A Dual-Region Collaborative Optimization Method Assisted by Global and Local Surrogate Models

Abstract

The present invention provides a dual-region collaborative optimization method assisted by global and local surrogate models, which relates to the field of truss plane structure design optimization. This method adopts a double-layer collaborative framework to distinguish and process different types of variables, and solves the expensive constraint problem of mixed integer variables. Specifically, the collaborative framework based on radial basis functions includes a local search strategy based on the historical potential region and a pre-screening strategy assisted by radial basis functions; the mixed integer collaborative framework based on Gaussian processes includes a local search strategy based on the current possible potential region and a pre-screening strategy assisted by Gaussian processes; by using the collaborative framework based on radial basis functions, the fast convergence ability of the classical surrogate model-based collaborative framework is fully utilized to quickly locate high-potential regions; by using the mixed integer collaborative framework based on Gaussian processes, the disconnected feasible regions are searched by providing a stable optimization trajectory, balancing the convergence and feasibility of high-potential regions.

Description

Technical Field

[0001] The present invention relates to the field of truss plane structure design optimization, and particularly relates to a dual-region collaborative optimization method assisted by global and local surrogate models. Background Art

[0002] The optimization design problem of truss plane structure needs to minimize the total mass of the structure on the premise of satisfying the maximum displacement of all nodes. The side length of the angle steel is an integer design variable, and the height of the node is a continuous design variable. This kind of problem is a classical mixed-variable expensive constraint optimization problem involving time-consuming simulation analysis.

[0003] The primary analysis and verification of structural displacement takes several minutes. Since common evolutionary methods usually require 5000D - 10000D (D represents the number of design parameters in the design space) function evaluations to obtain a satisfactory feasible solution in the actual engineering scenario, but the computational cost required by these evolutionary methods is unaffordable, so surrogate models are introduced to help evolutionary methods handle such problems. These methods predict the constraints and objective values of candidate solutions by constructing surrogate models based on historical data. Common surrogate models include support vector machines, radial basis functions, and Gaussian processes. Compared with actual simulations, they all have the ability of rapid modeling and prediction.

[0004] Currently, two classic combinations between surrogate and evolutionary methods, namely surrogate-assisted pre-screening and surrogate-assisted local search, have been widely collaborated in different collaborative frameworks. Existing research has proved that this kind of collaborative framework can effectively balance global exploration and local exploitation. They are not developed to solve the expensive constraint problem of mixed integer variables, but to solve other similar problems, such as the expensive constraint problem with only continuous variables. In fact, there is little research on designing efficient methods for the expensive constraint problem of mixed integer variables, and no collaborative framework has been designed in the existing research. In addition, many evolutionary methods are designed for mixed-variable problems, but the evaluation cost of objectives and constraints is low. These studies indicate that targeted evolutionary operations or optimization strategies are required for continuous variables and integer variables respectively. Subsequently, the widely used collaborative framework usually drives the optimization based on predefined priority rules of objectives and constraints such as first locating the feasible region and then optimizing the feasible solution. However, this is ineffective in solving the classical disconnected feasible regions in the expensive constraint problem of mixed integer variables. Summary of the Invention

[0005] Based on this, the object of the present invention is to provide a dual-region collaborative optimization method assisted by global and local surrogate models, which is used to solve the technical problem that the existing method of driving optimization based on the predetermined priority rules of objectives and constraints such as first locating the feasible region and then optimizing the feasible solution is ineffective in solving the classical discontinuous feasible region problem of expensive constraints with mixed integer variables.

[0006] On the one hand, the present invention provides a dual-region collaborative optimization method assisted by global and local surrogate models, including:

[0007] Sampling is carried out within the upper and lower bounds of the design space by the Latin hypercube sampling method to obtain initial population sample points. The design space includes multiple design variables, and the design variables include integer design variables of the angle steel side length and continuous design variables of the node height. The fitness values of the initial population sample points are evaluated through an optimization objective evaluation function to form an initial sample population. The initial sample population includes multiple series, and each series includes the values of all design variables within the design space;

[0008] Based on the radial basis function surrogate model, local search is carried out on the historical potential regions to locate the historical high-potential regions. The historical optimal solution is determined according to the historical high-potential regions. The historical optimal solution is evaluated by the true function and the population and the position of the historical optimal solution are updated in combination with the feasibility rules; According to the pre-screening strategy of the radial basis function surrogate model and in combination with the position of the historical optimal solution, global pre-screening is carried out to obtain the global optimal solution. The population and the position of the global optimal solution are updated according to the global optimal solution, and the global possible potential regions are located according to the position of the global optimal solution;

[0009] Based on the Gaussian process surrogate model, local search is carried out on the current possible potential regions to locate the current high-potential regions. The current optimal solution is determined according to the current high-potential regions. The current optimal solution is evaluated by the true function and the population and the position of the current optimal solution are updated in combination with the feasibility rules. According to the pre-screening strategy of the Gaussian process surrogate model and in combination with the position of the current optimal solution, discontinuous feasible regions are searched to obtain the global optimal solution. The values of all design variables within the design space are obtained according to the global optimal solution to obtain the optimized truss plane structure;

[0010] Judge whether the optimized truss plane structure simultaneously satisfies all node maximum displacement constraints and the reduction of the total structure mass;

[0011] If not, return to execute the step of local search on the historical potential regions based on the radial basis function surrogate model to locate the historical high-potential regions until the maximum number of evaluations is reached. Among them, the maximum number of evaluations is designed according to the actual engineering design cycle and the optimization accuracy requirements, and the key iteration parameters in the algorithm iteration process are initialized;

[0012] If so, optimize the planar truss structure by the values of all integer design variables of the side lengths of angle steels and the values of all continuous design variables of the node heights in the optimized planar truss structure to obtain the optimal planar truss structure.

[0013] The above-mentioned dual-region collaborative optimization method assisted by global and local surrogate models adopts a double-layer collaborative framework, specifically a collaborative framework based on radial basis functions and a mixed-integer collaborative framework based on Gaussian processes, to achieve the differentiated processing of different types of variables and solve the expensive constraint problem of mixed-integer variables. Specifically, the collaborative framework based on radial basis functions includes a local search strategy based on the historical potential region and a pre-screening strategy assisted by radial basis functions; the mixed-integer collaborative framework based on Gaussian processes includes a local search strategy based on the current possible potential region and a pre-screening strategy assisted by Gaussian processes; by using the collaborative framework based on radial basis functions, give full play to the fast convergence ability of the classical surrogate model-based collaborative framework and quickly locate the high-potential region; use the mixed-integer collaborative framework based on Gaussian processes to search for the disconnected feasible region by providing a stable optimization trajectory, and well balance the convergence and feasibility of these high-potential regions.

