CN113139334A - Simulation optimization method based on bee colony - Google Patents

Simulation optimization method based on bee colony Download PDF

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CN113139334A
CN113139334A CN202110373384.1A CN202110373384A CN113139334A CN 113139334 A CN113139334 A CN 113139334A CN 202110373384 A CN202110373384 A CN 202110373384A CN 113139334 A CN113139334 A CN 113139334A
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柳培忠
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Abstract

The invention provides a simulation optimization method based on a bee colony, which comprises the following steps: step 10, random sampling is carried out, n samples are extracted to serve as an initial sample point set, and an optimization process convergence error w is defined; step 20, constructing a mathematical model, and screening out m sample points meeting a multidisciplinary coupling equation; step 30, constructing different agent models through the m sample points, wherein the agent models comprise an RSM model, an RBF model and a Kriging model; step 40, verifying and confirming the agent model; step 50, constructing an optimization framework by combining an artificial bee colony algorithm to obtain a global optimal solution; and step 60, the EDA platform demodulates the parameters of the whole product design according to the global optimum, and then carries out simulation to obtain an optimized product model. The method can improve the global optimization capability, shorten the design period of engineering products and provide possibility for solving the design problem of modern engineering more effectively.

Description

Simulation optimization method based on bee colony
Technical Field
The invention relates to the field of EDA tool simulation optimization, in particular to a swarm-based simulation optimization method.
Background
With the rapid development of computer aided design technology, EDA technology has been applied to various stages in the product design process for improving the efficiency of product design. However, as the application of EDA technology in the field of electronic information increases, the coverage area increases, and some deep-level design service problems are faced. In the product design process, the design tool software is mature in the calculation analysis and the optimization design of respective field disciplines; however, tool software needed to be used in complex system design engineering is numerous, and it is difficult to establish a unified multidisciplinary design analysis and optimization mathematical model, which is a current urgent problem to be considered. To this end, the present inventors have developed a bee colony simulation-based optimization method to solve the above-mentioned problems.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a bee colony-based simulation optimization method, improve the global optimization capability, shorten the design period of engineering products and provide possibility for solving the modern engineering design problem more effectively.
The invention provides a simulation optimization method based on a bee colony, which comprises the following steps:
step 10, random sampling is carried out, n samples are extracted to serve as an initial sample point set, and an optimization process convergence error w is defined;
step 20, constructing a mathematical model, and screening out m sample points meeting a multidisciplinary coupling equation;
step 30, constructing different agent models through the m sample points, wherein the agent models comprise an RSM model, an RBF model and a Kriging model;
step 40, verifying and confirming the agent model;
step 50, constructing an optimization framework by combining an artificial bee colony algorithm to obtain a global optimal solution;
and step 60, the EDA platform demodulates the parameters of the whole product design according to the global optimum, and then carries out simulation to obtain an optimized product model.
Further, the random sampling is extracted by adopting a Latin hypercube sampling method.
Further, the step 20 further includes:
step 21, establishing a system level optimization and subject level optimization mathematical model, wherein the system level optimization mathematical model is expressed by the following formula:
min.F(z)
s.t.
Figure BDA0003010239330000021
wherein F (z) is an objective function of the entire system,
Figure BDA0003010239330000022
is to coordinate the consistency of the kth sub-disciplineThe bundle of the light-emitting diode is,
Figure BDA0003010239330000023
is the design vector optimization value, z, passed from the sub-discipline kkIn system level and in sub-discipline k
Figure BDA0003010239330000024
The corresponding shared design vector, epsilon is a relaxation factor, and the system level constraint conditions of the multidisciplinary optimization problem are set as follows:
Figure BDA0003010239330000025
Figure BDA0003010239330000026
wherein z is a shared design vector between disciplines,
Figure BDA0003010239330000027
is to reconcile the consistency constraint of the kth sub-discipline,
Figure BDA0003010239330000028
is to coordinate the consistency constraint of the (k + 1) th sub-discipline, lambda is a coefficient,
Figure BDA0003010239330000029
is optimized by the design vector of the sub-discipline k,
Figure BDA00030102393300000210
is the design vector optimization value of the sub-discipline k + 1;
step 22, setting the design vector initial target value (z) of the system level optimization problem*)0And assigning it to each sub-discipline;
step 23, executing the optimization process of the sub-disciplines to obtain the optimal solution of the design vector of each sub-discipline
Figure BDA00030102393300000211
And returns to the system level;
24, relaxing the consistency constraint condition of the system-level optimization mathematical model according to the value of the relaxation factor epsilon;
step 25, solving the system level optimization problem to obtain the optimal solution (z) of the design vector*)bestTaking the target value as a target value assigned to the sub-discipline in the next iteration step;
step 26, comparing the optimal solution (F) of the objective function at the system level*)bestObjective function value (F) corresponding to the target value of the design variable previously transmitted to the science level*)best-1If the difference value is within the convergence error range w, the iteration is ended to obtain a final optimization result, otherwise, the step 22 is skipped;
step 27, repeating steps 22 to 26 until convergence;
and step 28, screening m feasible sample points meeting multiple disciplines, and arranging the sample points in ascending order according to the dimension D value.
