Double-region collaborative optimization method based on global and local agent model assistance

Abstract

The invention provides a double-region collaborative optimization method based on global and local agent model assistance, relates to the field of truss plane structure design optimization, and solves the problem of expensive constraint of mixed integer variables by adopting a double-layer collaborative framework to distinguish and process different types of variables. Specifically, the collaborative framework based on the radial basis function comprises a local search strategy based on a historical potential area and a pre-screening strategy based on radial basis function assistance; the mixed integer collaborative framework based on the Gaussian process comprises a local search strategy based on a current possible potential area and a pre-screening strategy based on Gaussian process assistance; a collaborative framework based on a radial basis function is utilized, the rapid convergence capability of a classic collaborative framework based on an agent model is fully exerted, and a high-potential area is rapidly positioned; a mixed integer collaborative framework based on a Gaussian process is used for searching non-connected feasible regions by providing a stable optimized trajectory, and the convergence and feasibility of high-potential regions are balanced.

Description

Technical Field

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

[0002] The optimization design problem of truss plane structure needs to minimize the total mass of the structure under 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 type of problem is a classic mixed variable expensive constrained optimization problem involving time-consuming simulation analysis.

[0003] An analysis and verification of structural displacement takes several minutes. Since the commonly used evolutionary methods usually require 5000D-10000D (D represents the number of design parameters in the design space) function evaluation to obtain a satisfactory feasible solution in the actual engineering scenario, but the computational cost required by these evolutionary methods is unbearable, so the introduction of surrogate models helps evolutionary methods deal with such problems. Such methods predict the constraints and target values ​​of candidate solutions by building 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 to quickly model and predict.

[0004] At present, two classic combinations between agents and evolutionary methods, namely agent-assisted pre-screening and agent-assisted local search, have been widely cooperated in different collaborative frameworks. It has been shown that such collaborative frameworks can effectively balance global exploration and local exploitation. None of them are developed to solve the expensive constraint problem with mixed integer variables, but to solve other similar problems, such as the expensive constraint problem with only continuous variables. In fact, there are few studies on designing efficient methods for the expensive constraint problem with mixed integer variables, and the existing studies do not design any collaborative framework. In addition, many evolutionary methods are designed for mixed variable problems, but the evaluation cost of objectives and constraints is low. These studies show that targeted evolutionary operations or optimization strategies are required for continuous variables and integer variables, respectively. Subsequently, the widely used collaborative frameworks usually drive the optimization based on predetermined priority rules of objectives and constraints such as locating feasible regions first and then optimizing feasible solutions. However, this leads to ineffectiveness in solving the classical disconnected feasible regions in the expensive constraint problem with mixed integer variables. Summary of the invention

[0005] Based on this, the purpose of the present invention is to provide a dual-region collaborative optimization method assisted by global and local proxy models, which is used to solve the technical problem in the prior art that the optimization method is driven by predetermined priority rules based on objectives and constraints such as first locating the feasible region and then optimizing the feasible solution, which is invalid when solving the classic disconnected feasible region in the expensive constraint problem of mixed integer variables.

[0006] On the one hand, the present invention provides a dual-region collaborative optimization method based on global and local proxy models, comprising: 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.

[0007] The above-mentioned dual-region collaborative optimization method assisted by global and local agent models 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 differentiated processing of different types of variables, which is used to 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 historical potential areas 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 current potential areas and a pre-screening strategy assisted by Gaussian processes; the collaborative framework based on radial basis functions is used to give full play to the fast convergence ability of the classic collaborative framework based on agent models, and to quickly locate high-potential areas; the mixed integer collaborative framework based on Gaussian processes is used to search for unconnected feasible areas by providing stable optimization trajectories, which well balances the convergence and feasibility of these high-potential areas.

[0008] In addition, the dual-region collaborative optimization method based on the assistance of global and local proxy models according to the present invention may also have the following additional technical features: Furthermore, 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: 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.