[0014] In addition, according to the above-mentioned dual-region collaborative optimization method assisted by global and local surrogate models of the present invention, the following additional technical features may also be provided:

[0015] Further, the steps of sampling within the upper and lower bounds of the design space by the Latin hypercube sampling method to obtain the initial population sample points include:

[0016] Divide each dimension of the design space evenly into N intervals, where N is the size of the initial population;

[0017] Randomly select an interval for each dimension, and generate a uniformly distributed random number in the selected interval according to the uniform distribution;

[0018] Combine the random numbers of all dimensions to form a vector, and this vector is the current population individual;

[0019] Return to the step of randomly selecting an interval for each dimension and execute it until the number of loops reaches N - 1 times to obtain N population individuals, that is, obtain N population samples.

[0020] Further, in the step of performing local search on the historical potential region based on the radial basis function surrogate model to locate the historical high-potential region, determining the historical optimal solution according to the historical high-potential region, and evaluating the historical optimal solution by the real function and updating the positions of the population and the historical optimal solution in combination with the feasibility rule:

[0021] Determine the historical potential area based on all the maximum displacement constraints of the nodes corresponding to the sample points calculated by optimizing the objective evaluation function and the best Q sample points among the total mass of the structure. Construct the first sub-dataset from the best Q sample points to form the historical potential area, and use all the samples in the first sub-dataset to construct a local radial basis function;

[0022] Among them, the calculation formula for Q is:

[0023] Q = round (20 + rd * range );

[0024] range = min([20 * ( m + n ), NFE - 20, 150]);

[0025] In the formula, round represents round function, rd is a random number, m is the number of integer design variables of the angle steel side length, range represents the variable, n is the number of continuous design variables of the node height, NFE is the current number of function evaluations;

[0026] Among them, the calculation formula for the local search space range is:

[0027] ;

[0028] ; i = 1, …, Q; j = 1, …, m + n ;

[0029] In the formula: represents the lower limit of the j th dimension of the design variable in the local search space for local search of the historical potential area; represents the upper limit of the j th dimension of the design variable in the local search space for local search of the historical potential area; lb RBF represents the lower boundary vector composed of all the lower limits of the design variable dimensions in the local search space for local search of the historical potential area; ub RBF represents the upper boundary vector composed of all the upper limits of the design variable dimensions in the local search space for local search of the historical potential area; Represents the lower bound of the first dimension of the design variable in the local search space for local search in the historically potential region; Represents the upper bound of the first dimension of the design variable in the local search space for local search in the historically potential region; Represents the lower bound of the (m + n)-th dimension of the design variable in the local search space for local search in the historically potential region; Represents the upper bound of the (m + n)-th dimension of the design variable in the local search space for local search in the historically potential region; Represents the i -th sample in the first sub-dataset at the j -th dimension;

[0030] Among them, the determination range expression of the historically potential region is:

[0031] ;

[0032] ;

[0033] In the formula, j = 1, …, m + n; minimize Represents minimizing the constructed radial basis function surrogate model; Represents the radial basis function surrogate model constructed for the objective function evaluation of the truss planar structure optimization; Represents the radial basis function surrogate model constructed for the constraint evaluation function of the truss planar structure optimization; s.t. represents the label of the constraint conditions to be satisfied.

[0034] Furthermore, in the steps of global pre-screening to obtain the global optimal solution according to the pre-screening strategy of the radial basis function surrogate model and in combination with the position of the historical optimal solution, updating the population and the position of the global optimal solution according to the global optimal solution, and locating the globally potentially promising region according to the position of the global optimal solution:

[0035] Use DE / best / 2 to generate candidate offspring solutions;

[0036] Construct an approximate model for the objective function and constraint conditions according to the radial basis function surrogate model to approximately evaluate the candidate offspring solutions.

[0037] Furthermore, in the steps of local search in the currently potentially promising region based on the Gaussian process surrogate model to locate the currently highly promising region,

[0038] Obtain the position information of the Q samples closest to the current solution to obtain the second sub-dataset;

[0039] The current potential area is constructed based on the second sub-dataset, and a local Gaussian process is constructed using all samples in the second sub-dataset.

[0040] Among them, the calculation formula for the spatial range of local search is:

[0041] ;

[0042] ; i = 1, …, Q; j = 1, …, m + n ;

[0043] In the formula, represents the lower limit of the j -th dimension of the design variable in the local search space for local search in the current potential area; represents the upper limit of the j -th dimension of the design variable in the local search space for local search in the current potential area; lb Kriging represents the lower boundary vector composed of the lower limits of all dimensions of the design variable in the local search space for local search in the current potential area; ub Kriging represents the upper boundary vector composed of the upper limits of all dimensions of the design variable in the local search space for local search in the current potential area; represents the lower limit of the first dimension of the design variable in the local search space for local search in the current potential area; represents the upper limit of the first dimension of the design variable in the local search space for local search in the current potential area; represents the lower limit of the (m + n)-th dimension of the design variable in the local search space for local search in the current potential area; respectively represent the upper limits of the (m + n)-th dimension of the design variable in the local search space for local search in the current potential area; represents the value of the i -th sample in the second sub-dataset on the j -th dimension;

[0044] Among them, the expression for the determined range of the current potential area is:

[0045] ;

[0046] ;

[0047] In the formula, j = 1, …, m + n; minimize It represents minimizing the constructed Gaussian process surrogate model. It represents the Gaussian process surrogate model constructed by using all sample data in the second sub-dataset for the objective evaluation function of the planar truss structure optimization. It represents the Gaussian process surrogate model constructed for the optimization constraint evaluation function of the planar truss structure; s.t. represents the constraint condition label to be satisfied.

[0048] Furthermore, the steps of searching for a disconnected feasible region based on the pre-screening strategy of the Gaussian process surrogate model and combining with the position of the current optimal solution to obtain the global optimal solution include:

[0049] Generating candidate offspring solutions based on the cooperative mutation strategy of variable types.

