Three-dimensional space nestable layout scheme design method based on mixed meta-heuristic evolution

Abstract

The invention discloses a three-dimensional space nestable layout scheme design method based on mixed meta-heuristic evolution. The method comprises the following steps: firstly, constructing an inclusion body structure which completely envelops a three-dimensional space container, setting a safe distance for preventing interference of a three-dimensional component, and generating an initial three-dimensional layout concept design layout; thirdly, constructing a meta-heuristic operator strategy set, generating a meta-heuristic operator group by using a Markov chain Monte Carlo algorithm, and mixing four types of meta-heuristic operators; and solving a better meta-heuristic operator group in the evolution process, and updating a current three-dimensional prototype layout scheme by using the better meta-heuristic operator group to obtain a three-dimensional layout based on mixed meta-heuristic evolution. According to the method disclosed by the invention, the layout problem in the irregular three-dimensional space can be solved, the nested layout of the three-dimensional component is supported, the available space in the component is fully utilized, the problem that an existing method is difficult to deal with the arrangement of island-shaped containers or components is solved, and the three-dimensional space utilization rate and the layout efficiency are remarkably improved.

Description

TECHNICAL FIELD

[0001] The application relates to a three-dimensional component layout design method, in particular to a three-dimensional space nestable layout scheme design method based on a hybrid heuristic evolution. BACKGROUND

[0002] Layout scheme design, which can be understood as the design of generating a layout scheme and visualizing the layout, is a process of putting forward systematic, innovative, feasible and phased solutions according to overall demand analysis and technical feasibility, and is the basis for carrying out subsequent detailed design. It has important applications in the fields of intelligent factories, additive manufacturing, micro-nano manufacturing, stereolithography, atomic manufacturing, aerospace, warehousing logistics and conceptual design. The space nestable layout in a complex geometric irregular region has high computational complexity. On the one hand, it involves the assembly or placement layout of component geometries under the constraint of a safe distance for interference prevention. On the other hand, it needs to overcome the multiple contradictions between space utilization, assembly efficiency and calculation speed. Under this background, the hybrid heuristic evolution method has become an important technical path to solve the problem of three-dimensional component nestable layout in an irregular region. In view of this theme, existing literatures have carried out discussions from multiple aspects.

[0003] Firstly, the optimization and scheduling of manufacturing planning and nesting algorithm as the core of three-dimensional component layout problem, has been widely concerned. Bennell et al. of University of Leeds, UK, explored the irregular shape cutting and loading problem, which is widely used in clothing manufacturing, metal cutting and furniture making industries (Bennell J A, Oliveira J F. The geometry of nesting problems: A tutorial[J]. European journal of operational research, 2008, 184(2): 397-415.). U.S. patent (Sadovnik I. Method and systems for nesting objects: U.S. Patent 6,980,934[P]. 2005-12-27.) proposed a method to arrange two-dimensional and three-dimensional objects, which improved the utilization rate by minimizing the gap between objects. It combined topological analysis and numerical iteration to realize heuristic layout optimization to reduce the calculation time. However, it has certain limitations in dealing with highly irregular shapes or complex multi-object scenarios, making it difficult to continue the nesting. U.S. patent (Horn J. System and method to solve shape nesting problems: U.S. Patent 7,181,702[P]. 2007-2-20.) proposed a genetic algorithm method based on resource definition fitness sharing for solving simple shape nesting problems.

[0004] As a search-driven controller of hybrid heuristic algorithm, the meta-heuristic mechanism driven by Boltzmann distribution becomes a preferred solution due to its characteristics. On the one hand, this mechanism can achieve dynamic balance between global search and local search, and can combine and adjust other heuristic methods, showing robustness and flexibility. On the other hand, the random optimization paradigm based on thermodynamic principles has the characteristics of few parameters, simple structure, and lightweight algorithm, while it has global exploration ability and local refinement optimization ability, which is suitable as a search control driver for the performance of meta-heuristic strategy set in super-heuristic algorithm, providing a search engine for super-heuristic method.