[0009] Further, in the step of performing a 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 the historical high potential areas, performing real function evaluation on the historical optimal solutions, and updating the population and the position 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.

[0010] Furthermore, 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 constraints based on the radial basis function surrogate model to approximately evaluate the candidate sub-solutions.

[0011] Furthermore, in the step of performing a local search on the current potential area based on the Gaussian process agent model to locate the current high potential area, Obtain the position information of the 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 Krigingrepresents 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 local search of 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 expression for determining the range of the current potential area is: ; ; 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.

[0012] Furthermore, the steps of searching for unconnected feasible areas according to the pre-screening strategy of the Gaussian process proxy 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: ; .

[0013] Another aspect of the present invention provides a dual-region collaborative optimization system assisted by global and local proxy models, the system comprising: An acquisition module is used to sample within the upper and lower bounds of the 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 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 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.

[0014] Another aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the dual-region collaborative optimization method assisted by global and local proxy models as described above.

[0015] On the other hand, the present invention also provides a data processing device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the dual-region collaborative optimization method based on the assistance of global and local proxy models as described above is implemented. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flow chart of a dual-region collaborative optimization method based on the assistance of global and local proxy models in the first embodiment of the present invention; Figure 2 It is a system block diagram of a dual-region collaborative optimization system assisted by global and local proxy models in the second embodiment of the present invention; The following specific implementation manner will further illustrate the present invention in conjunction with the above-mentioned drawings. DETAILED DESCRIPTION

[0017] In order to facilitate the understanding of the present invention, the present invention will be described more fully 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, the purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive.

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art 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.

[0019] In order to solve the technical problem that the methods in the prior art that drive the optimization based on predetermined priority rules of objectives and constraints such as first locating feasible regions and then optimizing feasible solutions are invalid when solving the classic disconnected feasible regions in the expensive constraint problem of mixed integer variables, the present application provides a dual-region collaborative optimization method assisted by global and local agent models, which 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 differentiated processing of different types of variables, and is used to 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 historical potential regions 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 current potential regions and a pre-screening strategy assisted by Gaussian processes; the collaborative framework based on radial basis functions is used to give full play to the fast convergence ability of the classic collaborative framework based on agent models, and quickly locate high potential regions; the mixed integer collaborative framework based on Gaussian processes is used to search for disconnected feasible regions by providing stable optimization trajectories, which well balances the convergence and feasibility of these high potential regions.

[0020] In order to facilitate understanding of the present invention, several embodiments of the present invention are provided below. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive.

[0021] Embodiment 1 See also Figure 1 , which shows a dual-region collaborative optimization method based on global and local proxy models in the first embodiment of the present invention, including steps S101 to S108: S101. Sampling is performed 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, including angle steel side length integer design variables and node height continuous design variables. The fitness values ​​of the initial population sample points are 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 design variables in the design space.

[0022] In this embodiment, the step 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 includes: evenly dividing each dimension of the design space into N intervals, where N is the initial population size; randomly selecting an interval for each dimension, and generating a uniformly distributed random number in the selected interval according to a uniform distribution; merging the random numbers of all dimensions into a vector, which is the current population individual; returning to execute 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.

[0023] S102. 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, and the historical optimal solution is determined based on 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.

[0024] In this embodiment, 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, and 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.

[0025] S103, 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.

[0026] Specifically, DE / best / 2 is used to generate candidate sub-solutions; an approximate model is constructed for the objective function and constraints based on a radial basis function surrogate model to approximately evaluate the candidate sub-solutions.

[0027] S104, 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.

[0028] In the step of performing a local search for the current potential area based on the Gaussian process proxy model to locate the current high potential area: obtaining the position information of Q samples closest to the current solution to obtain a second sub-dataset; constructing the current potential area based on the second sub-dataset, and using all samples in the second sub-dataset to construct a local Gaussian process; 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 local search of 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 expression for determining the range of the current potential area is: ; ; 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.

[0029] S105, searching for unconnected feasible regions 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 obtaining the values ​​of all design variables in the design space according to the global optimal solution to obtain an optimized truss plane structure.

