patent 6,980,934[P]. 2005-12-27.) proposes a method for arranging two-dimensional and three-dimensional objects, which improves utilization by minimizing the gaps between objects. It combines topological analysis and numerical iteration to achieve heuristic layout optimization that reduces computation time. However, it has certain limitations when dealing with highly irregular shapes or complex multi-object scenes, making nesting difficult to sustain. US Patent (Horn J. System and method to solve shape nesting problems: US Patent 7,181,702[P]. 2007-2-20.) proposes a genetic algorithm method based on resource-defined fitness sharing for solving simple shape nesting problems.

[0004] The Boltzmann distribution-driven metaheuristic mechanism, as a search-driven controller for hybrid heuristic algorithms, is a preferred option due to its inherent characteristics. On the one hand, this mechanism achieves a dynamic balance between global and local search, while also being able to combine and adjust other heuristic methods, exhibiting robustness and flexibility. On the other hand, the stochastic optimization paradigm based on thermodynamic principles, with its few parameters, simple structure, and lightweight algorithm, possesses both global exploration and local refinement optimization capabilities, making it suitable as a search control driver in hyperheuristic algorithms for searching and optimizing the performance of metaheuristic policy sets, thus providing a search engine for hyperheuristic methods.

[0005] The application scenarios for 3D component layout optimization are constantly expanding, including smart manufacturing, additive manufacturing, and high-flow-rate fluid pressurization simulation and efficiency-enhancing design. In production scheduling and layout problems, achieving simultaneous optimization of production efficiency and space utilization, the partitioning and parallelization algorithms for irregular regions (non-rectangular regions) have become bottleneck challenges. A hybrid heuristic evolutionary approach to address the nesting problem of 3D components in irregular regions not only provides a theoretically widely adaptable optimization framework but also has applications in practical smart manufacturing, warehousing and logistics, and conceptual design. This research path, based on the combination of intelligent optimization and industrial applications, is providing efficient and feasible solutions to complex layout problems in the manufacturing field. Summary of the Invention

[0006] To address the problems existing in the background technology and improve the layout efficiency and adaptability in the nesting process of irregular 3D components, thereby further enhancing production efficiency, this invention proposes a 3D spatial nestable layout scheme design method based on hybrid element heuristic evolution. This invention employs a thermodynamic Markov chain Monte Carlo hybrid heuristic evolutionary algorithm to achieve nested layout of irregular objects in 3D space.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] I. A design method for nestable layout schemes in 3D space based on hybrid element-inspired evolution

[0009] Step 1: Generate the initial 3D nesting layout of the 3D component set to be nested in the 3D target space;

[0010] Step 2: Construct a set of metaheuristic operator strategies;

[0011] Step 3: Based on the current 3D nesting layout, use the Markov chain Monte Carlo algorithm to select and generate a set of metaheuristic operators from the set of metaheuristic operator strategies. Solve for the optimal set of metaheuristic operators during the optimization process to obtain the optimal set of metaheuristic operators. Then, use the optimal set of metaheuristic operators to optimize the current 3D nesting layout to obtain the optimized 3D nesting layout.

[0012] In step 1, the data structure of each 3D component to be arranged in the set of 3D components to be arranged includes a global nested compatibility matrix M=[m ij ] n×n m ij This indicates the degree of nesting compatibility between the three-dimensional component i and the three-dimensional component j to be nested, and n represents the number of three-dimensional components to be nested.

[0013] Step 1 specifically involves:

[0014] First, an adaptive spatial decomposition strategy is used to discretize and model the three-dimensional target space to generate an enclosing volume structure that completely encloses the three-dimensional space. The safe distances between the three-dimensional components to be arranged are set in the XOY plane and the Z direction, and the three-dimensional components to be arranged in the set are sorted. The three-dimensional components to be arranged are added to the enclosing volume structure that completely encloses the three-dimensional space in order to generate the initial three-dimensional layout.

[0015] The three-dimensional components to be sampled are arranged in descending order according to their corresponding evaluation values. The calculation formula for the evaluation value of each three-dimensional component to be sampled is as follows:

[0016] f(c i )=w1×V i +w2×A i +w3×p i

[0017] Where, f(c i ) is a three-dimensional component c i The evaluation value, V i For 3D component c i The volume of A i For 3D component c i Surface area, p i For 3D component c i The nesting priority is defined by w1, w2, and w3, which are three weight coefficients.

[0018] In the process of adding each three-dimensional component to be arranged sequentially into the containment structure that completely encloses the three-dimensional space, each three-dimensional component to be arranged is added at the lowest feasible position that satisfies the interference constraints.

[0019] In step 2, the metaheuristic operators in the metaheuristic operator strategy set include spatial transformation operators, nested optimization operators, local optimization operators, and global search operators.

[0020] II. A 3D spatial nestable layout design system based on hybrid element-inspired evolution

[0021] The initial layout generation unit is used to generate an initial three-dimensional layout of the three-dimensional component set to be laid out in the three-dimensional target space.

[0022] Operator set construction unit, used to construct metaheuristic operator strategy sets;

[0023] The operator set solving unit is used to select and generate a metaheuristic operator set from the metaheuristic operator strategy set based on the current 3D nesting layout using the Markov chain Monte Carlo algorithm. During the optimization process, the optimal metaheuristic operator set is solved to obtain the optimal metaheuristic operator set.

[0024] The layout optimization unit is used to optimize the current 3D nesting layout by using the optimal set of metaheuristic operators to obtain an optimized 3D nesting layout.

[0025] III. A computer device

[0026] The device includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the design method for a three-dimensional spatial nestable layout scheme based on hybrid element-inspired evolution.

[0027] IV. A computer-readable storage medium

[0028] The medium stores a computer program, which, when executed by a processor, implements the steps of the design method for a three-dimensional spatial nestable layout scheme based on hybrid element-inspired evolution.

[0029] V. A computer program product

[0030] The product includes a computer program / instruction that, when executed by a processor, implements the steps of the design method for a three-dimensional spatial nestable layout scheme based on hybrid element-inspired evolution.