Further, the formula for calculating the relaxation factor epsilon in step 24 is as follows:
ε＝(λ×Δ)2；
Figure BDA0003010239330000031
wherein Δ represents the amount of inconsistency between the sub-discipline k and the sub-discipline k +1,
Figure BDA0003010239330000032
and
Figure BDA0003010239330000033
respectively are the optimal solutions of the design vectors from the two sub-disciplines in the optimization process, and lambda is a coefficient.
Further, the calculation and comparison formula of the difference value in step 26 is as follows:
Figure BDA0003010239330000034
wherein (F)*)best-1For the value of the objective function obtained in the previous iteration of the final iteration, (F)*)bestAnd w is the convergence error for the optimal value of the objective function obtained by the final iteration.
Further, the step 50 further includes:
step 51, initializing an ABC algorithm, setting an initial population N, an individual dimension D, a maximum iteration number M, a threshold limit, an iteration number cycle of 0, and a counter trials of 0;
step 52, constructing an ALM function, and initializing and setting a Lagrange multiplier lambda0＝0，δ00, and 1;
step 53, generating an initial population, and performing initialization population by adopting the following formula:
Figure BDA0003010239330000035
wherein the content of the first and second substances,
Figure BDA0003010239330000036
is the jth individual of the 0 th generation population, N is the initial population number,
Figure BDA0003010239330000037
and
Figure BDA0003010239330000038
respectively setting the dimension of a design variable x as n and the dimension of an individual as D, wherein the n and the D are equal;
step 54, calculating the fitness value of the individual based on the ALM function, selecting the better half as the leading bee population and the other half as the observing bee population, wherein the fitness value calculation formula of the individual is as follows:
fitj＝0.1/(0.1+1/|lgf(xj)),0≤f(xj)≤10-γ；
therein, fitjIs a fitness value of the individual, f: (xj) Representing a new individual
Figure BDA0003010239330000047
The corresponding function value, γ ═ 8;
step 55, performing the search of the leading bees, generating new individuals, selecting more optimal individuals to update the leading bee population, wherein the generation mode of the new individuals is as follows:
Figure BDA0003010239330000041
Figure BDA0003010239330000042
the cell is a new individual, and the cell is a new individual,
Figure BDA0003010239330000043
represents the ith dimension in the jth generation, j ∈ [1, N [ ]]，i∈[1,D]And r is the number of randomly selected individuals for cross search, r belongs to {1, 2., N/2} and r is not equal to j, individual preference is carried out, and the leading bee population is updated in the following mode:
Figure BDA0003010239330000044
and 56, searching for observation bees, searching for new individuals and updating the observation bee population according to the following formula in a roulette mode based on the superior individuals in the previous step:
Figure BDA0003010239330000045
step 57, searching for scout bees, and combining the leading bee population and the observation bee population in the two steps to form an iterative population;
step 58, judging whether the trial limit is established, if so, skipping to step 57 to enter a scout bee stage to generate a new iterative population; otherwise, the current solution is the optimal solution, and the step 59 is carried out;
step 59, judging whether the iteration times are smaller than the maximum iteration times, if so, updating the augmented Lagrange multiplier according to an iteration formula of the Lagrange multiplier, and returning to the step 54 for next iteration; otherwise, outputting the optimal solution and finishing the optimization.