[0030] In this embodiment, the steps of searching for unconnected feasible areas according to the pre-screening strategy of the Gaussian process proxy model and combining the position of the current optimal solution to obtain the global optimal solution include: Generate candidate offspring solutions based on the cooperative mutation strategy of variable types; construct an approximate model for the objective function and constraints according to the Gaussian process to approximately evaluate the candidate offspring solutions; select the best offspring individuals from the evaluated candidate offspring solutions based on the complete expected improvement matrix function of the hypervolume; perform true function evaluation on the selected best offspring individuals, and update the population and the position of the best solution; Where: 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 krepresents 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: ; .

[0031] S106. Determine 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.

[0032] 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, step S107 is executed; if the optimized truss plane structure can simultaneously satisfy the maximum displacement constraints of all nodes and the reduction of the total mass of the structure, step S108 is executed.

[0033] S107. Determine whether the number of optimization times reaches the maximum number of evaluation times. If the number of optimization times does not reach the maximum number of evaluation times, return to execute step S102; if the number of optimization times reaches the maximum number of evaluation times, execute step S108; wherein, the maximum number of evaluation times 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.

[0034] S108. Optimize the truss plane structure based on 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.

[0035] In summary, the dual-region collaborative optimization method based on the assistance of global and local agent models in the above-mentioned 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 differentiated processing of variables of different types, and is used to 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 historical potential areas 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 current potential areas and a pre-screening strategy assisted by Gaussian processes; the collaborative framework based on radial basis functions is utilized to give full play to the fast convergence ability of the classic collaborative framework based on agent models, and to quickly locate high-potential areas; the mixed integer collaborative framework based on Gaussian processes is utilized to search for unconnected feasible areas by providing stable optimization trajectories, which well balances the convergence and feasibility of these high-potential areas.

[0036] Embodiment 2 See also Figure 2 , which shows a dual-region collaborative optimization system based on global and local proxy models in the second embodiment of the present invention, the system includes: An acquisition module is used to sample within the upper and lower bounds of the 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 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 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.

[0037] In summary, the dual-region collaborative optimization system assisted by global and local agent models in the above-mentioned 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 differentiated processing of different types of variables, which is used to 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 historical potential areas 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 current potential areas and a pre-screening strategy assisted by Gaussian processes; the collaborative framework based on radial basis functions is used to give full play to the fast convergence ability of the classic collaborative framework based on agent models, and to quickly locate high-potential areas; the mixed integer collaborative framework based on Gaussian processes is used to search for unconnected feasible areas by providing stable optimization trajectories, which well balances the convergence and feasibility of these high-potential areas.

[0038] In addition, an embodiment of the present invention further provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps of the method in the above embodiment are implemented.

[0039] In addition, an embodiment of the present invention further provides a data processing device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the method in the above embodiment when executing the program.

[0040] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0041] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or processing in another suitable manner as necessary, and then stored in a computer memory.

[0042] 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-mentioned embodiments, 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, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0043] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0044] Although the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that 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.

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: In the step of performing a local search on historical potential areas based on a radial basis function proxy model to locate historical high potential areas, determining historical optimal solutions based on 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 local search of historical potential areas; 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.

4. The dual-region collaborative optimization method based on global and local proxy models as claimed in claim 3 is characterized in that: In the steps of performing global pre-screening based on 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 based on the global optimal solution, and locating the global potential area based on 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 constraints based on the radial basis function surrogate model to approximately evaluate the candidate sub-solutions.

5. The dual-region collaborative optimization method based on global and local proxy models according to claim 1 is characterized in that: 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 the 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 local search of 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 expression for determining the range of the current potential area is: ； ； 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.

6. The dual-region collaborative optimization method based on global and local proxy models as claimed in claim 5 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: ； 。 7. 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 the 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 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 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.

8. 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 6.

9. 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 is implemented as described in any one of claims 1 to 6.

Images