[0031] The beneficial effects of this invention are:

[0032] This invention constructs a hybrid heuristic evolutionary framework based on controlled parameterized Markov chain Monte Carlo, where both the containment structure and the components to be laid out can be irregular in shape (non-rectangular), thus achieving an efficient solution to the layout problem of irregular nestable 3D components.

[0033] The method of this invention can adaptively handle the multidimensional nested layout problem of "large wrapping small" of three-dimensional components of different shapes and sizes in complex and irregular regions by dynamically adjusting the combination of metaheuristic operators. It supports the mutual nesting between three-dimensional components and significantly improves the global search capability and local convergence performance of the algorithm.

[0034] Compared with traditional layout methods, this invention effectively solves the design problem of layout schemes in irregular three-dimensional spatial containers, overcomes the problem that existing methods cannot handle the array of complex island-shaped containers or components, and has significant improvements in space utilization, computational efficiency and layout stability. It significantly improves the utilization of three-dimensional space and layout efficiency, and is particularly suitable for the optimized layout design of complex three-dimensional components in industrial fields such as aerospace, automotive manufacturing, and 3D printing. Attached Figure Description

[0035] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting engineering examples with reference to the accompanying drawings:

[0036] Figure 1 This is a flowchart of the method of the present invention.

[0037] Figure 2 The diagram shows the original voxelized structure of the irregular space to be sorted, where (a) is the voxelized sorting matrix at a grid resolution of 100×100×100, and (b) is the voxelized sorting matrix at a grid resolution of 300×300×300.

[0038] Figure 3 This is a schematic diagram of the model of the first set of three-dimensional components to be arranged in this invention.

[0039] Figure 4 These are the initial and final designs for the 0.5-meter height irregular three-dimensional layout of two types of UAV blades, with a safe arrangement distance of 1.5mm in the xOy plane. (a) is the initial design for the 0.5-meter height irregular three-dimensional layout of two types of UAV blades, with a safe arrangement distance of 1.5mm in the xOy plane; (b) is the final design for the 0.5-meter height irregular three-dimensional layout of two types of UAV blades, with a safe arrangement distance of 1.5mm in the xOy plane.

[0040] Figure 5 This is a three-dimensional layout design for irregular cavities at heights of 0.2, 0.5, and 0.7 for two types of UAV blades, with a safe layout distance of 1.5mm in the xOy plane.

[0041] Figure 6 These are the initial and final designs for the 0.5-height irregular three-dimensional layout of two types of UAV blades with a safe arrangement distance of 2mm in the xOy plane. (a) is the initial design for the 0.5-height irregular three-dimensional layout of two types of UAV blades with a safe arrangement distance of 2mm in the xOy plane; (b) is the final design for the 0.5-height irregular three-dimensional layout of two types of UAV blades with a safe arrangement distance of 2mm in the xOy plane.

[0042] Figure 7 This is a three-dimensional layout design for irregular cavities at heights of 0.2, 0.5, and 0.7 for two types of UAV blades, with a safe layout distance of 2mm in the xOy plane.

[0043] Figure 8 This is a schematic diagram of the model of the second group of three-dimensional components to be arranged in this invention.

[0044] Figure 9These are the initial and final designs for a nested three-dimensional layout of various aerodynamic components with a safe arrangement distance of 2mm in the xOy plane; where (a) is the initial design for a nested irregular three-dimensional layout of various aerodynamic components with a safe arrangement distance of 2mm in the xOy plane; and (b) is the final design for a nested irregular three-dimensional layout of various aerodynamic components with a safe arrangement distance of 2mm in the xOy plane.

[0045] Figure 10 These are the initial and final designs for the irregular three-dimensional layout of various aerodynamic components in the xOy plane with a safe arrangement distance of 1.5mm. Among them, (a) is the initial design for the nestable irregular three-dimensional layout of various aerodynamic components in the xOy plane with a safe arrangement distance of 1.5mm; (b) is the final design for the nestable irregular three-dimensional layout of various aerodynamic components in the xOy plane with a safe arrangement distance of 1.5mm.

[0046] Figure 11 This is a three-dimensional layout design for the arrangement of various aerodynamic components in irregular cavities at heights of 0.2, 0.5, and 0.7, with a safe arrangement distance of 1.5mm in the xOy plane.

[0047] Figure 12 These are the initial and final designs for the irregular three-dimensional layout of various aerodynamic components in the xOy plane with a safe arrangement distance of 2mm. (a) is the initial design for the nestable irregular three-dimensional layout of various aerodynamic components in the xOy plane with a safe arrangement distance of 2mm; (b) is the final design for the nestable irregular three-dimensional layout of various aerodynamic components in the xOy plane with a safe arrangement distance of 2mm.

[0048] Figure 13 This is a three-dimensional layout design for the arrangement of various aerodynamic components in irregular cavities at heights of 0.2, 0.5, and 0.7, with a safe arrangement distance of 2mm in the xOy plane.

[0049] Figure 14 This is a comparison of the space utilization effect before and after optimization of the three-dimensional space nestable layout design method based on hybrid element-inspired evolution under different layout cases. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to the accompanying drawings and examples.

[0051] like Figure 1 As shown, the design method for a nestable layout scheme in three-dimensional space based on hybrid element-inspired evolution proposed in this invention specifically includes the following steps:

[0052] Step 1: Generate the initial 3D nesting layout of the 3D component set to be nested in the 3D target space;