[0050] Constructing an approximate model for the objective function and constraint conditions according to the Gaussian process to approximately evaluate the candidate offspring solutions.

[0051] Selecting the optimal offspring individual from the evaluated candidate offspring solutions based on the complete expected improvement matrix function of hypervolume.

[0052] Performing a true function evaluation on the selected optimal offspring individual, and updating the population and the position of the optimal solution.

[0053] Where:

[0054] minimize F (x) = { f (x), G (x)};

[0055] x ∈ off 2;

[0056] In the formula, minimize F (x) represents minimizing the objective vector composed of the objective function and the constraint violation value function; x represents an individual. f (x) represents the objective function expression for the individual x. G (x) represents the constraint violation value function expression for the individual x, G (x) = max(g(x), 0); off 2 is the candidate offspring solution;

[0057] The current Pareto front containing k non-dominated individuals is represented as follows:

[0058] ;

[0059] In the formula, k represents the k-th non-dominated individual; f k represents the objective function value for the k-th non-dominated individual;G k Denote the constraint violation function value for the k-th non-dominated individual;

[0060] Among them, the expression of the complete expected improvement matrix function based on hypervolume is:

[0061] ;

[0062] In the formula, j Denote the j -th non-dominated individual; r =( r f , r G ) is the reference point selected by the user, r f Denote the objective function value corresponding to the reference point, r G Denote the constraint violation function value corresponding to the reference point; f j Denote the objective value of the j -th non-dominated individual; G j Denote j -th non-dominated individual constraint violation function value; Denote j -th non-dominated individual objective function expected improvement value; Denote j -th non-dominated individual constraint violation function expected improvement value;

[0063] and The calculation formulas of are respectively:

[0064] ;

[0065] .

[0066] On the other hand, the present invention provides a dual-region collaborative optimization system assisted by a global and local surrogate model, and the system includes:

[0067] An acquisition module, configured to sample within the upper and lower bounds of the design space by the Latin hypercube sampling method to obtain an initial population sample point. The design space includes multiple design variables, and the design variables include integer design variables of the side length of the angle steel and continuous design variables of the node height. The fitness value of the initial population sample point is evaluated through an optimization objective evaluation function to form an initial sample population. The initial sample population includes multiple series, and each sequence includes the values of all design variables in the design space;

[0068] The first optimization module is used to perform local search on the historical potential regions based on the radial basis function surrogate model to locate the historical high-potential regions, determine the historical optimal solution according to the historical high-potential regions, perform real function evaluation on the historical optimal solution and update the population and the position of the historical optimal solution in combination with the feasibility rules; perform global pre-screening based on the pre-screening strategy of the radial basis function surrogate model and in combination with the position of the historical optimal solution to obtain the global optimal solution, update the population and the position of the global optimal solution according to the global optimal solution, and locate the globally possible potential regions according to the position of the global optimal solution;

[0069] The second optimization module is used to perform local search on the current possible potential regions based on the Gaussian process surrogate model to locate the current high-potential regions, determine the current optimal solution according to the current high-potential regions, perform real function evaluation on the current optimal solution and update the population and the position of the current optimal solution in combination with the feasibility rules, search for unconnected feasible regions based on the pre-screening strategy of the Gaussian process surrogate model and in combination with the position of the current optimal solution to obtain the global optimal solution, and obtain the values of all design variables within the design space according to the global optimal solution to obtain the optimized truss plane structure;

[0070] The judgment module is used to judge whether the optimized truss plane structure simultaneously satisfies all node maximum displacement constraints and the reduction of the total structure mass;

[0071] The first execution module is used to, if the optimized truss plane structure cannot simultaneously satisfy all node maximum displacement constraints and the reduction of the total structure mass, return to execute the step of performing local search on the historical potential regions based on the radial basis function surrogate model to locate the historical high-potential regions until the maximum number of evaluations is reached, wherein the maximum number of evaluations is designed according to the actual engineering design cycle and the optimization accuracy requirements, and key iterative parameters in the algorithm iteration process are initialized;

[0072] The second execution module is used to, if the optimized truss plane structure simultaneously satisfies all node maximum displacement constraints and the reduction of the total structure mass, optimize the truss plane structure with the values of all angle steel side length integer design variables and the values of all node height continuous design variables of the optimized truss plane structure to obtain the optimal truss plane structure.

[0073] On the other hand, the present invention provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it implements the dual-region collaborative optimization method assisted by the global and local surrogate models as described above.

[0074] On the other hand, the present invention also provides a data processing device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, and when the processor executes the program, it implements the dual-region collaborative optimization method assisted by the global and local surrogate models as described above. Description of the Drawings

[0075] Figure 1 It is a flowchart of the dual-region collaborative optimization method assisted by the global and local surrogate models in the first embodiment of the present invention;

[0076] Figure 2 It is a system block diagram of the dual-region collaborative optimization system assisted by the global and local surrogate models in the second embodiment of the present invention;

[0077] The following specific embodiments will further illustrate the present invention in conjunction with the above drawings. Specific Embodiments

[0078] To facilitate the understanding of the present invention, the present invention will be described more comprehensively below with reference to the relevant drawings. Several embodiments of the present invention are given in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, these embodiments are provided to make the disclosure of the present invention more thorough and comprehensive.

[0079] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs. The terms used herein in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more of the related listed items.

[0080] In order to solve the technical problem that the existing method of driving optimization based on the predetermined priority rules of objectives and constraints such as first locating the feasible region and then optimizing the feasible solution is ineffective in solving the expensive constraint problem of mixed integer variables in the classical disconnected feasible region, the present application provides a dual-region collaborative optimization method assisted by the global and local surrogate models. By adopting a two-layer collaborative framework, specifically a collaborative framework based on radial basis functions and a mixed integer collaborative framework based on Gaussian processes, to achieve the differentiated processing of different types of variables and solve the expensive constraint problem of mixed integer variables; specifically, the collaborative framework based on radial basis functions includes a local search strategy based on the historical potential region and a pre-screening strategy assisted by radial basis functions; the mixed integer collaborative framework based on Gaussian processes includes a local search strategy based on the current potentially promising region and a pre-screening strategy assisted by Gaussian processes; by using the collaborative framework based on radial basis functions, the fast convergence ability of the classical collaborative framework based on surrogate models is fully utilized to quickly locate the high-potential region; by using the mixed integer collaborative framework based on Gaussian processes to search for the disconnected feasible region by providing a stable optimization trajectory, the convergence and feasibility of these high-potential regions are well balanced.