[0005] The application scenarios of three-dimensional component layout optimization are expanding, such as intelligent manufacturing, additive manufacturing, fluid high-flow pressure simulation and efficiency design, etc. In production scheduling and layout problems, in order to realize the simultaneous optimization of production efficiency and space utilization, the partitioning and parallel algorithm of irregular regions (non-rectangular regions) becomes a bottleneck problem. The hybrid heuristic evolution method is used to solve the irregular region three-dimensional component nesting problem, which not only provides a widely adaptable optimization framework in theory, but also has applications in the fields of intelligent manufacturing, warehouse logistics and conceptual design, etc. This research path based on the combination of intelligent optimization and industrial application is providing efficient and feasible solutions for complex layout problems in the manufacturing field. SUMMARY

[0006] In order to solve the problems in the background art and improve the layout efficiency and adaptability in the process of irregular three-dimensional component layout, and further improve the production efficiency, the application provides a three-dimensional space nestable layout scheme design method based on hybrid heuristic evolution.

[0007] To achieve the above object, the technical scheme adopted by the application is as follows:

[0008] One. A three-dimensional space nestable layout scheme design method based on hybrid heuristic evolution

[0009] Step 1: generating an initial three-dimensional layout of a set of three-dimensional components to be laid out in a three-dimensional target space;

[0010] Step 2: constructing a set of heuristic operator strategies;

[0011] Step 3: based on the current three-dimensional layout, using the Markov chain Monte Carlo algorithm to select and generate a set of heuristic operators from the set of heuristic operator strategies, solving the optimal set of heuristic operators in the optimization process, and obtaining the optimal set of heuristic operators; then using the optimal set of heuristic operators to optimize the current three-dimensional layout, and obtaining the optimized three-dimensional layout.

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

[0013] The step 1 is specifically:

[0014] Firstly, a self-adaptive spatial decomposition strategy is adopted to discretize and model the three-dimensional target space, to generate a containment body structure completely enveloping the three-dimensional space; safety distances of the three-dimensional components to be laid out in the XOY plane and Z direction are set, and each three-dimensional component to be laid out in the three-dimensional component set is sorted, and each three-dimensional component to be laid out is added to the containment body structure completely enveloping the three-dimensional space in sequence, so as to generate an initial three-dimensional layout.

[0015] The three-dimensional components to be laid out are arranged in descending order according to the corresponding evaluation values, and the calculation formula of the evaluation value of each three-dimensional component to be laid out is as follows:

[0016] f(c i )=w1×V i +w2×A i +w3×p i

[0017] Wherein, 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 , and w1, w2 and w3 are three weight coefficients.

[0018] In the process of adding each three-dimensional component to be laid out to the containment body structure completely enveloping the three-dimensional space in sequence, each three-dimensional component to be laid out is added to the lowest feasible position meeting the interference constraint.

[0019] In step 2, the meta-heuristic operators in the meta-heuristic operator strategy set include a space transformation operator, a nesting optimization operator, a local optimization operator and a global search operator.

[0020] II. A three-dimensional space nestable layout scheme design system based on a hybrid meta-heuristic evolution

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

[0022] An operator set construction unit is configured to construct a meta-heuristic operator strategy set;

[0023] An operator group solving unit is configured to select and generate a meta-heuristic operator group from the meta-heuristic operator strategy set based on the current three-dimensional layout by using a Markov chain Monte Carlo algorithm, to solve the optimal meta-heuristic operator group in the optimization process, and to obtain the optimal meta-heuristic operator group.

[0024] The layout optimization unit is used for obtaining an optimized three-dimensional layout by optimizing the current three-dimensional layout using an optimal meta-heuristic operator group.

[0025] Three, a computer device

[0026] The device comprises a memory and a processor, the memory stores a computer program, and the processor implements the steps of the three-dimensional space nestable layout scheme design method based on hybrid meta-heuristic evolution when executing the computer program.

[0027] Four, a computer readable storage medium

[0028] The medium stores a computer program, and the computer program implements the steps of the three-dimensional space nestable layout scheme design method based on hybrid meta-heuristic evolution when executed by a processor.

[0029] Five, a computer program product

[0030] The product comprises a computer program / instruction, and the computer program / instruction implements the steps of the three-dimensional space nestable layout scheme design method based on hybrid meta-heuristic evolution when executed by a processor.

[0031] The beneficial effects of the present application are:

[0032] The present application constructs a hybrid heuristic evolution framework based on control parameterized Markov chain Monte Carlo, and the body structure and the components to be laid out can be irregular (non-rectangular), so that the irregular nestable three-dimensional component layout problem is efficiently solved.