[0053] For each 3D component c i ∈C, its data structure includes geometric synthetic features D i ={G i ,P i N i ,S i O i} and the global nested compatibility matrix M=[m ij ] n×n The geometric synthetic features satisfy D i ={G i ,P i N i ,S i O i}, where the geometric information structure G i ={V i ,F i E i ,BB i CH i} contains vertex set V i ={v1,...,v j ,...,v ni} (v j ∈R 3 (j=1,…,ni, where ni represents the total number of vertices of the i-th 3D component), face set F i ={f1,...,f k ,...,f mi} (each face f) k Defined by the vertex index triple, k=1,…,mi, where mi represents the total number of faces of the i-th 3D component), E i For edge set, axis-aligned bounding box BB i ={(p min ,p max )} and convex hull CH i ={V CH ,F CH}, p min ,p max These are the minimum and maximum vertex coordinates, respectively. A minimum axis-aligned cuboid containing the entire geometry is defined, V. CH ,F CH Let P be the vertex set and face set of the convex hull, respectively, representing the minimal convex polyhedron containing the original geometry; physical property structure P i ={c i ,I i A i ,m i ,ρi (x)} stores the centroid location c i V i Let be the volume of the i-th 3D component, and be the inertia matrix. I pq Let A be the product of inertia about the p-axis and q-axis. When p = q, A is the moment of inertia; when p ≠ q, A is the product of inertia. p, q = x, y, z. The principal axis matrix is ​​A. i =[a1,a2,a3] (through I) i (Obtained through eigenvalue decomposition), a1, a2, a3 are unit eigenvectors along the three principal inertial axes, m i For mass, ρ i (x) represents the density distribution; nested feature structure N i ={R i H i ,K i} Contains a set of concave regions R i ={r1,...,r j ,...,r ki} (Each recessed region r j ={V r depth r ,n r The region vertex V r The set of vertices of the concave region, depth r The maximum depth of the depression region is given by the normal n. r Let j = 1, ..., ki, where ki represents the average normal vector of the concave region (where j = 1, ..., ki, and ki represents the total number of concave regions of the i-th component), and let H be the set of cavity structures. i ={h1,...,h j ,...,h li} (each cavity h) j ={V h volume h ,entry h}Includes cavity volume and inlet information, V h For the set of boundary vertices of the cavity, volume h The volume of the cavity, entry h (geometric information of the cavity inlet), surface curvature field K i :S i →R 2 (Gaussian curvature and mean curvature, K) i S is a function that maps each point on the surface of the i-th 3D component to a two-dimensional vector of its Gaussian curvature and mean curvature. i (where i is the surface manifold of the i-th 3D component).

[0054] Global nested compatibility matrix M=[m ij] n×n m ij ∈[0,1] is used to quantify the nesting compatibility between the three-dimensional component i and the three-dimensional component j to be laid out, and n represents the number of three-dimensional components to be laid out. m ij =0 indicates that the components are completely incompatible (e.g., two convex components or material conflicts); m ij ∈(0,0.3] indicates low compatibility; nesting is detrimental to layout design; m ij ∈(0.3,0.7] indicates moderate compatibility, allowing for effective nesting; m ij ∈(0.7,1) indicates high compatibility, with highly complementary component shapes; m ij =1 indicates perfect compatibility, achieving the theoretically optimal space utilization. M is an asymmetric matrix, i.e., m ij ≠m ji This data structure reflects the directional characteristics of nested relationships. It enables efficient querying through hash tables or octree indexes, supports interference detection with a time complexity of O(logn) and attribute access with O(1), and provides complete geometric and physical information support for subsequent sorting algorithms.

[0055] Step 1 is as follows:

[0056] First, an adaptive spatial decomposition strategy is used to discretize and model the three-dimensional target space, generating an enclosing volume structure O∈{0,1}^(n) that completely encloses the three-dimensional space. x ×n y ×n z ), ^ represents exponentiation, n x n y n z The dimensions in the X, Y, and Z directions are represented, i.e., an octree is used to represent the 3D target space in three dimensions; a safe layout distance is set for the 3D components to be laid out in the XOY plane and the Z direction; the 3D components to be laid out are sorted according to their evaluation values ​​in the set of 3D components to be laid out; and each 3D component to be laid out is added to the containing volume structure that completely encloses the 3D space in sequence using a 3D bottom-left-back approach, generating an initial 3D layout L0={(p i ,R i ,Φ i |i=1,...,n},Φ i It is a nested set of relationships.

[0057] The 3D components to be laid out are arranged in descending order according to their corresponding evaluation values. The formula for calculating the evaluation value of each 3D component to be laid out is as follows:

[0058] f(c i )=w1×V i +w2×A i +w3×pi

[0059] Among them, f(c i ) is the evaluation value of the three-dimensional component c i , V i is the volume of the three-dimensional component c i , A i is the surface area of the three-dimensional component c i , p i is the nesting priority of the three-dimensional component c i . The nesting priority p i ∈ [0, 1] quantifies the processing priority degree p of the three-dimensional component i in the nesting layout i > 0.5 indicates that the component has a positive priority and is suitable to be added as the accommodating party first (such as a component with a cavity or hole); p i = 0.5 indicates a neutral priority and can be arranged flexibly; p i < 0.5 indicates a negative priority and is suitable to be filled later as the nested party (such as a small solid component). w1, w2, and w3 are three weight coefficients respectively.

[0060] During the process of adding each three-dimensional component to be arranged in order to the enclosure structure that completely envelopes the three-dimensional space, each three-dimensional component to be arranged is added at the lowest feasible position p i ’. The interference constraint is specifically Ψ(c i , c j ) = 0, j < i, Ψ(c i , c j ) = 0, j < i means that the current component c i has no interference or overlap with all the added components c j (j < i). The lowest feasible position satisfies p i ’ = argmin p {z|(p, R i ) ∈ F}, p i ’ represents the optimal addition position of component i, p represents the three-dimensional coordinate vector of the candidate addition position, R i represents the rotation matrix of component i, and F represents the set of all feasible addition schemes that satisfy the interference constraint.

[0061] Step 2: Construct a set of metaheuristic operator strategies;

[0062] In a feasible implementation, the metaheuristic operators in the set of metaheuristic operator strategies include the space transformation operator H S = {h S (1) , h S (2)Nested optimization operator H N ={h N (1) ,h N (2) ,h N (3)}, Local optimization operator H L ={h L (1) ,h L (2)}, global search operator H G ={h G (1) ,h G (2) ,h G (3) In the process of generating metaheuristic operator sets, by setting fixed or constrained combination rules, adjusting the operator sequence length, or assigning different weights to operators, the strategy set can exhibit diverse spatial distribution patterns to adapt to the complex nested layout requirements of irregular 3D components in a limited space.

[0063] In one feasible implementation, the metaheuristic operator policy set is defined as H = H S ∪H N ∪H L ∪H G .