[0081] To facilitate the understanding of the present invention, several embodiments of the present invention will be given below. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, these embodiments are provided to make the disclosure of the present invention more thorough and comprehensive.

[0082] Embodiment 1

[0083] Please refer to Figure 1 , which shows the dual-region collaborative optimization method assisted by the global and local surrogate models in the first embodiment of the present invention, including steps S101 to S108:

[0084] S101. Samples are taken within the upper and lower bounds of the design space by the Latin hypercube sampling method to obtain initial population sample points. The design space includes multiple design variables, and the design variables include integer design variables of the side length of angle steel and continuous design variables of the node height. The fitness values of the initial population sample points are evaluated by the optimization objective evaluation function to form an initial sample population. The initial sample population includes multiple series, and each series includes the values of all design variables within the design space.

[0085] In this embodiment, the step of taking samples within the upper and lower bounds of the design space by the Latin hypercube sampling method includes: evenly dividing each dimension of the design space into N intervals, where N is the size of the initial population; randomly selecting an interval for each dimension, and generating a uniformly distributed random number within the selected interval according to the uniform distribution; combining the random numbers of all dimensions to form a vector, and this vector is the current population individual; returning to execute the step of randomly selecting an interval for each dimension until the number of loops reaches N - 1 times to obtain N population individuals, that is, obtaining N population samples.

[0086] S102. Based on the radial basis function surrogate model, local search is performed on the historical potential regions to locate the historical high-potential regions. The historical optimal solution is determined according to the historical high-potential regions, and the historical optimal solution is evaluated by the real function and combined with the feasibility rule to update the positions of the population and the historical optimal solution.

[0087] In this embodiment, the historical potential regions are determined by the maximum displacement constraints of all nodes and the best Q sample points in the total mass of the structure corresponding to the sample points calculated by the optimization objective evaluation function. The first sub-dataset is constructed by the best Q sample points to form the historical potential regions, and the local radial basis function is constructed by using all the samples in the first sub-dataset;

[0088] Among them, the calculation formula of Q is:

[0089] Q = round (20 + rd *range ); range = min([20 * ( m + n ), NFE - 20, 150]);

[0090] In the formula, round represents round the function, rd is a random number, m is the number of integer design variables of the angle steel side length, range represents the variable, n is the number of continuous design variables of the node height, NFE is the current number of function evaluations;

[0091] Among them, the calculation formula for the local search space range is:

[0092] ;

[0093] ; i = 1, …, Q; j = 1, …, m + n ;

[0094] In the formula: represents the lower limit of the j th dimension in the local search space where the design variable performs local search for the historical potential area; represents the upper limit of the j th dimension in the local search space where the design variable performs local search for the historical potential area; lb RBF represents the lower boundary vector composed of all dimension lower limits of the design variable in the local search space for local search of the historical potential area; ub RBF represents the upper boundary vector composed of all dimension upper limits of the design variable in the local search space for local search of the historical potential area; represents the lower limit of the first dimension of the design variable in the local search space for local search of the historical potential area; represents the upper limit of the first dimension of the design variable in the local search space for local search of the historical potential area; represents the lower limit of the (m + n)th dimension of the design variable in the local search space for local search of the historical potential area; represents the upper limit of the (m + n)th dimension of the design variable in the local search space for local search of the historical potential area; represents the i th sample in the first sub-dataset in thej The values in a dimension;

[0095] Among them, the expression for determining the range of the historical potential area is:

[0096] ;

[0097] ;

[0098] In the formula, j = 1, …, m + n; minimize Indicates minimizing the constructed radial basis function surrogate model; Indicates the radial basis function surrogate model constructed for the objective function evaluation function of the planar truss structure optimization; Indicates the radial basis function surrogate model constructed for the optimization constraint evaluation function of the planar truss structure; s.t. indicates the label of the constraint conditions to be satisfied.

[0099] S103. Perform global pre-screening based on the pre-screening strategy of the radial basis function surrogate model and in combination with the position of the historical optimal solution to obtain the global optimal solution, update the population and the position of the global optimal solution according to the global optimal solution, and locate the globally possible potential area according to the position of the global optimal solution.

[0100] Specifically, use DE / best / 2 to generate candidate offspring solutions; construct an approximate model for the objective function and constraint conditions according to the radial basis function surrogate model to approximately evaluate the candidate offspring solutions.

[0101] S104. Perform local search on the current possible potential area based on the Gaussian process surrogate model to locate the current high-potential area, determine the current optimal solution according to the current high-potential area, perform real function evaluation on the current optimal solution, and update the population and the position of the current optimal solution in combination with the feasibility rules.

[0102] In the step of performing local search on the current possible potential area based on the Gaussian process surrogate model to locate the current high-potential area: Obtain the position information of Q samples closest to the current solution to obtain the second sub-dataset; construct the current possible potential area according to the second sub-dataset, and use all the samples in the second sub-dataset to construct a local Gaussian process;

[0103] Among them, the calculation formula for the spatial range of the local search is:

[0104] ;

[0105] ; i = 1, …, Q; j = 1, …, m + n;

[0106] In the formula, represents the lower limit of the j th dimension of the design variable in the local search space for local search in the current potential region; represents the upper limit of the j th dimension of the design variable in the local search space for local search in the current potential region; lb Kriging represents the lower boundary vector composed of the lower limits of all dimensions of the design variable in the local search space for local search in the current potential region; ub Kriging represents the upper boundary vector composed of the upper limits of all dimensions of the design variable in the local search space for local search in the current potential region; represents the lower limit of the 1st dimension of the design variable in the local search space for local search in the current potential region; represents the upper limit of the 1st dimension of the design variable in the local search space for local search in the current potential region; represents the lower limit of the (m + n)th dimension of the design variable in the local search space for local search in the current potential region; respectively represent the upper limits of the (m + n)th dimension of the design variable in the local search space for local search in the current potential region; represents the value of the i th sample in the second sub - dataset on the j th dimension;

[0107] Among them, the determination range expression of the current potential region is:

[0108] ;

[0109] ;

[0110] In the formula, j = 1, …, m + n; minimize represents minimizing the constructed Gaussian process surrogate model, represents the Gaussian process surrogate model constructed using all sample data in the second sub - dataset for the optimization objective evaluation function of the truss plane structure; represents the Gaussian process surrogate model constructed for the optimization constraint evaluation function of the truss plane structure; s.t. represents the constraint condition label to be satisfied.