Further, the ALM function is specifically as follows:
Figure BDA0003010239330000046
wherein f (x) is an objective function, hi(x) For equality constraint, gi(x) Is inequality constraint, λiAnd deltajIs lagrange multiplier, σiAnd σjIs a constant, penalty factor;
a is saidjExpressed as:
Figure BDA0003010239330000051
further, the iterative formula of the lagrangian multiplier is as follows:
Figure BDA0003010239330000052
Figure BDA0003010239330000053
the invention has the advantages that: the method combines the collaborative optimization and the artificial bee colony algorithm to form a new simulation optimization method, effectively improves the convergence of the collaborative optimization method by adopting a dynamic relaxation factor method, screens out an effective sample set according to a mathematical model and constructs a plurality of agent models, and then constructs an optimization framework by combining the artificial bee colony algorithm, so that the method has higher accuracy and high efficiency on the global optimization capability, thereby shortening the design period of engineering products and rapidly coping with various engineering design problems.
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The invention will be further described with reference to the following examples with reference to the accompanying drawings.
Fig. 1 is an execution flow chart of a swarm simulation optimization-based method according to the present invention.
Detailed Description
As shown in fig. 1, a bee colony simulation-based optimization method of the present invention includes:
step 10, random sampling is carried out, n samples are extracted to serve as an initial sample point set, and an optimization process convergence error w is defined; preferably, the random sampling is extracted by a Latin hypercube sampling method.
Step 20, constructing a mathematical model, and screening out m sample points meeting a multidisciplinary coupling equation;
preferably, the step 20 further includes steps 21 to 27:
step 21, establishing a system level optimization and subject level optimization mathematical model according to a structural framework of the collaborative optimization method, wherein the system level optimization mathematical model is expressed by the following formula:
min.F(z)
s.t.
Figure BDA0003010239330000054
wherein F (z) is an objective function of the entire system,
Figure BDA0003010239330000055
is to reconcile the consistency constraint of the kth sub-discipline,
Figure BDA0003010239330000061
is the design vector optimization value, z, passed from the sub-discipline kkIn system level and in sub-discipline k
Figure BDA0003010239330000062
The corresponding shared design vector, epsilon is a relaxation factor and is a tiny positive number, and the system-level constraint condition (namely, the discipline-level optimization mathematical model) of the multidisciplinary optimization problem is set as follows:
Figure BDA0003010239330000063
Figure BDA0003010239330000064
wherein z is a shared design vector between disciplines,
Figure BDA0003010239330000065
is to reconcile the consistency constraint of the kth sub-discipline,
Figure BDA0003010239330000066
is to coordinate the consistency constraint of the (k + 1) th sub-discipline, wherein lambda is a coefficient used for determining a feasible domain for the system-level optimization problem,
Figure BDA0003010239330000067
is optimized by the design vector of the sub-discipline k,
Figure BDA0003010239330000068
is the design vector optimization value of the sub-discipline k + 1;
step 22, setting the design vector initial target value (z) of the system level optimization problem*)0And assigning it to each sub-discipline;
step 23, executing the optimization process of the sub-disciplines to obtain the optimal solution of the design vector of each sub-discipline
Figure BDA0003010239330000069
And returns to the system level;
24, relaxing the consistency constraint condition of the system-level optimization mathematical model according to the value of the relaxation factor epsilon; preferably, the formula for calculating the relaxation factor epsilon is as follows:
ε＝(λ×Δ)2；
Figure BDA00030102393300000610
wherein Δ represents the amount of inconsistency between the sub-discipline k and the sub-discipline k +1,
Figure BDA00030102393300000611
and
Figure BDA00030102393300000612
respectively are the optimal solution of the design vectors from the two sub-disciplines in the optimization process, and lambda is a coefficient and is used for determining a feasible domain for the system level optimization problem.
Step 25, solving the system level optimization problem to obtain the optimal solution (z) of the design vector*)bestTaking the target value as a target value assigned to the sub-discipline in the next iteration step;
step 26, comparing the optimal solution (F) of the objective function at the system level*)bestObjective function value (F) corresponding to the target value of the design variable previously transmitted to the science level*)best-1If the difference value is within the convergence error range w, the iteration is ended to obtain a final optimization result, otherwise, the step 22 is skipped; the calculation and comparison formula of the difference value is as follows:
Figure BDA0003010239330000071
wherein (F)*)best-1For the value of the objective function obtained in the previous iteration of the final iteration, (F)*)bestFor the optimal value of the objective function obtained by final iteration, w is the convergence error;
step 27, repeating steps 22 to 26 until convergence;
and step 28, screening m feasible sample points meeting multiple disciplines, and arranging the sample points in ascending order according to the dimension D value.