[0033] The method of the present application can adaptively process the multi-dimensional nested layout problem of three-dimensional components of different shapes and sizes in a complex irregular region by dynamically adjusting the combination of meta-heuristic operators, support the mutual nesting of three-dimensional components, and significantly improve the global search ability and local convergence performance of the algorithm.

[0034] Compared with the traditional layout method, the present application effectively solves the layout scheme design problem in the irregular three-dimensional space container, overcomes the array problem of complex island-type containers or components that the existing method is difficult to deal with, and significantly improves the space utilization rate, calculation efficiency and stability of the layout scheme, significantly improves the three-dimensional space utilization rate and layout efficiency, and is particularly suitable for the optimization layout design of complex three-dimensional components in the fields of aerospace, automobile manufacturing, 3D printing and the like. BRIEF DESCRIPTION OF DRAWINGS

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

[0036] Figure 1 is a flow chart of the method of the present application.

[0037] Figure 2 is a raw cavity voxelized configuration map of the irregular space to be laid out, wherein (a) is a voxelized layout matrix under a 100×100×100 grid resolution, and (b) is a voxelized layout matrix under a 300×300×300 grid resolution.

[0038] Figure 3 is a model schematic diagram of the first group of three-dimensional components to be laid out in the present application.

[0039] Figure 4 is an initial scheme and a final scheme of the 0.5-height irregular space three-dimensional layout design of two models of unmanned aerial vehicle blades under a safety layout distance of 1.5 mm in the xOy plane; wherein (a) is an initial scheme of the 0.5-height irregular space three-dimensional layout design of two models of unmanned aerial vehicle blades under a safety layout distance of 1.5 mm in the xOy plane; (b) is a final scheme of the 0.5-height irregular space three-dimensional layout design of two models of unmanned aerial vehicle blades under a safety layout distance of 1.5 mm in the xOy plane.

[0040] Figure 5 is a layout three-dimensional layout design of two models of unmanned aerial vehicle blades in irregular cavities of 0.2, 0.5 and 0.7 heights under a safety layout distance of 1.5 mm in the xOy plane.

[0041] Figure 6 is an initial scheme and a final scheme of the 0.5-height irregular space three-dimensional layout design of two models of unmanned aerial vehicle blades under a safety layout distance of 2 mm in the xOy plane; wherein (a) is an initial scheme of the 0.5-height irregular space three-dimensional layout design of two models of unmanned aerial vehicle blades under a safety layout distance of 2 mm in the xOy plane; (b) is a final scheme of the 0.5-height irregular space three-dimensional layout design of two models of unmanned aerial vehicle blades under a safety layout distance of 2 mm in the xOy plane.

[0042] Figure 7 is a layout three-dimensional layout design of two models of unmanned aerial vehicle blades in irregular cavities of 0.2, 0.5 and 0.7 heights under a safety layout distance of 2 mm in the xOy plane.

[0043] Figure 8 is a model schematic diagram of the second group of three-dimensional components to be laid out in the present application.

[0044] Figure 9are initial and final schemes of nestable three-dimensional layout design of multiple aerodynamic components under the safety layout distance of 2mm on the xOy plane; wherein (a) is an initial scheme of nestable irregular space three-dimensional layout design of multiple aerodynamic components under the safety layout distance of 2mm on the xOy plane; (b) is a final scheme of nestable irregular space three-dimensional layout design of multiple aerodynamic components under the safety layout distance of 2mm on the xOy plane.

[0045] Figure 10 are initial and final schemes of irregular space three-dimensional layout design of multiple aerodynamic components under the safety layout distance of 1.5mm on the xOy plane; wherein (a) is an initial scheme of nestable irregular space three-dimensional layout design of multiple aerodynamic components under the safety layout distance of 1.5mm on the xOy plane; (b) is a final scheme of nestable irregular space three-dimensional layout design of multiple aerodynamic components under the safety layout distance of 1.5mm on the xOy plane.

[0046] Figure 11 are three-dimensional layout design schemes of multiple aerodynamic components in irregular cavities with heights of 0.2, 0.5 and 0.7 under the safety layout distance of 2mm on the xOy plane.