[0064] In one feasible implementation, the spatial transformation operator set H S Includes three-dimensional rotation operator h S (1) (p i ,R)=R×p i +c i , where p i ∈R 3 For 3D components The current position coordinates, R=R x (α)×R y (β)×R z (γ) is the product of matrices after rotations about the X, Y, and Z axes, R x (α),R y (β),R z (γ) are the rotation matrices for rotating about the x-axis by an angle α, about the y-axis by an angle β, and about the z-axis by an angle γ, respectively. i The operator, which rotates the component from its current pose to a new pose, is the centroid of the 3D component i; the 3D translation operator h... S (2) (p i ,△p)=p i +△p, where △p=(△x,△y,△z)∈R3 As a translation vector, this operator moves the component a specified distance in three-dimensional space.

[0065] In one feasible implementation, the nested optimization operator set H N Includes nested safe distance adjustment operator h N (1) (d ij ,δ)=min(d ij +δ,d ij,max ), where d ij ∈R + Let δ∈R be the current nesting safety distance for embedding component i into component j, and d be the nesting safety distance adjustment amount. ij,max This operator adjusts the nesting safety distance relationship between two components to a predefined maximum allowed nesting safety distance. Nesting direction search operator h N (2) (n ij C j )=argmax <n,▽V j >, n∈R Nj , where n ij ∈S 2 C is the unit vector of the current nested direction. j Let Nj be the set of recessed regions of component j, and Nj be the set of feasible nested directions, ▽V j Let h be the volume gradient of component j. This operator seeks the optimal nesting direction to maximize space utilization. Cavity filling operator h N (3) (V j C j )=1(V i C j ), where V i Let C be the three-dimensional volume domain of component i. j Let i be the cavity region of component j, and 1() be an indicator function. This operator determines and executes whether component i can be completely filled into the cavity of component j.

[0066] In one feasible implementation, the local optimization operator set H L Includes gravity settlement operator h L (1) (p i ,g')=p i +∫0 t g'×1 collision-free dt, where p i For the component position, g'=(0,0,-g) T Let g be the gravitational acceleration vector (g is the gravitational constant), T denote the transpose operation, and t be the settling time. collision-freeAs the interferometric detection indicator function, this operator simulates gravity causing the component to sink naturally until interference occurs; the vibration-adhering operator h... L (2) (X,A)= X+A×sin(wt)×e rand Where X = {p1,...,p} n} represents the set of all component positions, A>0 represents the vibration amplitude, w represents the vibration frequency, and e rand ∈S 2 Given a random unit direction vector, this operator uses random vibrations to rearrange components to achieve a tighter layout while maintaining a safe nesting distance.

[0067] In one feasible implementation, the global search operator set H G Includes component exchange operator h G (1) (π,i,j)=(π1,...,π j ,..,π i ,...,π n ), where π = (π1, ..., π) n ) represents the component arrangement sequence, π i This indicates that the i-th component is... To swap position indices, this operator exchanges the positions of two components in the sequence to explore different stacking orders; the sequence rearrangement operator h G (2) (π,f)=sort(π,f), where π is the current permutation sequence, f:C→R is the second evaluation function (sorting by volume), which reorders the entire sequence according to a specific criterion; grouping nested operator h G (3) (C,M)=(G1,G2,..,G i ,...,G k ),in For the set of all components, θ∈(0,1) is the compatibility threshold, G i ={c j ∈C:m ij >θ} represents the i-th nested group. This operator clusters mutually nestable components to achieve batch nesting optimization.

[0068] Step 3: Based on the current 3D nesting layout, use the Markov chain Monte Carlo algorithm to select and generate a set of metaheuristic operators from the metaheuristic operator strategy set. During the optimization process, solve for the optimal set of metaheuristic operators to obtain the optimal set. Then, use the optimal set of metaheuristic operators to optimize the current 3D nesting layout to obtain the optimized 3D nesting layout. Output the optimized 3D nesting layout and use it as a basis for the layout design and manufacturing of the 3D component set to be nested.

[0069] Step 3 specifically involves:

[0070] Step 3.1: Initialize the relevant parameters of the Markov chain Monte Carlo algorithm, including initial control parameters, minimum threshold control parameters, cooling rate, maximum number of steps in the isothermal process, target search space for 3D component layout, layout optimization objective function, and the maximum number of modules allowed by the metaheuristic structure; among them, the initial control parameter ξ0 is used to control the search range in the early stage of the algorithm; the minimum threshold control parameter ξ min As the algorithm termination condition; the proportional cooling rate δ∈(0,1) is used to control the rate of decrease of the control parameter; the current maximum number of steps S of the isothermal process. max Used to limit the local search depth; target search space Ξ R D Define the layable area of ​​the 3D component; objective function Used to evaluate the space utilization of 3D component layout schemes Inter-component interference and stability , where w u w i w s There are three weighting coefficients; metaheuristic MH κ As a solution operator, a layout scheme is generated by combining κ heuristic rules. Its performance is determined by the objective function F(MH). κ |Ξ)=f(MH κ (Ξ)) is evaluated; the maximum number of modules allowed within the metaheuristic structure κ max The ≥1 constraint limits the complexity of operator combinations.

[0071] Step 3.2: Randomly select heuristic operators from the metaheuristic operator strategy set and record them as the initial heuristic operator group. Then, conduct a preliminary evaluation of their performance on the 3D component layout problem. That is, use the initial heuristic operator group to optimize the initial 3D nesting layout, obtain the optimized 3D nesting layout, and generate the objective function value corresponding to the optimized layout.

[0072] In one feasible implementation, the initial heuristic operator set MH κ The construction method is as follows:

[0073] Heuristic rules are randomly selected from the metaheuristic operator policy set H to construct an initial heuristic operator group, where the number of modules κ can be in [1, κ]. max Random initialization within the range or set according to the problem size; at the same time, set the initial number of steps s=0, control parameter ξ=ξ0, and initialize the current solution as the current optimal solution.

[0074] Step 3.3: When the control parameters meet the threshold condition and the number of iterations does not exceed the upper limit, obtain the neighborhood solution by perturbing the current metaheuristic combination, construct a new set of heuristic operators and use it for 3D component layout optimization;

[0075] In one feasible implementation, the generation of neighborhood solutions is specifically designed for the 3D component layout problem: a new heuristic operator group MH is formed by adding new operator modules (such as rotation operators, translation operators, nesting depth adjustment operators), deleting redundant operators, or replacing existing operators in the current heuristic operator group. κ C This allows it to explore different arrangements and nesting strategies for 3D components.