[0111] S105. Search for disconnected feasible regions according to the pre-screening strategy of the Gaussian process surrogate model and in combination with the position of the current optimal solution to obtain the global optimal solution, and obtain the values of all design variables within the design space according to the global optimal solution to obtain the optimized truss plane structure.

[0112] In this embodiment, the steps of searching for disconnected feasible regions according to the pre-screening strategy of the Gaussian process surrogate model and in combination with the position of the current optimal solution to obtain the global optimal solution include:

[0113] Generate candidate offspring solutions based on the cooperative mutation strategy of variable types; construct an approximate model for the objective function and constraint conditions according to the Gaussian process to approximately evaluate the candidate offspring solutions; select the optimal offspring individuals from the evaluated candidate offspring solutions based on the complete expected improvement matrix function of hypervolume; perform real function evaluation on the selected optimal offspring individuals, and update the population and the position of the optimal solution;

[0114] Where: minimize F (x) = { f (x), G (x)}; x ∈ off 2;

[0115] In the formula, minimize F (x) represents minimizing the objective vector composed of the objective function and the constraint violation value function; x represents an individual; f (x) represents the objective function expression for the individual x; G (x) represents the constraint violation value function expression for the seismic intensity individual x, G (x) = max(g(x), 0); off 2 is the candidate offspring solution;

[0116] The current Pareto front containing k non-dominated individuals is expressed as follows:

[0117] ;

[0118] In the formula, k represents the k-th non-dominated individual; f k represents the objective function value for the k-th non-dominated individual; G k represents the constraint violation function value for the k-th non-dominated individual;

[0119] Among them, the expression of the complete expected improvement matrix function based on hypervolume is:

[0120] ;

[0121] In the formula, j represents thej a non-dominated individual; r =( r f , r G ) is the reference point selected by the user, r f denotes the objective function value corresponding to the reference point, r G denotes the constraint violation function value corresponding to the reference point; f j denotes the j th objective value of the non-dominated individual; G j denotes j the constraint violation function value of the non-dominated individual; denotes j the expected improvement value of the objective function of the non-dominated individual; denotes j the expected improvement value of the constraint violation function of the non-dominated individual;

[0122] and are calculated as follows:

[0123] ;

[0124] .

[0125] S106. Determine whether the optimized planar truss structure simultaneously satisfies all the maximum displacement constraints of the nodes and the reduction of the total structure mass.

[0126] If the optimized planar truss structure cannot simultaneously satisfy all the maximum displacement constraints of the nodes and the reduction of the total structure mass, then execute step S107; if the optimized planar truss structure can simultaneously satisfy all the maximum displacement constraints of the nodes and the reduction of the total structure mass, then execute step S108.

[0127] S107. Determine whether the number of optimizations has reached the maximum evaluation number. If the number of optimizations has not reached the maximum evaluation number, then return to execute step S102; if the number of optimizations has reached the maximum evaluation number, then execute step S108; wherein, the maximum evaluation number is designed according to the actual engineering design cycle and the optimization accuracy requirement, and the key iteration parameters in the algorithm iteration process are initialized.

[0128] S108. Optimize the planar truss structure with the values of all the integer design variables of the angle steel side lengths and the values of all the continuous design variables of the node heights in the optimized planar truss structure to obtain the optimal planar truss structure.

[0129] In summary, the dual-region collaborative optimization method based on the global and local surrogate model assistance in the above embodiments of the present invention adopts a two-layer collaborative framework, specifically a collaborative framework based on radial basis functions and a mixed-integer collaborative framework based on Gaussian processes, to achieve the differential processing of different types of variables and solve the expensive constraint problem of mixed-integer variables. Specifically, the collaborative framework based on radial basis functions includes a local search strategy based on the historical potential region and a pre-screening strategy assisted by radial basis functions; the mixed-integer collaborative framework based on Gaussian processes includes a local search strategy based on the currently possible potential region and a pre-screening strategy assisted by Gaussian processes. By using the collaborative framework based on radial basis functions, the fast convergence ability of the classical surrogate model-based collaborative framework is fully utilized to quickly locate the high-potential region. By using the mixed-integer collaborative framework based on Gaussian processes to search for the disconnected feasible region by providing a stable optimization trajectory, the convergence and feasibility of these high-potential regions are well balanced.

[0130] Embodiment 2

[0131] Please refer to Figure 2 , which shows the dual-region collaborative optimization system based on the global and local surrogate model assistance in the second embodiment of the present invention. The system includes:

[0132] An acquisition module, configured to sample within the upper and lower bounds of the design space by the Latin hypercube sampling method to obtain initial population sample points. The design space includes multiple design variables, and the design variables include integer design variables of the angle steel side length and continuous design variables of the node height. The fitness values of the initial population sample points are evaluated through an optimization objective evaluation function to form an initial sample population. The initial sample population includes multiple series, and each sequence includes the values of all design variables in the design space;

[0133] A first optimization module, configured to perform local search on the historical potential region based on the radial basis function surrogate model to locate the historical high-potential region, determine the historical optimal solution according to the historical high-potential region, perform real function evaluation on the historical optimal solution and update the positions of the population and the historical optimal solution in combination with the feasibility rule; perform global pre-screening according to the pre-screening strategy of the radial basis function surrogate model and in combination with the position of the historical optimal solution to obtain the global optimal solution, update the population and the global optimal solution position according to the global optimal solution, and locate the globally possible potential region according to the global optimal solution position;

[0134] The second optimization module is used to perform local search on the current potentially promising regions based on the Gaussian process surrogate model to locate the current high-potential regions, determine the current optimal solution according to the current high-potential regions, perform real function evaluation on the current optimal solution and update the population and the position of the current optimal solution in combination with the feasibility rules, search for disconnected feasible regions based on the pre-screening strategy of the Gaussian process surrogate model and in combination with the position of the current optimal solution to obtain the global optimal solution, and obtain the values of all design variables within the design space based on the global optimal solution to obtain the optimized truss plane structure;

[0135] The judgment module is used to judge whether the optimized truss plane structure simultaneously satisfies all node maximum displacement constraints and the reduction of the total structure mass;

[0136] The first execution module is used to, if the optimized truss plane structure cannot simultaneously satisfy all node maximum displacement constraints and the reduction of the total structure mass, return to execute the step of performing local search on the historical potentially promising regions based on the radial basis function surrogate model to locate the historical high-potential regions until the maximum number of evaluations is reached, where the maximum number of evaluations is designed according to the actual engineering design cycle and the optimization accuracy requirements, and key iterative parameters in the algorithm iteration process are initialized;

[0137] The second execution module is used to, if the optimized truss plane structure simultaneously satisfies all node maximum displacement constraints and the reduction of the total structure mass, optimize the truss plane structure based on the values of all angle steel side length integer design variables and all node height continuous design variables of the optimized truss plane structure to obtain the optimal truss plane structure.