[0047] Figure 12 are initial and final schemes of nestable three-dimensional layout design of multiple aerodynamic components under the safety layout distance of 2mm on the xOy plane; wherein (a) is an initial scheme of nestable irregular space three-dimensional layout design of multiple aerodynamic components under the safety layout distance of 2mm on the xOy plane; (b) is a final scheme of nestable irregular space three-dimensional layout design of multiple aerodynamic components under the safety layout distance of 2mm on the xOy plane.

[0048] Figure 13 are three-dimensional layout design schemes of multiple aerodynamic components in irregular cavities with heights of 0.2, 0.5 and 0.7 under the safety layout distance of 2mm on the xOy plane.

[0049] Figure 14 is a comparison of space utilization effects before and after optimization of the three-dimensional space nestable layout design method based on hybrid element heuristic evolution under different layout cases. DETAILED DESCRIPTION

[0050] The application will be further described in detail below in combination with the drawings and examples.

[0051] As shown in Figure 1 , the three-dimensional space nestable layout scheme design method based on hybrid element heuristic evolution specifically includes the following steps:

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

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

[0054] Global nested compatibility matrix M=[m ij] n×n , m ij ∈[0,1] is used to quantify the nesting compatibility of the to-be-laid-out three-dimensional component i and the to-be-laid-out three-dimensional component j, and n represents the number of to-be-laid-out three-dimensional components. m ij =0 indicates that the components are completely incompatible for nesting (such as two convex components or material conflicts); m ij ∈(0,0.3] indicates low compatibility, which is not conducive to layout design; m ij ∈(0.3,0.7] indicates medium compatibility, which can achieve effective nesting; m ij ∈(0.7,1) indicates high compatibility, and the component shapes are highly complementary; m ij =1 indicates perfect compatibility, which can achieve the theoretical optimal space utilization. M is a non-symmetric matrix, that is, m ij ≠m ji , reflecting the directional characteristics of the nesting relationship. This data structure realizes efficient query through a hash table or octree index, 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 layout algorithms.

[0055] Step 1 is specifically:

[0056] First, an adaptive spatial decomposition strategy is used to discretize and model the three-dimensional target space to generate an inclusive body structure O∈{0,1}^(n x ×n y ×n z ), ^ represents power, n x , n y , n z represent the dimensions in the X, Y, and Z directions, that is, an octree is used to represent the three-dimensional target space; set the safe layout distance of the to-be-laid-out three-dimensional component in the XOY plane and the Z direction, sort each to-be-laid-out three-dimensional component in the to-be-laid-out three-dimensional component set according to the evaluation value, and add each to-be-laid-out three-dimensional component to the inclusive body structure of the completely enveloping three-dimensional space using three-dimensional bottom-left-back in order to generate an initial three-dimensional layout L0={(p i ,R i ,Φ i |i=1,...,n}, Φ i is a set of nesting relationships.

[0057] The to-be-laid-out three-dimensional components are arranged in descending order according to the corresponding evaluation values, and the calculation formula of the evaluation value of each to-be-laid-out three-dimensional component is as follows:

[0058] f(c i )=w1×V i +w2×A i +w3×pi

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

[0060] During the process of sequentially adding each three-dimensional component to be laid out into a containing body structure that completely envelopes the three-dimensional space, each three-dimensional component to be laid out is added at a lowest feasible position p i ’ that satisfies the interference constraint. The interference constraint is specifically Ψ(c i ,c j )=0, j<i, Ψ(c i ,c j )=0, j<i indicates that the current component c i does not interfere or overlap with all the added components c j (j<i), and the lowest feasible position satisfies p i ’=argmin p {z|(p,R i )∈F}, where 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 meta-heuristic operator strategies;

[0062] In a feasible implementation, the meta-heuristic operators in the set of meta-heuristic operator strategies include a 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 For a translation vector, the operator moves the component in three-dimensional space by a specified distance.

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

[0066] In one possible implementation, the local optimization operator set H L includes a gravity settling operator h L (1) (p i ,g’)=p i +∫0 t g’×1 collision-free dt, where p i is the component position, g’=(0,0,-g) T is the gravity acceleration vector (g is the gravitational constant), T represents the transpose operation, and t is the settling time, 1 collision-freeFor interference detection indicator function, the operator simulates the gravity effect to make the components naturally sink until interference; vibration close operator h L (2) (X,A)= X+A×sin(wt)×e rand , where X={p1,...,p n} is the set of all component positions, A>0 is the vibration amplitude, w is the vibration frequency, e rand ∈S 2 is a random unit direction vector, the operator re-arranges the components to achieve a more compact layout under the premise of meeting the safe layout distance through random vibration.