[0076] Step 3.4: Evaluate the performance of the new heuristic operator set on 3D component layout, calculate the difference in the objective function before and after optimization, and determine whether to accept the new metaheuristic combination based on the acceptance probability criterion based on control parameters; in one feasible implementation, the acceptance probability function is constructed based on the Metropolis-Hastings algorithm framework as follows:

[0077] P(ΔE,ξ)=exp(-ΔE / κξ)

[0078] Where, ΔE=F(MH) κ C |Ξ)-F(MH κ |Ξ) represents the difference in the objective function between the old and new layout schemes, ξ is the current temperature control parameter, and k is the Boltzmann constant. The specific acceptance mechanism is as follows: Generate uniformly distributed random numbers u r ∈[0,1], if u r If ≤ P(ΔE,ξ), then accept the new solution MH. κ C Otherwise, retain the original solution MH. κ When ΔE < 0 (the new solution is better), P(ΔE,ξ) > 1, and it must be accepted; when ΔE > 0 (the new solution is worse), it is still accepted with probability P(ΔE,ξ), and this probability decreases as the temperature ξ decreases, ensuring that the algorithm can escape the local optimum layout scheme in the high temperature stage.

[0079] Step 3.5: Update the control parameters according to the preset cooling rate. If the layout effect of the new combination is better, update the optimal solution and reset the counter; otherwise, increase the iteration step count.

[0080] In one feasible implementation, the control parameter update follows the cooling law of ξ←ξ(1-δ), and dynamic control is achieved by introducing a control parameter scheduling function T(t); when a better three-dimensional component layout scheme is found, i.e., F(MH) κ C |Ξ) <F(MHκ |Ξ), update the current optimal solution MH κ * ←MH κ C And reset the step count s=0; this process ensures the stationary distribution π of the system. T(x) ∝e^(-f(x) / ξ) gradually converges to the globally optimal layout scheme.

[0081] Step 3.6: Repeat steps 3.2 to 3.5 until the control parameters are reduced to the minimum threshold or the number of iterations reaches the upper limit. Output the optimal metaheuristic combination scheme, which is applied to the final layout design of nestable 3D components in 3D space. That is, through operations such as rotation, translation, and nesting depth adjustment, the layout of 3D components in irregular regions is maximized under the premise of no interference between components and stability constraints. This process satisfies the detailed equilibrium condition π(x)P(x→y)=π(y)P(y→x), which ensures the ergodicity and asymptotic convergence of the Markov chain.

[0082] The parameterized Markov Chain Monte Carlo (MCMC) optimization strategy originates from the principle of thermal equilibrium in statistical physics, and its mathematical foundation is built upon the Metropolis-Hastings algorithm framework. The core of this strategy lies in constructing a time-varying acceptance probability function P(ΔE,ξ)=e^(-ΔE / kξ), where ΔE represents the change in the objective function, ξ is the control parameter, and k is the Boltzmann constant. Mathematically, this optimization strategy essentially constructs a non-homogeneous Markov chain in the solution space, whose stationary distribution dynamically evolves with the control parameter, i.e., π... T(x) ∝e^(-f(x) / ξ), which eventually converges to the Dirac measure δ in the set of global optima of the objective function. x’ This invention provides a theoretically guaranteed probabilistic convergence framework for complex optimization problems. It fully leverages the flexibility of a probabilistic optimization paradigm based on thermodynamic principles as a search controller, not only efficiently exploring and optimizing combinations of metaheuristic operators in the policy set but also enhancing adaptability to different optimization problems, thereby significantly improving the performance optimization effect of metaheuristic algorithms.

[0083] The voxelized fully enveloping three-dimensional spatial container containing the structure described in this invention example is as follows: Figure 2 As shown. For a given three-dimensional irregularly shaped layout space Ω, a uniform voxel mesh W is established within the space. G The grid resolution is (n x ,n y ,n z This generates a binary voxelized matrix. ,in Indicates the point from the voxel center p ijk Along direction The number of intersections between the emitted ray and the mesh boundary, V ijk =1 indicates that the voxel (i,j,k) is located inside the packing space, V ijk =0 indicates that it is located outside, and mod indicates the remainder operation after integer division. The voxelized nesting space Ω voxel ={(x i ,y j ,z k )∈W G |V ijk =1} represents all conditions that satisfy V. ijk The coordinates of the voxel center point p = 1 ijk =(x i ,y j ,z k The set, i.e., the coordinates of all voxel points located within the nesting space, constitutes the discretized available nesting space. This voxelization supports space occupancy queries with O(1) time complexity and O(n) time complexity. x ×n y ×n z The storage of spatial complexity provides a discretized spatial representation basis for subsequent optimization of 3D component nesting. Taking the internal spatial layout of an irregular 3D vortex shell as an example, the design process of a nestable layout scheme is illustrated. The shell structure has a volume of 9230046.22 mm³ and a surface area of ​​588457.20 mm². Figure 2 (a) and Figure 2 (b) are respectively (n x =100,n y =100,n z =100) and (n x =300,n y =300,n z =300) Voxelized nesting matrix at grid resolution. In this invention, the height of the three-dimensional irregular nesting space Ω is denoted as 1, and the heights of 0.2, 0.5, and 0.7 are proportional heights corresponding to 1. For example, if the actual height is 40mm, then the height of 0.2 is 8mm, the height of 0.5 is 20mm, and the height of 0.7 is 35mm.

[0084] A schematic diagram of the model of the first set of three-dimensional components to be sorted in this invention is shown below. Figure 3 As shown, the models are UAV V1 dual-blade propeller prototype 1 and UAV V2 dual-blade propeller prototype 2, respectively.