Step 30, constructing different agent models through the m sample points, wherein the agent models comprise an RSM model, an RBF model and a Kriging model;
step 40, verifying and confirming the agent model; the method uses three agent models, one of the three agent models is finally judged to be the optimal agent model through an evaluation criterion, the calculation efficiency is improved, the robustness is better, and the optimal agent model can be selected through cross validation and testing for subsequent optimization calculation;
and step 50, constructing an optimization framework by combining an artificial bee colony algorithm to obtain a global optimal solution. And constructing an optimization framework by combining an artificial bee colony algorithm based on the agent model constructed in the steps, and obtaining an optimal value through simulation optimization.
Preferably, the step 50 further comprises:
step 51, initializing an ABC algorithm, setting an initial population N, an individual dimension D, a maximum iteration number M, a threshold limit, an iteration number cycle of 0, and a counter trials of 0;
step 52, constructing an ALM function, and initializing and setting a Lagrange multiplier lambda0＝0，δ00, and 1; preferably, the ALM function is specifically as follows:
Figure BDA0003010239330000072
wherein f (x) is an objective function, hi(x) For equality constraint, gi(x) Is inequality constraint, λiAnd deltajIs lagrange multiplier, σiAnd σjFor the penalty factor, it is a constant, and can take a suitable positive number;
a is saidjExpressed as:
Figure BDA0003010239330000073
step 53, generating an initial population, and performing initialization population by adopting the following formula:
Figure BDA0003010239330000081
wherein the content of the first and second substances,
Figure BDA0003010239330000082
is the jth individual of the 0 th generation population, N is the initial population number,
Figure BDA0003010239330000083
and
Figure BDA0003010239330000084
respectively setting the dimension of a design variable x as n and the dimension of an individual as D, wherein the n and the D are equal;
step 54, calculating the fitness value of the individual based on the ALM function, selecting the better half as the leading bee population and the other half as the observing bee population, wherein the fitness value calculation formula of the individual is as follows:
fitj＝0.1/(0.1+1/|lgf(xj)),0≤f(xj)≤10-γ；
therein, fitjIs the fitness value of the individual, f (x)j) Representing a new individual VjThe corresponding function value, gamma is determined by the calculation precision of the computer, and gamma is 8;
step 55, performing the search of the leading bees, generating new individuals, selecting more optimal individuals to update the leading bee population, wherein the generation mode of the new individuals is as follows:
Figure BDA0003010239330000085
Figure BDA0003010239330000086
the cell is a new individual, and the cell is a new individual,
Figure BDA0003010239330000087
represents the ith dimension in the jth generation, j ∈ [1, N [ ]]，i∈[1,D]And r is the number of randomly selected individuals for cross search, r belongs to {1, 2., N/2} and r is not equal to j, individual preference is carried out, and the leading bee population is updated in the following mode:
Figure BDA0003010239330000088
and 56, searching for observation bees, searching for new individuals and updating the observation bee population according to the following formula in a roulette mode based on the superior individuals in the previous step:
Figure BDA0003010239330000089
step 57, searching for scout bees, and combining the leading bee population and the observation bee population in the two steps to form an iterative population;
step 58, judging whether the trial limit is established, if so, skipping to step 57 to enter a scout bee stage to generate a new iterative population; otherwise, the current solution is the optimal solution, and the step 59 is carried out;
step 59, judging whether the iteration times are smaller than the maximum iteration times, if so, updating the augmented Lagrange multiplier according to an iteration formula of the Lagrange multiplier, and returning to the step 54 for next iteration; otherwise, outputting the optimal solution and finishing the optimization. The iterative formula of the lagrange multiplier is as follows:
Figure BDA0003010239330000091
Figure BDA0003010239330000092
and step 60, the EDA platform demodulates the parameters of the whole product design according to the global optimum, and then carries out simulation to obtain an optimized product model.