[0067] In a feasible implementation, the global search operator set H G contains the component exchange operator h G (1) (π,i,j)=(π1,...,π j ,..,π i ,...,π n ), where π=(π1,...,π n ) is the component arrangement sequence, and π i indicates that the i-th added component is is the exchange position index, the operator exchanges the positions of two components in the sequence to explore different layout orders; the sequence rearrangement operator h G (2) (π,f)=sort(π,f), where π is the current arrangement sequence, and f:C→R is the second evaluation function (volume ordering), the operator reorders the entire sequence according to specific criteria; the grouping nesting operator h G (3) (C,M)=(G1,G2,..,G i ,...,G k ), where is the set of all components, θ∈(0,1) is the compatibility threshold, and G i ={c j ∈C:m ij >θ} is the i-th nested group, the operator clusters the components that can be nested with each other to achieve batch nesting optimization.

[0068] Step 3: Based on the current three-dimensional layout, use the Markov chain Monte Carlo algorithm to select and generate a set of meta-heuristic operators from the meta-heuristic operator strategy set, solve the optimal meta-heuristic operator set in the optimization process, and obtain the optimal meta-heuristic operator set; then use the optimal meta-heuristic operator set to optimize the current three-dimensional layout, and obtain the optimized three-dimensional layout. Output the optimized three-dimensional layout and perform layout design and manufacturing of the set of three-dimensional components to be laid out based on the optimized three-dimensional layout.

[0069] Step 3 is specifically:

[0070] Step 3.1: Initialize the related parameters of the Markov Chain Monte Carlo algorithm, including the initial control parameter, the minimum threshold control parameter, the cooling rate, the maximum number of steps in the isothermal process, the target search space of the three-dimensional component layout, the layout optimization objective function, and the maximum number of modules allowed in the meta-heuristic structure; wherein the initial control parameter ξ0 is used to control the search range in the initial stage of the algorithm; the minimum threshold control parameter ξmin is used to control the lower limit of the control parameter; the cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. min max The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. R D The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. u The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. i The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. s The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. κ The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. κ The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. κ The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme. max The cooling rate δ ∈ (0, 1) is used to control the control parameter descending speed; the current maximum number of steps in the isothermal process Smax is used to limit the local search depth; the target search space Ξ is used to define the layout area of the three-dimensional component; the objective function F is used to evaluate the space utilization, the interference degree between components, and the stability of the three-dimensional component layout scheme.

[0071] Step 3.2: Randomly select heuristic operators from the meta-heuristic operator strategy set and record them as the initial heuristic operator group, and preliminarily evaluate their performance on the three-dimensional component layout problem, i.e. use the initial heuristic operator group to optimize the initial three-dimensional layout, obtain the optimized three-dimensional layout and generate the objective function value corresponding to the optimized layout;

[0072] In a feasible implementation, the construction method of the initial heuristic operator group MH κ is as follows:

[0073] Randomly select heuristic rules from the meta-heuristic operator strategy set H to construct the initial heuristic operator group, wherein the number of modules κ can be randomly initialized in the range of [1, κ max ] or set according to the problem size; at the same time, set the initial step number s = 0, the control parameter ξ = ξ0, and the current solution as the current optimal solution.

[0074] ​Step 3.3: When the control parameter meets the threshold condition and the number of iterations does not exceed the upper limit, obtain the neighborhood solution by perturbing the current meta-heuristic combination, construct a new set of heuristic operators and use it for three-dimensional component layout optimization;

[0075] In a feasible implementation, the generation of neighborhood solutions is specially designed for three-dimensional component layout problems: by adding new operator modules (such as rotation operators, translation operators, and nesting depth adjustment operators) to the current set of heuristic operators, deleting redundant operators, or replacing existing operators, a new set of heuristic operators MH κ C is formed, which enables the exploration of different three-dimensional component arrangement modes and nesting strategies.