[0138] In summary, the dual-region collaborative optimization system based on global and local surrogate model assistance in the above embodiments of the present invention adopts a double-layer collaborative framework, specifically a collaborative framework based on the radial basis function and a hybrid integer collaborative framework based on the Gaussian process, to achieve differentiated processing of different types of variables and solve the expensive constraint problem of mixed integer variables; specifically, the collaborative framework based on the radial basis function includes a local search strategy based on historical potentially promising regions and a pre-screening strategy assisted by the radial basis function; the hybrid integer collaborative framework based on the Gaussian process includes a local search strategy based on current potentially promising regions and a pre-screening strategy assisted by the Gaussian process; by using the collaborative framework based on the radial basis function, the fast convergence ability of the classical surrogate model-based collaborative framework is fully utilized to quickly locate high-potential regions; by using the hybrid integer collaborative framework based on the Gaussian process to search for disconnected feasible regions by providing a stable optimization trajectory, the convergence and feasibility of these high-potential regions are well balanced.

[0139] In addition, an embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the steps of the method in the above embodiment are implemented.

[0140] In addition, an embodiment of the present invention further provides a data processing device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, and when the processor executes the program, the steps of the method in the above embodiment are implemented.

[0141] The logic and / or steps represented in the flowchart or described in other ways herein, for example, can be considered as a definite sequence list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other systems that can fetch instructions from the instruction execution system, apparatus, or device and execute the instructions), or in combination with these instruction execution systems, apparatus, or devices. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device.

[0142] More specific examples (non-exhaustive list) of computer-readable media include the following: an electrical connection part with one or more wirings (electronic device), a portable computer disk cartridge (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium can even be paper or other suitable media on which a program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpretation, or other suitable processing if necessary, and then stored in a computer memory.

[0143] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware, or a combination thereof. In the above embodiment, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one or a combination of the following techniques well known in the art can be used: discrete logic circuits having logic gate circuits for implementing logical functions on data signals, application specific integrated circuits having appropriate combinational logic gate circuits, programmable gate arrays (PGA), field programmable gate arrays (FPGA), etc.

[0144] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "examples", "specific examples", or "some examples", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in a suitable manner in any one or more embodiments or examples.

[0145] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the claims and their equivalents.

Claims

1. A dual-region collaborative optimization method based on global and local proxy models, characterized in that: include: The Latin hypercube sampling method is used to sample the upper and lower bounds of the design space to obtain the initial population sample points. The design space includes multiple design variables, including the angle steel edge length integer design variable and the node height continuous design variable. The fitness value of the initial population sample points is evaluated by optimizing the objective evaluation function to form an initial sample population. The initial sample population includes multiple series, and each series includes the values ​​of all the design variables in the design space. Based on the radial basis function proxy model, a local search is performed on the historical potential area to locate the historical high potential area, the historical optimal solution is determined according to the historical high potential area, the historical optimal solution is evaluated by a real function and the population and the position of the historical optimal solution are updated in combination with the feasibility rule; according to the pre-screening strategy of the radial basis function proxy model and in combination with the position of the historical optimal solution, a global pre-screening is performed to obtain the global optimal solution, the population and the position of the global optimal solution are updated according to the global optimal solution, and the global potential area is located according to the position of the global optimal solution; Based on the Gaussian process proxy model, a local search is performed on the current potential area to locate the current high potential area, the current optimal solution is determined according to the current high potential area, the current optimal solution is evaluated by a real function and the population and the position of the current optimal solution are updated in combination with the feasibility rule, and the unconnected feasible area is searched according to the pre-screening strategy of the Gaussian process proxy model and in combination with the position of the current optimal solution to obtain a global optimal solution, and the values ​​of all design variables in the design space are obtained according to the global optimal solution to obtain an optimized truss plane structure; Determine whether the optimized truss plane structure satisfies the maximum displacement constraints of all nodes and the total mass of the structure is reduced; If not, return to the step of performing a local search for historical potential areas based on the radial basis function proxy model to locate historical high potential areas until the maximum number of evaluations is reached, wherein the maximum number of evaluations is designed according to the actual engineering design cycle and optimization accuracy requirements, and the key iteration parameters in the algorithm iteration process are initialized; If so, the truss plane structure is optimized by taking the values ​​of all the integer design variables of the angle steel side lengths and the values ​​of all the continuous design variables of the node heights of the optimized truss plane structure to obtain the optimal truss plane structure; Among them, in the step of performing local search on historical potential areas based on the radial basis function proxy model to locate historical high potential areas, determining historical optimal solutions according to historical high potential areas, performing real function evaluation on the historical optimal solutions and updating the population and the location of the historical optimal solutions in combination with feasibility rules: The historical potential area is determined by optimizing the maximum displacement constraints of all nodes corresponding to the sample points calculated by the objective evaluation function and the best Q sample points in the total mass of the structure. The first sub-dataset is constructed by the best Q sample points to form the historical potential area, and all samples in the first sub-dataset are used to construct the local radial basis function; The calculation formula of Q is: Q= round (20+ rd * range )； range =min([20*( m + n ), NFE -20,150]); In the formula, round express round function, rd is a random number, m is the number of integer design variables of angle steel side length, range Represents a variable, n is the number of node height continuous design variables, NFE The number of times the current function is evaluated; Among them, the calculation formula for the spatial range of local search is: ； ； i =1,…,Q； j =1,…, m + n ； Where: It represents the design variable in the local search space for local search of historical potential areas. j The lower limit of the dimension; It represents the design variable in the local search space for local search of historical potential areas. j The upper limit of the dimension; lb RBF represents the lower boundary vector consisting of the lower limits of all dimensions of the design variables in the local search space for the historical potential area; ub RBF represents the upper boundary vector consisting of the upper limits of all dimensions of the design variables in the local search space for local search of historical potential areas; It represents the lower limit of the first dimension of the design variable in the local search space for local search of historical potential areas; It represents the upper limit of the first dimension of the design variable in the local search space for local search of historical potential areas; represents the lower limit of the m+nth dimension of the design variable in the local search space for local search of historical potential areas; represents the upper limit of the m+nth dimension of the design variable in the local search space for local search of historical potential areas; Indicates the first sub-dataset i The sample in j The values ​​in the dimensions; Among them, the expression for determining the range of historical potential areas is: ； ； In the formula, j =1,…,m+n;minimize Indicates minimization of the constructed radial basis function proxy model; represents the radial basis function proxy model constructed for the objective evaluation function of the truss plane structure optimization; represents the radial basis function proxy model constructed for the optimization constraint evaluation function of the truss plane structure; st represents the constraint label that needs to be satisfied; Among them, in the steps of performing global pre-screening according to the pre-screening strategy of the radial basis function proxy model and combining the position of the historical optimal solution to obtain the global optimal solution, updating the population and the position of the global optimal solution according to the global optimal solution, and locating the global potential area according to the position of the global optimal solution: Use DE / best / 2 to generate candidate sub-generation solutions; An approximate model is constructed for the objective function and the constraint conditions according to the radial basis function surrogate model to approximately evaluate the candidate sub-generation solutions; Among them, in the step of performing a local search for the current potential area based on the Gaussian process agent model to locate the current high potential area, Obtain the position information of Q samples closest to the current solution to obtain the second sub-dataset; The current potential area is constructed based on the second sub-dataset, and a local Gaussian process is constructed using all samples in the second sub-dataset; Among them, the calculation formula for the spatial range of local search is: ； ； i =1,…,Q； j =1,…, m + n ； In the formula, It indicates that the design variable is the first in the local search space for the current potential area. j The lower limit of the dimension; It indicates that the design variable is the first in the local search space for the current potential area. j The upper limit of the dimension; lb Kriging represents the lower boundary vector consisting of the lower limits of all dimensions of the design variables in the local search space for the current potential area; ub Kriging represents the upper boundary vector consisting of the upper limits of all dimensions of the design variables in the local search space for the current potential area; It represents the lower limit of the first dimension of the design variable in the local search space for the current potential area; It represents the upper limit of the first dimension of the design variable in the local search space for the current potential area; It represents the lower limit of the design variable in the m+nth dimension in the local search space for the current potential area; They respectively represent the upper limit of the m+nth dimension of the design variable in the local search space for local search of the current potential area; Indicates the second sub-dataset i The sample in j The values ​​in the dimensions; Among them, the current range of potential areas is determined as follows: ； ； In the formula, j =1,…,m+n;minimize Indicates minimization of the constructed Gaussian process surrogate model. It represents the Gaussian process surrogate model constructed by using all sample data in the second sub-dataset to optimize the objective evaluation function of the truss plane structure; represents the Gaussian process agent model constructed for the optimization constraint evaluation function of the truss plane structure; st represents the constraint label that needs to be satisfied.