[0085] The safe layout distance in the xOy plane is D. s xoy =1.5mm, Z-direction safe spacing distance Ds Z At a height of 20mm, the initial design schemes for the 3D layout of the blades of two UAV models with an irregular spatial shape at a height of 0.5m are as follows: Figure 4 As shown in (a), the total area occupied by the layout parts is A. total =298.631mm 2 The total area of ​​the container is A. template =1295.3421mm 2 The two-dimensional space utilization efficiency is Ratio total =23.0542%, with a projected centroid of (26.4621, 26.7284). The prototype UAV V2 has N1=17 dual-bladed propellers, occupying an area of ​​A1=210.0255mm². 2 The space utilization efficiency is Ratio1 = 16.2139%; the number of dual-bladed propellers of the No. 2 prototype UAV V1 is N2 = 19, and the occupied area is A2 = 87.8786 mm². 2 The space utilization efficiency is Ratio2=6.7842%.

[0086] The safe layout distance in the xOy plane is D. s xoy =1.5mm, Z-direction safe spacing distance D s Z At a height of 20mm, the final design schemes for the 0.5-meter height irregular three-dimensional layout of the blades of two drone models are as follows: Figure 4 As shown in (b). A total =346.4954mm 2 A template =1295.3421mm 2 Ratio total =26.7493%, the total number of layout parts is 33. Prototype No. 1 N1=25 pieces, A1=308.7492mm 2 Ratio1 = 23.8353%. Prototype 2: N2 = 8 units, A2 = 37.0913 mm. 2 Ratio2 = 2.8634%. The centroid coordinates of the prototype projections under the two schemes are shown in Table 1.

[0087] Table 1. Blade layout design for two UAV models with an xOy plane spacing of 1.5mm.

[0088]

[0089] The safe layout distance in the xOy plane is D. s xoy =1.5mm, Z-direction safe spacing distance D sZ At a thickness of 20mm, the three-dimensional layout design of irregular cavities at heights of 0.2, 0.5, and 0.7 meters for the blades of two different UAV models is as follows: Figure 5 As shown.

[0090] The safe layout distance in the xOy plane is D. s xoy =2mm, Z-direction safe spacing distance D s Z At a height of 20mm, the initial design schemes for the 3D layout of the blades of two UAV models with an irregular spatial shape at a height of 0.5m are as follows: Figure 6 As shown in (a), the total area occupied by the layout parts is A. total =210.4533mm 2 The total area of ​​the container is A. template =1295.3421mm 2 The two-dimensional space utilization efficiency is Ratio total =16.2469%, with a projected centroid of (26.4485, 27.1981). The prototype UAV V2 has N1=11 dual-bladed propellers, occupying an area of ​​A1=135.6799 mm². 2 The space utilization efficiency is Ratio1 = 10.4744%; the number of dual-bladed propellers of the No. 2 prototype UAV V1 is N2 = 16, and the occupied area is A2 = 74.078 mm². 2 The space utilization efficiency is Ratio2=5.7188%.

[0091] The safe layout distance in the xOy plane is D. s xoy =2mm, Z-direction safe spacing distance D s Z At a height of 20mm, the final design schemes for the 0.5-meter height irregular three-dimensional layout of the blades of two drone models are as follows: Figure 6 As shown in (b). A total =281.553mm 2 A template =1295.3421mm 2 Ratio total =21.7358%, projection centroid is (27.6611, 26.8374). Prototype 1 N1=19, A1=234.4941mm 2 Ratio1 = 19.1029%. Prototype 2: N2 = 10 units, A2 = 46.2424 mm. 2 Ratio2 = 3.5699%. The centroid coordinates of the prototype projections under the two schemes are shown in Table 2.

[0092] Table 2. Blade layout design for two UAV models with an xOy plane spacing of 2mm.

[0093]

[0094] The safe layout distance in the xOy plane is D. s xoy =2mm, Z-direction safe spacing distance D s Z At a thickness of 20mm, the three-dimensional layout design of irregular cavities at heights of 0.2, 0.5, and 0.7 meters for the blades of two different UAV models is as follows: Figure 7 As shown.

[0095] A schematic diagram of the second set of three-dimensional components to be sampled according to the present invention is shown below. Figure 8 As shown, the prototypes are 22-bladed turbine blade prototype 3, 72-bladed turbine blade disk prototype 4 (with a large internal cavity area, laying the foundation for the "large-enclosing-small" nested layout design), 18-bladed small turbine blade prototype 5, V2 UAV quadcopter fuselage prototype 6, and single-bladed wind turbine blade prototype 7.

[0096] The safe layout distance in the xOy plane is D. s xoy =2mm, Z-direction safe spacing distance D s Z At a thickness of 20mm, the initial design scheme for a nestable three-dimensional layout of various aerodynamic components is as follows: Figure 9 As shown in (a). A total =673.9966mm 2 A template =2500mm 2 Space utilization efficiency is Ratio total =26.9599%, total number of layout parts: 30. Prototype No. 1, N1=10 parts, occupying an area of ​​A1=46.2744mm². 2 The space utilization efficiency is Ratio1 = 1.851%. Prototype No. 2 has N2 = 7 units, and A2 = 86.5085 mm. 2 Ratio2 = 3.4603%. Prototype No. 3 has N3 = 7 units, A3 = 26.6998 mm. 2 Ratio3 = 1.068%. There are a total of N4 = 3 prototypes of size 4, with A4 = 444.4503 mm. 2 Ratio4 = 17.778%. There are a total of 7 prototypes (N5 = 7), with A5 = 21.9123 mm. 2 Ratio5 = 0.87649%. There are a total of N7 = 2 prototypes of size 7, with A7 = 46.7752 mm. 2Ratio7 = 1.871%. The safe nesting distance in the xOy plane is D. s xoy =2mm, Z-direction safe spacing distance D s Z At a thickness of 20mm, the final design scheme for a nestable three-dimensional layout of various aerodynamic components is as follows: Figure 9 As shown in (b).

[0097] A total =792.0478mm 2 A template =2500mm 2 Ratio total =31.6819%, the projected centroid coordinates are C total =(24.6132, 25.1556) Total number of layout parts: 37. Prototype 1, N1 = 4 parts, A1 = 292.1329mm 2 Ratio1 = 11.6853%. Prototype 2: N2 = 4 units, A2 = 49.4143 mm. 2 Ratio2 = 1.9766%. Prototype 3, N3 = 7 units, A3 = 186.9022 mm. 2 Ratio3 = 7.4761%. There is a total of N4 = 1 prototype of type 4, with A4 = 148.1648 mm. 2 Ratio4 = 5.9266%. There are a total of 14 prototypes (N5 = 14), with A5 = 43.8244 mm. 2 Ratio5 = 1.753%. There are a total of N6 = 5 prototypes of size 6, with A6 = 23.1335 mm. 2 Ratio6 = 0.92534%. There are a total of N7 = 2 prototypes, A7 = 47.1409 mm. 2 Ratio7 = 1.8856%.

