Surrogate model-assisted parallel collaborative approach for high-dimensional expensive optimization problems

Abstract

The present invention discloses a parallel collaborative method assisted by an agent model for high-dimensional expensive optimization problems, including: (1) determining a design space and an optimization target, initializing a population and key iteration parameters, and providing a convergence condition; (2) constructing a parallel dimensional perturbation mutation operation based on a multi-objective non-dominated sorting technique; (3) constructing a two-layer real offspring individual screening mechanism based on local prediction information and individual distribution; (4) using DE / current-to-pbest / 2 / bin to perform collaborative mutation guided by high-potential individuals; (5) constructing a two-layer real offspring individual screening mechanism based on global prediction information and individual distribution; (6) designing a local search strategy based on a local radial basis function; (7) updating population and key iteration parameter information, judging whether the convergence condition is reached, and outputting an optimized solution if converged, otherwise going to step (2) until the convergence condition is reached. The present invention can accelerate the convergence speed, and has strong applicability and good flexibility for high-dimensional problems.

Description

Technical Field

[0001] The present invention relates to the field of computer technology, and more specifically, to a parallel collaborative method assisted by an agent model for high-dimensional expensive optimization problems. Background Art

[0002] Practical engineering optimization problems usually involve time-consuming simulation analysis. For example, in the optimization design of vehicle body structures, multiple complex simulation analyses are often required. Each simulation analysis takes several minutes to several hours of computation time. This makes it impossible for traditional optimization algorithms such as gradient optimization algorithms or evolutionary algorithms to effectively handle such practical engineering optimization problems involving time-consuming simulation analysis. Therefore, how to effectively solve these problems remains a common technical difficulty faced by the field of engineering optimization.

[0003] In recent years, evolutionary algorithms assisted by machine learning models (also called proxy models) can effectively integrate the high-precision learning ability of machine learning with the global optimization ability of evolutionary algorithms, thereby accelerating the overall optimization speed of the algorithm. In this type of method, the modeling efficiency and prediction speed of machine learning models such as radial basis functions are significantly faster than the time-consuming simulation analysis required in actual engineering, and this type of model can give accurate prediction outputs for new parameter inputs. Therefore, machine learning models can be used to screen a large number of offspring individuals generated during the optimization process of evolutionary algorithms, ensuring that time-consuming simulation analysis is only used for high-potential offspring individuals, significantly reducing the number of time-consuming simulation analyses required during the optimization process of evolutionary algorithms, and ensuring that satisfactory feasible optimization solutions are obtained within an acceptable design cycle.

[0004] However, the existing evolutionary algorithms assisted by machine learning models cannot effectively deal with the two major technical difficulties brought about by a large number of design variables in the field of engineering optimization: first, the design space grows exponentially with the increase of design variables, resulting in low efficiency of algorithm optimization; second, the prediction accuracy of machine learning models has the "dimensionality curse" limitation for high-dimensional problems, resulting in poor algorithm optimization accuracy.

[0005] In summary, the existing machine learning model-assisted evolutionary algorithms have technical problems of low optimization efficiency and poor optimization accuracy for high-dimensional expensive optimization problems. Developing machine learning model-assisted evolutionary algorithms that can efficiently solve high-dimensional expensive optimization problems is a major technical requirement to address the core technical difficulties of current engineering optimization problems. Summary of the invention

[0006] In view of the above limitations of the prior art or the need for improved technology, the present invention proposes a proxy model-assisted parallel collaborative method for high-dimensional expensive optimization problems. Based on the characteristics of existing engineering optimization problems involving time-consuming and expensive simulations and high-dimensional design variables, an efficient and high-precision proxy model-assisted parallel collaborative method for high-dimensional expensive optimization problems is studied and designed. The method effectively enhances the local rapid convergence characteristics of dimensional perturbation mutation under a parallel framework, improves the greedy information efficient utilization ability and global search ability of the algorithm by designing efficient differential evolution collaborative mutation operations, and realizes efficient solution to high-dimensional expensive optimization problems with the help of a local search mechanism based on space partitioning, thereby improving optimization efficiency and optimization accuracy, and is suitable for solving high-dimensional expensive optimization problems in the field of engineering optimization.

[0007] To achieve the above object, according to one aspect of the present invention, a proxy model-assisted parallel collaboration method for high-dimensional expensive optimization problems is provided, the method comprising the following steps:

[0008] (1) Determine the design space and optimization target evaluation function of the optimization problem according to the actual engineering problem to be optimized, sample the initial population sample points within the upper and lower bounds of the design space, and evaluate them through the optimization target function to form an initial population. All evaluated individuals in the initial population are used to build a database. Convergence conditions are designed according to the actual engineering design cycle and optimization accuracy requirements, and key iteration parameters in the algorithm iteration process are initialized;

[0009] (2) Determine the set of non-dominated individuals through a multi-objective non-dominated sorting method, and perform parallel dimensional perturbation and mutation operations on all non-dominated individuals to generate multiple local candidate offspring pools;

[0010] (3) Based on the local radial basis function prediction value and the distribution characteristics of candidate offspring individuals, a two-layer real offspring individual screening mechanism is constructed to evaluate the real offspring and update the population and key iteration information;

[0011] (4) DE / current-to-pbest / 2 / bin was used to perform collaborative mutation guided by high-potential individuals to generate multiple global candidate progeny pools;

[0012] (5) Based on the global radial basis function prediction value and the distribution characteristics of candidate offspring individuals, a two-layer real offspring individual screening mechanism is constructed to evaluate the real offspring and update the population and key iteration information;

[0013] (6) Construct a local radial basis function training sample selection strategy based on space partitioning, and design an efficient local search strategy based on local radial basis function in the two constructed local design spaces;

[0014] (7) Update the population and key iteration parameter information to determine whether the convergence condition is met. If converged, output the optimized solution; otherwise, go to step (2) until the convergence condition is met.