2. The dual-region collaborative optimization method based on global and local proxy models according to claim 1 is characterized in that: The steps of sampling the initial population sample points within the upper and lower bounds of the design space by the Latin hypercube sampling method include: Divide each dimension of the design space evenly into N intervals, where N is the initial population size; For each dimension, a random interval is randomly selected, and a uniformly distributed random number is generated in the selected interval according to the uniform distribution; Combine the random numbers of all dimensions into a vector, which is the individual of the current population; Return to the step of randomly selecting an interval for each dimension until the number of cycles reaches N-1 times to obtain N population individuals, that is, to obtain N population samples.

3. The dual-region collaborative optimization method based on global and local proxy models according to claim 1 is characterized in that: The steps of searching for unconnected feasible areas according to the pre-screening strategy of the Gaussian process surrogate model and combining the position of the current optimal solution to obtain the global optimal solution include: The cooperative mutation strategy based on variable types generates candidate offspring solutions; An approximate model is constructed for the objective function and the constraints according to the Gaussian process to approximately evaluate the candidate sub-generation solutions; The optimal offspring individual is selected from the evaluated candidate offspring solutions based on the complete expected improvement matrix function of the hypervolume; Perform true function evaluation on the selected optimal offspring individuals, and update the population and the position of the optimal solution; in: minimize F (x)={ f (x), G (x)}; x∈ off 2； In the formula, minimize F (x) represents minimization of the target vector composed of the objective function and the constraint violation value function; x represents an individual; f (x) represents the objective function expression for individual x; G (x) represents the constraint violation value function expression of the seismic individual x, G (x)=max(g(x),0); off 2 is the candidate sub-generation solution; The current Pareto front containing k non-dominated individuals is expressed as follows: ； In the formula, k represents the kth non-dominated individual; f k represents the objective function value for the kth non-dominated individual; G k represents the constraint violation function value for the kth non-dominated individual; Among them, the expression of the complete expected improvement matrix function based on the hypervolume is: ； In the formula, j Indicates j non-dominant individuals; r =( r f , r G ) is a reference point selected by the user, r f represents the objective function value corresponding to the reference point, r G Indicates the constraint violation function value corresponding to the reference point; f j Indicates j The target value of non-dominated individuals; G j express j Non-dominated individuals constrain the violation function value; express j The expected improvement of the objective function of non-dominated individuals; express j The expected improvement of the constraint violation function of non-dominated individuals; and The calculation formulas are: ； 。 4. A dual-region collaborative optimization system based on global and local agent models, characterized in that: The system comprises: An acquisition module is used to sample within the upper and lower bounds of a design space by a Latin hypercube sampling method to obtain initial population sample points, wherein the design space includes multiple design variables, including angle steel edge length integer design variables and node height continuous design variables, and to evaluate the fitness values ​​of the initial population sample points by optimizing the target evaluation function to form an initial sample population, wherein the initial sample population includes multiple series, and each series includes the values ​​of all design variables in the design space; The first optimization module is used to perform local search on historical potential areas based on the radial basis function proxy model to locate historical high potential areas, determine historical optimal solutions based on historical high potential areas, perform real function evaluation on the historical optimal solutions and update the population and the position of the historical optimal solutions in combination with feasibility rules; perform global pre-screening based on the pre-screening strategy of the radial basis function proxy model and in combination with the position of the historical optimal solutions to obtain the global optimal solution, update the population and the position of the global optimal solution based on the global optimal solution, and locate the global potential area based on the position of the global optimal solution; The second optimization module is used to perform a local search on the current potential area based on the Gaussian process proxy model to locate the current high potential area, determine the current optimal solution according to the current high potential area, perform a true function evaluation on the current optimal solution and update the population and the position of the current optimal solution in combination with the feasibility rule, search for unconnected feasible areas according to the pre-screening strategy of the Gaussian process proxy model and in combination with the position of the current optimal solution to obtain a global optimal solution, and obtain the values ​​of all design variables in the design space according to the global optimal solution to obtain an optimized truss plane structure; A judgment module is used to judge whether the optimized truss plane structure satisfies the maximum displacement constraints of all nodes and the total mass reduction of the structure at the same time; The first execution module is used for returning to the step of performing a local search for historical potential areas based on a radial basis function proxy model to locate historical high potential areas if the optimized truss plane structure cannot simultaneously satisfy the maximum displacement constraints of all nodes and the reduction of the total mass of the structure, until a maximum number of evaluations is reached, wherein the maximum number of evaluations is designed according to the actual engineering design cycle and the optimization accuracy requirements, and the key iteration parameters in the algorithm iteration process are initialized; The second execution module is used to optimize the truss plane structure by taking values ​​of integer design variables of all angle steel side lengths and continuous design variables of all node heights of the optimized truss plane structure to obtain the optimal truss plane structure if the optimized truss plane structure satisfies