[0098] The centroid coordinates of the prototype projections under both schemes are shown in Table 3, which demonstrates the advantages of using the available space inside the components to design nestable layout schemes.

[0099] Table 3. Nestable layout design of various aerodynamic components with an xOy plane spacing of 2mm.

[0100]

[0101] The safe layout distance in the xOy plane is D. s xoy =1.5mm, Z-direction safe spacing distance D s ZInitial design scheme for irregular three-dimensional spatial layout of various aerodynamic components at a thickness of 20mm is as follows: Figure 10 As shown in (a). A total =384.0467mm 2 A template =1295.3421mm 2 Ratio total =29.6483%, with a projected centroid of (28.1968, 26.1288). To ensure the universality and efficiency of the experimental results, this sampling selected prototypes other than the 72-bladed turbine blade disk of prototype No. 4 and the V2 fuselage of prototype No. 6 for scheme verification. Prototype No. 1 has N1=5 blades and A1=61.7199mm. 2 Ratio1 = 4.7648%. Prototype 2: N2 = 9 units, A2 = 41.6267 mm. 2 Ratio2 = 3.2136%. Prototype No. 3, N3 = 7 units, A3 = 186.9022 mm. 2 Ratio3 = 14.4287%. There are a total of 7 prototypes (N5 = 7), with A5 = 21.9124 mm. 2 Ratio5 = 1.6916%. There are a total of N7 = 3 prototypes, A7 = 70.1995 mm. 2 Ratio7 = 5.4194%.

[0102] The safe layout distance in the xOy plane is D. s xoy =1.5mm, Z-direction safe spacing distance D s Z The final design scheme for the irregular three-dimensional layout of various aerodynamic components at a thickness of 20mm is as follows: Figure 10 As shown in (b). Layout component A total =425.9044mm 2 A template =1295.3421mm 2 Ratio total =32.8797%, projection centroid is (26.8183, 28.0048). Prototype 1 N1=6, A1=74.0231mm 2 Ratio1 = 5.7146%. Prototype 2: N2 = 7 units, A2 = 32.377 mm. 2 Ratio2 = 2.4995%. Prototype No. 3: N3 = 10 units, A3 = 267.003 mm. 2 Ratio3 = 20.6125%. There are a total of N5 = 9 prototypes of size 5, with A5 = 28.173 mm. 2Ratio5 = 2.1749%. There is a total of N7 = 1 prototype of type 7, with A7 = 23.5425 mm. 2 Ratio7 = 1.8175%. The centroid coordinates of the prototype projections under the two schemes are shown in Table 4.

[0103] Table 4. Nestable layout design of various aerodynamic components with an xOy plane spacing of 1.5mm.

[0104]

[0105] The safe layout distance in the xOy plane is D. s xoy =1.5mm, Z-direction safe spacing distance D s Z At a height of 20mm, the three-dimensional layout design of various aerodynamic components in irregular cavities at heights of 0.2, 0.5, and 0.7 is as follows: Figure 11 As shown.

[0106] The safe layout distance in the xOy plane is D. s xoy =2mm, Z-direction safe spacing distance D s Z At a thickness of 20mm, the initial design scheme for a nestable three-dimensional layout of various aerodynamic components is as follows: Figure 12 As shown in (a). A total =239.2507mm 2 A template =1295.3421mm 2 Space utilization efficiency is Ratio total =18.4701%, the projected centroid coordinates are C total =(27.7493, 25.9973). There are 2 prototypes N1, occupying an area of ​​A1 = 26.6774 mm². 2 The space utilization efficiency is Ratio1 = 1.9051%. Prototype No. 2 has N2 = 8 units and A2 = 37.0272 mm. 2 Ratio2 = 2.8585%. There are a total of 11 prototypes (N5 = 11), with A5 = 34.4336 mm. 2 Ratio5 = 2.6573%. There are a total of N7 = 6 prototypes of type 7, with A7 = 140.9346 mm. 2 Ratio7 = 10.8801%. The safe nesting distance in the xOy plane is D. s xoy =2mm, Z-direction safe spacing distance D s ZAt a thickness of 20mm, the final design scheme for a nestable three-dimensional layout of various aerodynamic components is as follows: Figure 12 As shown in (b).

[0107] A total =370.9082mm 2 A template =1295.3421mm 2 Ratio total =28.634%, projected centroid coordinates (28.3618, 25.8021), total number of layout parts: 37. Prototype No. 1 N1=7 parts, A1=86.3464mm 2 Ratio1 = 6.6659%. Prototype 2: N2 = 4 units, A2 = 18.4716 mm. 2 Ratio2 = 1.426%. Prototype 3, N3 = 8 units, A3 = 213.6007 mm. 2 Ratio3 = 16.4899%. There are a total of N5 = 9 prototypes of size 5, with A5 = 28.1731 mm. 2 Ratio5 = 2.175%. There is a total of N7 = 1 prototype of type 7, with A7 = 23.7365 mm. 2 Ratio7 = 1.8325%. The centroid coordinates of the prototype projections under the two schemes are shown in Table 5.

[0108] Table 5. Nestable layout design of various aerodynamic components with an xOy plane spacing of 2mm.

[0109]

[0110] The safe layout distance in the xOy plane is D. s xoy =2mm, Z-direction safe spacing distance D s Z At a height of 20mm, the three-dimensional layout design of various aerodynamic components in irregular cavities at heights of 0.2, 0.5, and 0.7 is as follows: Figure 13 As shown.