The invention combines a collaborative optimization method with an improved artificial bee colony algorithm to form a new simulation optimization method, screens out an effective sample set and constructs a plurality of agent models by adopting a dynamic relaxation factor method to construct a mathematical model, selects an optimal agent model to construct a multidisciplinary optimization model, introduces an augmented Lagrange multiplier method on the artificial bee colony method, solves the complex equality constraint condition contained in the mathematical model, updates a fitness calculation method, and finally constructs an optimization framework, so that the method has higher convergence, accuracy and high efficiency, and when the solution obtained by the process is applied to the design of each parameter (such as the thinness of the material adopted by a chip product) in the design process of a corresponding product in an EDA tool, the parameter can be optimized on an EDA platform according to the obtained optimal solution after the method is adopted, and then carrying out simulation to obtain a thin layer model after the chip material is optimized), and realizing the optimization of product design.
Although specific embodiments of the invention have been described above, it will be understood by those skilled in the art that the specific embodiments described are illustrative only and are not limiting upon the scope of the invention, and that equivalent modifications and variations can be made by those skilled in the art without departing from the spirit of the invention, which is to be limited only by the appended claims.

Claims (8)

1. A simulation optimization method based on bee colony is characterized in that: the method comprises the following steps:
step 10, random sampling is carried out, n samples are extracted to serve as an initial sample point set, and an optimization process convergence error w is defined;
step 20, constructing a mathematical model, and screening out m sample points meeting a multidisciplinary coupling equation;
step 30, constructing different agent models through the m sample points, wherein the agent models comprise an RSM model, an RBF model and a Kriging model;
step 40, verifying and confirming the agent model;
step 50, constructing an optimization framework by combining an artificial bee colony algorithm to obtain a global optimal solution;
and step 60, the EDA platform demodulates the parameters of the whole product design according to the global optimum, and then carries out simulation to obtain an optimized product model.
2. The bee colony simulation-based optimization method of claim 1, wherein: and the random sampling adopts a Latin hypercube sampling method for extraction.
3. The bee colony simulation-based optimization method of claim 1, wherein: the step 20 further comprises:
step 21, establishing a system level optimization and subject level optimization mathematical model, wherein the system level optimization mathematical model is expressed by the following formula:
min.F(z)
Figure FDA0003010239320000011
wherein F (z) is an objective function of the entire system,
Figure FDA0003010239320000012
is to reconcile the consistency constraint of the kth sub-discipline,
Figure FDA0003010239320000013
is the design vector optimization value, z, passed from the sub-discipline kkIn system level and in sub-discipline k
Figure FDA0003010239320000014
The corresponding shared design vector, epsilon is a relaxation factor, and the system level constraint conditions of the multidisciplinary optimization problem are set as follows:
Figure FDA0003010239320000015
Figure FDA0003010239320000016
wherein z is a shared design vector between disciplines,
Figure FDA0003010239320000021
is to reconcile the consistency constraint of the kth sub-discipline,
Figure FDA0003010239320000022
is to coordinate the consistency constraint of the (k + 1) th sub-discipline, lambda is a coefficient,
Figure FDA0003010239320000023
is optimized by the design vector of the sub-discipline k,
Figure FDA0003010239320000024
is the design vector optimization value of the sub-discipline k + 1;
step 22, setting the design vector initial target value (z) of the system level optimization problem*)0And assigning it to each sub-discipline;
step 23, executing the optimization process of the sub-disciplines to obtain the optimal solution of the design vector of each sub-discipline
Figure FDA0003010239320000025
And returns to the system level;
24, relaxing the consistency constraint condition of the system-level optimization mathematical model according to the value of the relaxation factor epsilon;
step 25, solving the system level optimization problem to obtain the optimal solution (z) of the design vector*)bestTaking the target value as a target value assigned to the sub-discipline in the next iteration step;
step 26, comparing the optimal solution (F) of the objective function at the system level*)bestObjective function value (F) corresponding to the target value of the design variable previously transmitted to the science level*)best-1If the difference value is within the convergence error range w, the iteration is ended to obtain a final optimization result, otherwise, the step 22 is skipped;
step 27, repeating steps 22 to 26 until convergence;
and step 28, screening m feasible sample points meeting multiple disciplines, and arranging the sample points in ascending order according to the dimension D value.