[0076] Step 3.4: Evaluate the performance of the new set of heuristic operators in three-dimensional component layout, calculate the difference in objective function before and after optimization, and determine whether to accept the new meta-heuristic combination based on the acceptance probability criterion based on the control parameter. In a feasible implementation, the acceptance probability function is based on the Metropolis-Hastings algorithm framework and is constructed as:

[0077] P(ΔE,ξ)=exp(-ΔE / κξ)

[0078] where ΔE=F(MH κ C |Ξ)-F(MH κ |Ξ) represents the difference in objective function between the new and old layout schemes, ξ is the current temperature control parameter, and k is the Boltzmann constant. The specific acceptance mechanism is: generate a uniformly distributed random number u r ∈[0,1], if u r ≤P(ΔE,ξ), accept the new solution MH κ C , otherwise keep the original solution MH κ . When ΔE<0 (new solution is better), P(ΔE,ξ)>1, it is necessarily accepted; when ΔE>0 (new solution is worse), it is still accepted with probability P(ΔE,ξ), and the probability decreases as the temperature ξ decreases, ensuring that the algorithm can jump out of the local optimal layout scheme at high temperature.

[0079] Step 3.5: Update the control parameter 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 a feasible implementation, the control parameter update follows the cooling law ξ←ξ(1-δ), and dynamic control is achieved by introducing the 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 MH, update the current optimal solution MH κ * ← MH κ C and reset the step number 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 parameter is reduced to a minimum threshold or the number of iterations reaches an upper limit, and output the optimal meta-heuristic combination scheme, which is applied to the final layout design of the nestable three-dimensional components in three-dimensional space, i.e., through rotation, translation, nesting depth adjustment, etc., to realize the maximum space utilization rate layout of three-dimensional components in irregular region space under the premise of meeting the non-interference and stability constraints between components; this process satisfies the detailed balance condition π(x)P(x→y)=π(y)P(y→x), ensuring the ergodicity and asymptotic convergence of the Markov chain.

[0082] The control parameterized Markov Chain Monte Carlo (MCMC) optimization strategy is derived from the principle of thermal equilibrium in statistical physics, and its mathematical foundation is based on the Metropolis-Hastings algorithm framework. The core of this strategy is to construct a time-varying acceptance probability function P(ΔE,ξ)=e^(-ΔE / kξ), where ΔE represents the change of the objective function, ξ is the control parameter, and k is the Boltzmann constant. From a mathematical point of view, this optimization strategy essentially constructs a non-homogeneous Markov chain on the solution space, and its stationary distribution evolves dynamically with the control parameter, i.e., π T(x) ∝e^(-f(x) / ξ), and finally converges to the Dirac measure δ x’ of the global optimal point set of the objective function, providing a probabilistic convergence framework that theoretically guarantees complex optimization problems. The present invention can fully utilize the flexibility of the probability optimization paradigm based on the principle of thermodynamics as a search controller, not only efficiently exploring and optimizing the combination of meta-heuristic operators in the strategy set, but also enhancing the adaptability to different optimization problems, thereby significantly improving the performance optimization effect of meta-heuristic algorithms.

[0083] The inclusion body structure of the voxelized complete envelope three-dimensional space container described in the examples of the present invention is shown in Figure 2 For a given three-dimensional irregular packing space Ω, a uniform voxel grid W G is established within the spatial range, with a grid resolution of (n x ,n y ,n z ), and a binary voxel matrix is generated therefrom, where represents the center point p of the voxel ijk in the direction The number of intersection points of the emitted rays and the grid boundary, V ijk =1 represents that the voxel (i,j,k) is located inside the layout space, V ijk =0 represents that it is located outside, and mod represents the remainder operation after the integer division. The voxelized layout space Ω voxel ={(x i ,y j ,z k )∈W G |V ijk =1} represents the set of all voxel center point coordinates p ijk =(x i ,y j ,z k ) that satisfy V ijk =1, that is, all voxel points located inside the layout space, which constitute the discretized available layout space. This voxelization supports O(1) time complexity space occupancy query and O(n x ×n y ×n z ) space complexity storage, providing a discretized spatial representation basis for subsequent three-dimensional component layout optimization. Taking the irregular three-dimensional vortex shell interior space layout as an example, the process of designing a nestable layout scheme is described. The volume of the shell structure is 9230046.22 mm³, and the surface area is 588457.20 mm². Among them Figure 2 (a) and (b) of Figure 2 are the voxelized layout matrices under the grid resolution of (n x =100, n y =100, n z =100) and (n x =300, n y =300, n z =300), respectively. The height of the three-dimensional irregular layout space Ω in the present application is 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 40 mm, then the height of 0.2 is 8 mm, the height of 0.5 is 20 mm, and the height of 0.7 is 35 mm.