[0111] The space utilization effect of the 3D nestable layout design method based on hybrid element-inspired evolution in different layout cases is shown in the following examples. Figure 14As shown, Case 1 compares the two-dimensional space utilization of two types of UAV blades in irregular three-dimensional layout design at a height of 0.5 mm with a safe arrangement distance of 1.5 mm in the xOy plane, resulting in a 16.03% increase in space utilization; Case 2 compares the space utilization of two types of UAV blades in irregular three-dimensional layout design at a height of 0.5 mm with a safe arrangement distance of 2 mm in the xOy plane, resulting in a 33.78% increase in space utilization; Case 3 compares the space utilization of nestable three-dimensional layout design of various aerodynamic components with a safe arrangement distance of 2 mm in the xOy plane, resulting in a 17.51% increase in space utilization; Case 4 compares the space utilization of irregular three-dimensional layout design of various aerodynamic components with a safe arrangement distance of 1.5 mm in the xOy plane, resulting in a 10.90% increase in space utilization; and Case 5 compares the space utilization of irregular three-dimensional layout design of various aerodynamic components with a safe arrangement distance of 2 mm in the xOy plane, resulting in a 55.03% increase in space utilization. Therefore, it can be concluded that space utilization is related to settings such as safety distance. When the safety spacing distance in the xOy plane is larger, the space utilization optimization effect is more obvious.

[0112] This invention also proposes a three-dimensional spatial nestable layout design system based on hybrid element-inspired evolution, the system comprising:

[0113] The initial layout generation unit is used to generate an initial three-dimensional layout of the three-dimensional component set to be laid out in the three-dimensional target space.

[0114] Operator set construction unit, used to construct metaheuristic operator strategy sets;

[0115] The operator set solving unit is used to select and generate a metaheuristic operator set from the metaheuristic operator strategy set based on the current 3D nesting layout using the Markov chain Monte Carlo algorithm. During the optimization process, the optimal metaheuristic operator set is solved to obtain the optimal metaheuristic operator set.

[0116] The layout optimization unit is used to optimize the current 3D nesting layout using the optimal meta-heuristic operator set, obtain the optimized 3D nesting layout and output it, and design and manufacture design templates based on the optimized 3D nesting layout.

Claims

1. A method for designing nestable layout schemes in three-dimensional space based on hybrid element-inspired evolution, characterized in that, Includes the following steps: Step 1: Generate the initial 3D nesting layout of the 3D component set to be nested in the 3D target space; The set of three-dimensional components to be arranged includes a data structure for each component, which comprises a global nested compatibility matrix M=[m ij ] n×n m ij This indicates the degree of nesting compatibility between the three-dimensional component i and the three-dimensional component j to be nested, and n represents the number of three-dimensional components to be nested. Step 2: Construct a set of metaheuristic operator strategies; the metaheuristic operators in the set include spatial transformation operators, nested optimization operators, local optimization operators, and global search operators; among them, the nested optimization operators include nested safety distance adjustment operators, nested direction search operators, and cavity filling operators. The nested safety distance adjustment operator is used to adjust the nested safety distance relationship between two 3D components. The nested direction search operator is used to find the optimal nested direction to maximize space utilization. The cavity filling operator is used to determine and execute whether 3D component i can completely fill the cavity of 3D component j. Step 3: Based on the current 3D nesting layout, use the Markov chain Monte Carlo algorithm to select and generate a set of metaheuristic operators from the set of metaheuristic operator strategies. Solve for the optimal set of metaheuristic operators during the optimization process to obtain the optimal set of metaheuristic operators. Then, use the optimal set of metaheuristic operators to optimize the current 3D nesting layout to obtain the optimized 3D nesting layout. In step 3, during the optimization process of the metaheuristic operator group, new heuristic operator groups are formed by adding new operator modules, deleting redundant operators, or replacing existing operators in the current metaheuristic operator group, enabling them to explore different arrangements and nesting strategies of three-dimensional components.

2. The method for designing a nestable layout scheme in three-dimensional space based on hybrid element-inspired evolution as described in claim 1, characterized in that, Step 1 specifically involves: First, an adaptive spatial decomposition strategy is used to discretize and model the three-dimensional target space, generating an enclosing volume structure that completely encloses the three-dimensional space. Then, the three-dimensional components to be arranged in the set of three-dimensional components to be arranged are sorted. Based on the safe arrangement distance, the three-dimensional components to be arranged are added to the enclosing volume structure that completely encloses the three-dimensional space in sequence, thereby generating the initial three-dimensional arrangement layout.

3. The method for designing a nestable layout scheme in three-dimensional space based on hybrid element-inspired evolution according to claim 2, characterized in that, The three-dimensional components to be sampled are arranged in descending order according to their corresponding evaluation values. The calculation formula for the evaluation value of each three-dimensional component to be sampled is as follows: f(c i )=w1×V i +w2×A i +w3×p i Where, f(c i ) is a three-dimensional component c i The evaluation value, V i For 3D component c i The volume of A i For 3D component c i Surface area, p i For 3D component c i The nesting priority is defined by w1, w2, and w3, which are three weight coefficients.

4. The method for designing a nestable layout scheme in three-dimensional space based on hybrid element-inspired evolution according to claim 2, characterized in that, In the process of adding each three-dimensional component to be arranged sequentially into the containment structure that completely encloses the three-dimensional space, each three-dimensional component to be arranged is added at the lowest feasible position that satisfies the interference constraints.

5. A three-dimensional spatial nestable layout scheme design system based on hybrid element heuristic evolution for implementing the three-dimensional spatial nestable layout scheme design method of claim 1, characterized in that, include: The initial layout generation unit is used to generate an initial three-dimensional layout of the three-dimensional component set to be laid out in the three-dimensional target space. Operator set construction unit, used to construct metaheuristic operator strategy sets; The operator set solving unit is used to select and generate a metaheuristic operator set from the metaheuristic operator strategy set based on the current 3D nesting layout using the Markov chain Monte Carlo algorithm. During the optimization process, the optimal metaheuristic operator set is solved to obtain the optimal metaheuristic operator set. The layout optimization unit is used to optimize the current 3D nesting layout by using the optimal set of metaheuristic operators to obtain an optimized 3D nesting layout.

6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the three-dimensional spatial nestable layout scheme design method based on hybrid element heuristic evolution as described in any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the three-dimensional spatial nestable layout scheme design method based on hybrid element heuristic evolution as described in any one of claims 1 to 4.

8. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the three-dimensional spatial nestable layout scheme design method based on hybrid element heuristic evolution as described in any one of claims 1 to 4.

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