4. A bee colony simulation-based optimization method according to claim 3, characterized in that:
the formula for calculating the relaxation factor epsilon in step 24 is as follows:
ε＝(λ×Δ)2；
Figure FDA0003010239320000026
wherein Δ represents the amount of inconsistency between the sub-discipline k and the sub-discipline k +1,
Figure FDA0003010239320000027
and
Figure FDA0003010239320000028
respectively are the optimal solutions of the design vectors from the two sub-disciplines in the optimization process, and lambda is a coefficient.
5. A bee colony simulation-based optimization method according to claim 3, characterized in that:
the calculation and comparison formula of the difference in step 26 is as follows:
Figure FDA0003010239320000029
wherein (F)*)best-1For the value of the objective function obtained in the previous iteration of the final iteration, (F)*)bestAnd w is the convergence error for the optimal value of the objective function obtained by the final iteration.
6. The bee colony simulation-based optimization method of claim 1, wherein: the step 50 further comprises:
step 51, initializing an ABC algorithm, setting an initial population N, an individual dimension D, a maximum iteration number M, a threshold limit, an iteration number cycle of 0, and a counter trials of 0;
step 52, constructing an ALM function, and initializing and setting a Lagrange multiplier lambda0＝0，δ00, and 1;
step 53, generating an initial population, and performing initialization population by adopting the following formula:
Figure FDA0003010239320000031
wherein the content of the first and second substances,
Figure FDA0003010239320000032
is the jth individual of the 0 th generation population, N is the initial population number,
Figure FDA0003010239320000033
and
Figure FDA0003010239320000034
respectively setting the dimension of a design variable x as n and the dimension of an individual as D, wherein the n and the D are equal;
step 54, calculating the fitness value of the individual based on the ALM function, selecting the better half as the leading bee population and the other half as the observing bee population, wherein the fitness value calculation formula of the individual is as follows:
fitj＝0.1/(0.1+1/|lgf(xj)|),0≤f(xj)≤10-γ；
therein, fitjIs the fitness value of the individual, f (x)j) Representing a new individual
Figure FDA0003010239320000035
The corresponding function value, γ ═ 8;
step 55, performing the search of the leading bees, generating new individuals, selecting more optimal individuals to update the leading bee population, wherein the generation mode of the new individuals is as follows:
Figure FDA0003010239320000036
Figure FDA0003010239320000037
the cell is a new individual, and the cell is a new individual,
Figure FDA0003010239320000038
represents the ith dimension in the jth generation, j ∈ [1, N [ ]]，i∈[1,D]And r is the number of randomly selected individuals for cross search, r belongs to {1, 2., N/2} and r is not equal to j, individual preference is carried out, and the leading bee population is updated in the following mode:
Figure FDA0003010239320000039
and 56, searching for observation bees, searching for new individuals and updating the observation bee population according to the following formula in a roulette mode based on the superior individuals in the previous step:
Figure FDA0003010239320000041
step 57, searching for scout bees, and combining the leading bee population and the observation bee population in the two steps to form an iterative population;
step 58, judging whether the trial limit is established, if so, skipping to step 57 to enter a scout bee stage to generate a new iterative population; otherwise, the current solution is the optimal solution, and the step 59 is carried out;
step 59, judging whether the iteration times are smaller than the maximum iteration times, if so, updating the augmented Lagrange multiplier according to an iteration formula of the Lagrange multiplier, and returning to the step 54 for next iteration; otherwise, outputting the optimal solution and finishing the optimization.
7. The bee colony simulation-based optimization method of claim 6, wherein: the ALM function is specifically as follows:
Figure FDA0003010239320000042
wherein f (x) is an objective function, hi(x) For equality constraint, gi(x) Is inequality constraint, λiAnd deltajIs lagrange multiplier, σiAnd σjIs a constant, penalty factor;
a is saidjExpressed as:
Figure FDA0003010239320000043
8. the bee colony simulation-based optimization method of claim 6, wherein: the iterative formula of the lagrange multiplier is as follows:
Figure FDA0003010239320000044
Figure FDA0003010239320000045
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113987806A (en) * 2021-10-29 2022-01-28 吉林大学 Atmospheric mode optimization method based on proxy model

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113987806A (en) * 2021-10-29 2022-01-28 吉林大学 Atmospheric mode optimization method based on proxy model
CN113987806B (en) * 2021-10-29 2024-04-26 吉林大学 Atmosphere mode optimization method based on proxy model

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Application publication date: 20210720