the maximum displacement constraints of all nodes and the total mass of the structure is reduced at the same time; Among them, in the step of performing local search on historical potential areas based on the radial basis function proxy model to locate historical high potential areas, determining historical optimal solutions according to historical high potential areas, performing real function evaluation on the historical optimal solutions and updating the population and the location of the historical optimal solutions in combination with feasibility rules: The historical potential area is determined by optimizing the maximum displacement constraints of all nodes corresponding to the sample points calculated by the objective evaluation function and the best Q sample points in the total mass of the structure. The first sub-dataset is constructed by the best Q sample points to form the historical potential area, and all samples in the first sub-dataset are used to construct the local radial basis function; The calculation formula of Q is: Q= round (20+ rd * range )； range =min([20*( m + n ), NFE -20,150]); In the formula, round express round function, rd is a random number, m is the number of integer design variables of angle steel side length, range Represents a variable, n is the number of node height continuous design variables, NFE The number of times the current function is evaluated; Among them, the calculation formula for the spatial range of local search is: ； ； i =1,…,Q； j =1,…, m + n ； Where: It represents the design variable in the local search space for local search of historical potential areas. j The lower limit of the dimension; It represents the design variable in the local search space for local search of historical potential areas. j The upper limit of the dimension; lb RBF represents the lower boundary vector consisting of the lower limits of all dimensions of the design variables in the local search space for the historical potential area; ub RBF represents the upper boundary vector consisting of the upper limits of all dimensions of the design variables in the local search space for local search of historical potential areas; It represents the lower limit of the first dimension of the design variable in the local search space for local search of historical potential areas; It represents the upper limit of the first dimension of the design variable in the local search space for local search of historical potential areas; represents the lower limit of the m+nth dimension of the design variable in the local search space for local search of historical potential areas; represents the upper limit of the m+nth dimension of the design variable in the local search space for local search of historical potential areas; Indicates the first sub-dataset i The sample in j The values ​​in the dimensions; Among them, the expression for determining the range of historical potential areas is: ； ； In the formula, j =1,…,m+n;minimize Indicates minimization of the constructed radial basis function proxy model; represents the radial basis function proxy model constructed for the objective evaluation function of the truss plane structure optimization; represents the radial basis function proxy model constructed for the optimization constraint evaluation function of the truss plane structure; st represents the constraint label that needs to be satisfied; Among them, in the steps of performing global pre-screening according to the pre-screening strategy of the radial basis function proxy model and combining the position of the historical optimal solution to obtain the global optimal solution, updating the population and the position of the global optimal solution according to the global optimal solution, and locating the global potential area according to the position of the global optimal solution: Use DE / best / 2 to generate candidate sub-generation solutions; An approximate model is constructed for the objective function and the constraint conditions according to the radial basis function surrogate model to approximately evaluate the candidate sub-generation solutions; Among them, in the step of performing a local search for the current potential area based on the Gaussian process agent model to locate the current high potential area, Obtain the position information of Q samples closest to the current solution to obtain the second sub-dataset; The current potential area is constructed based on the second sub-dataset, and a local Gaussian process is constructed using all samples in the second sub-dataset; Among them, the calculation formula for the spatial range of local search is: ； ； i =1,…,Q； j =1,…, m + n ； In the formula, It indicates that the design variable is the first in the local search space for the current potential area. j The lower limit of the dimension; It indicates that the design variable is the first in the local search space for the current potential area. j The upper limit of the dimension; lb Kriging represents the lower boundary vector consisting of the lower limits of all dimensions of the design variables in the local search space for the current potential area; ub Kriging represents the upper boundary vector consisting of the upper limits of all dimensions of the design variables in the local search space for the current potential area; It represents the lower limit of the first dimension of the design variable in the local search space for the current potential area; It represents the upper limit of the first dimension of the design variable in the local search space for the current potential area; It represents the lower limit of the design variable in the m+nth dimension in the local search space for the current potential area; They respectively represent the upper limit of the m+nth dimension of the design variable in the local search space for local search of the current potential area; Indicates the second sub-dataset i The sample in j The values ​​in the dimensions; Among them, the current range of potential areas is determined as follows: ； ； In the formula, j =1,…,m+n;minimize Indicates minimization of the constructed Gaussian process surrogate model. It represents the Gaussian process surrogate model constructed by using all sample data in the second sub-dataset to optimize the objective evaluation function of the truss plane structure; represents the Gaussian process agent model constructed for the optimization constraint evaluation function of the truss plane structure; st represents the constraint label that needs to be satisfied.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, a dual-region collaborative optimization method based on the assistance of global and local proxy models is implemented as described in any one of claims 1 to 3.

6. A data processing device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the dual-region collaborative optimization method based on the assistance of global and local proxy models as described in any one of claims 1 to 3 is implemented.

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