[0084] The model of the first group of three-dimensional components to be laid out in the present application is shown in Figure 3 , wherein the models are unmanned aerial vehicle V1 double-blade propeller prototype 1 and unmanned aerial vehicle V2 double-blade propeller prototype 2, respectively.

[0085] The safe layout distance of the xOy plane is D s xoy =1.5 mm, and the safe layout distance in the z direction is 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 The 3D layout design of the irregular cavities at the height of 0.2, 0.5 and 0.7 of the unmanned aerial vehicle blades of the two models under the safe layout distance D Figure 5 = 20 mm is shown in FIG. 8(a).

[0090] The safe layout distance in the xOy plane is D s xoy = 2 mm, and the safe layout distance in the z direction is D s Z The initial scheme of the 3D layout design of the irregular space at the height of 0.5 of the unmanned aerial vehicle blades of the two models under the safe layout distance D Figure 6 = 20 mm is shown in FIG. 8(a). The total area occupied by the layout parts is A total = 210.4533 mm 2 , the total area of the container is A template = 1295.3421 mm 2 , the 2D space utilization efficiency is Ratio total = 16.2469%, and the projection centroid is (26.4485, 27.1981). The number of the V2 double-blade propellers of the first prototype unmanned aerial vehicle is N1 = 11, the occupied area is A1 = 135.6799 mm 2 , and the space utilization efficiency is Ratio1 = 10.4744%; the number of the V1 double-blade propellers of the second prototype unmanned aerial vehicle is N2 = 16, the occupied area is A2 = 74.078 mm 2 , and the space utilization efficiency is Ratio2 = 5.7188%.

[0091] The safe layout distance in the xOy plane is D s xoy = 2 mm, and the safe layout distance in the z direction is D s Z The final scheme of the 3D layout design of the irregular space at the height of 0.5 of the unmanned aerial vehicle blades of the two models under the safe layout distance D Figure 6 = 20 mm is shown in FIG. 8(b). A total = 281.553 mm 2 , A template = 1295.3421 mm 2 , Ratio total = 21.7358%, and the projection centroid is (27.6611, 26.8374). The first prototype has N1 = 19, A1 = 234.4941 mm 2 , and Ratio1 = 19.1029%; the second prototype has N2 = 10, A2 = 46.2424 mm 2 , and Ratio2 = 3.5699%. The projection centroid coordinates of each prototype 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. 2, Ratio7=1.871%. The safe layout distance of xOy plane is D s xoy =2mm, the safe layout distance of z direction is D s Z =20mm, the final solution of the nestable three-dimensional layout design of various aerodynamic components is as shown in Figure 9 (b) of the figure.

[0097] A total =792.0478mm 2 , A template =2500mm 2 , Ratio total =31.6819%, the projection centroid coordinates are C total =(24.6132, 25.1556), and the total number of layout parts is 37. The first prototype N1=4, A1=292.1329mm 2 , Ratio1=11.6853%. The second prototype N2=4, A2=49.4143mm 2 , Ratio2=1.9766%. The third prototype N3=7, A3=186.9022mm 2 , Ratio3=7.4761%. The fourth prototype N4=1, A4=148.1648mm 2 , Ratio4=5.9266%. The fifth prototype N5=14, A5=43.8244mm 2 , Ratio5=1.753%. The sixth prototype N6=5, A6=23.1335mm 2 , Ratio6=0.92534%. The seventh prototype N7=2, A7=47.1409mm 2 , Ratio7=1.8856%.

[0098] The projection centroid coordinates of each prototype under the two solutions are shown in Table 3, which shows the advantage of using the available space inside the components for the nestable layout design.

[0099] Table 3 Nestable layout design of various aerodynamic components under the layout distance of xOy plane being 2mm

[0100]

[0101] The safe layout distance of xOy plane is D s xoy =1.5mm, the safe layout distance of z direction is D s ZThe initial scheme of irregular spatial three-dimensional layout design of various aerodynamic components under D Figure 10 = 20 mm is shown in (a) of FIG. 1. A total = 384.0467 mm 2 , A template = 1295.3421 mm 2 , Ratio total = 29.6483%, and the projection centroid is (28.1968, 26.1288). To ensure the universality and efficiency of the experimental results, the present layout selection selects other prototypes except the 4th prototype 72-blade turbine blade disc and the 6th prototype V2 aircraft fuselage. The 1st prototype N1 = 5, A1 = 61.7199 mm 2 , Ratio1 = 4.7648%. The 2nd prototype N2 = 9, A2 = 41.6267 mm 2 , Ratio2 = 3.2136%. The 3rd prototype N3 = 7, A3 = 186.9022 mm 2 , Ratio3 = 14.4287%. The 5th prototype has N5 = 7, A5 = 21.9124 mm 2 , Ratio5 = 1.6916%. The 7th prototype has N7 = 3, A7 = 70.1995 mm 2 , Ratio7 = 5.4194%.

[0102] The safe layout distance of the xOy plane is D s xoy = 1.5 mm, and the safe layout distance in the z direction is D s Z = 20 mm. The final scheme of irregular spatial three-dimensional layout design of various aerodynamic components under D Figure 10 is shown in (b) of FIG. 1. The layout part A total = 425.9044 mm 2 , A template = 1295.3421 mm 2 , Ratio total = 32.8797%, and the projection centroid is (26.8183, 28.0048). The 1st prototype N1 = 6, A1 = 74.0231 mm 2 , Ratio1 = 5.7146%. The 2nd prototype N2 = 7, A2 = 32.377 mm 2 , Ratio2 = 2.4995%. The 3rd prototype N3 = 10, A3 = 267.003 mm 2 , Ratio3 = 20.6125%. The 5th prototype has N5 = 9, 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, wherein Case1 represents the 0.5 height irregular space three-dimensional layout design two-dimensional space utilization rate comparison of two models of unmanned aerial vehicle blades under the safety layout distance of 1.5mm in the xOy plane, and the final space utilization rate is improved by 16.03%; Case2 represents the space utilization rate comparison of two models of unmanned aerial vehicle blades under the safety layout distance of 2mm in the xOy plane, and the final space utilization rate is improved by 33.78%; Case3 represents the space utilization rate comparison of a plurality of aerodynamic components under the safety layout distance of 2mm in the xOy plane, and the final space utilization rate is improved by 17.51%; Case4 represents the space utilization rate comparison of a plurality of aerodynamic components under the safety layout distance of 1.5mm in the xOy plane, and the final space utilization rate is improved by 10.90%; Case5 represents the space utilization rate comparison of a plurality of aerodynamic components under the safety layout distance of 2mm in the xOy plane, and the final space utilization rate is improved by 55.03%. Thus, the space utilization rate is related to the safety distance setting, and when the safety layout distance in the xOy plane is larger, the optimization effect of the space utilization rate is more obvious.

[0112] The application further provides a three-dimensional space nestable layout design system based on hybrid heuristic evolution, which comprises:

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

[0114] An operator set construction unit is configured to construct a set of heuristic operator strategies.

[0115] An operator group solving unit is configured to select and generate a set of heuristic operators from the set of heuristic operator strategies by using a Markov chain Monte Carlo algorithm based on the current three-dimensional layout, solve the optimal set of heuristic operators in the optimization process, and obtain the optimal set of heuristic operators.

[0116] A layout optimization unit is configured to optimize the current three-dimensional layout by using the optimal set of heuristic operators, obtain an optimized three-dimensional layout and output the same, and design and manufacture a design template based on the optimized three-dimensional 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; Step 2: Construct a set of metaheuristic operator strategies; 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.

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, The data structure of each 3D component to be laid out in the step 1 includes a global nested compatibility matrix M=[m ij ] n×n , m ij represents the degree of nested compatibility between the 3D component i and the 3D component j, and n represents the number of 3D components to be laid out.

3. The method for designing a nestable layout scheme in three-dimensional space based on hybrid element-inspired evolution according to 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.

4. The method for designing a nestable layout scheme in three-dimensional space based on hybrid element-inspired evolution according to claim 3, 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.

5. The method for designing a nestable layout scheme in three-dimensional space based on hybrid element-inspired evolution according to claim 3, 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.

6. The method for designing a nestable layout scheme in three-dimensional space based on hybrid element-inspired evolution according to claim 1, characterized in that, 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.

7. A design system for nestable layout schemes in three-dimensional space based on hybrid element-inspired evolution, 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.

8. 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 6.

9. 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 6.

10. 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 6.

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