[0015] Furthermore, the method of determining the non-dominated individual set by the multi-objective non-dominated sorting method specifically includes the following steps:

[0016] (21) For each individual in the database, calculate the minimum Euclidean distance from the individual to the rest of the individuals in the database, and take the negative value of the minimum Euclidean distance as the distribution density score of the individual;

[0017] (22) Taking the optimization objective function value and distribution density score of the individual as two separate objectives, the non-dominated hierarchy of all individuals in the database is obtained according to the efficient fast non-dominated sorting method;

[0018] (23) All individuals with non-dominated level 1 are combined to form the final optimal non-dominated individual set.

[0019] Furthermore, the parallel dimensional perturbation and mutation operation is performed on all non-dominated individuals to generate multiple local candidate offspring pools. The specific steps are as follows:

[0020] (24) A dimensional perturbation mutation operation is performed on each individual in the non-dominated individual set. The specific expression is as follows:

[0021]

[0022] In the formula, v i,j,m Nx represents the m-th dimension component of the j-th variant individual generated for the i-th non-dominated individual; i,j,m is the m-th dimension component of the i-th non-dominated individual used to generate the j-th variant individual; Z m means the mean is 0 and the standard deviation is 0.2 (ub m -lb m )'s normally distributed random number; ub m With lb m are the upper and lower bounds of the design space in the mth dimension; rand is a uniformly distributed random number in the interval [0,1]; n is the dimension of the design space of the current optimization problem; FEs is the number of true function evaluations consumed so far in the optimization; MaxFEs is the maximum number of true function evaluations allowed for the overall optimization; NP is the current population size;

[0023] (25) All candidate offspring individuals generated by each non-dominated individual are used to construct the corresponding local candidate offspring pool. The specific expression is as follows:

[0024] V i = {v i,j,m|j=1,...N 1 ,m=1,...,n},i=1,...ND 1

[0025] Where V i represents the local candidate offspring pool generated for the i-th non-dominated individual; N 1 Represents the number of candidate offspring individuals in the local candidate offspring pool; ND 1 represents the number of non-dominated individuals; j represents the j-th candidate offspring individual generated for the ith non-dominated individual; m represents the m-th dimension component of the j-th candidate offspring individual generated for the ith non-dominated individual.

[0026] Furthermore, the two-layer real offspring individual screening mechanism is constructed based on the local radial basis function prediction value and the candidate offspring individual distribution characteristics, and the specific steps are as follows:

[0027] (31) For each candidate offspring pool, calculate the maximum and minimum values ​​of all candidate offspring individuals in each dimension;

[0028] (32) Combining the maximum and minimum values ​​of all dimensions in the order of the dimensions to form the upper and lower bounds of the local region containing all candidate offspring individuals in each candidate offspring pool;

[0029] (33) Select all the individuals evaluated so far in the optimization within the upper and lower bounds of the local region to construct a local radial basis function proxy model, and use the local proxy model to predict all individuals in the corresponding candidate offspring pool to obtain the optimization target prediction value of the candidate offspring;

[0030] (34) For each candidate offspring pool, select the candidate offspring with the smallest optimization target prediction value as the optimal candidate offspring individual of the candidate offspring pool, and combine the optimal candidate offspring of all candidate offspring pools to form a temporary offspring set;

[0031] (35) using the method described in the above steps (21), (22) and (23) to calculate the distribution density scores of all offspring individuals in the temporary offspring set that can measure the individual distribution characteristics, and determining the optimal non-dominated temporary offspring individual set by a fast non-dominated sorting method;

[0032] (36) Select two individuals with the smallest predicted value of the optimization objective from the optimal set of non-dominated temporary offspring individuals as the real offspring.

[0033] Furthermore, the DE / current-to-pbest / 2 / bin is used to perform collaborative mutation guided by high-potential individuals to generate multiple global candidate progeny pools. The specific steps are as follows:

[0034] (41) Construct a high-potential database that adapts to iterative information and provides diverse high-potential parent individual position information for collaborative mutation;

[0035] (42) Construct a high-potential population and elite individual screening strategy that balances target greed and spatial distribution characteristics, providing effective elite guiding individuals for collaborative mutation;

[0036] (43) For each parent individual in the high-potential population, the corresponding global candidate offspring pool is generated by realizing the coordinated variation between the elite individuals and the diverse individuals in the high-potential database. The specific expression is as follows:

[0037] vv i,j =Gx i,j +F 1 (Ex k -Gx i,j )+F 2 (Px r1 -Px r2 )

[0038] In the formula, vv i,j Gx represents the jth mutant individual generated for the i-th parent individual; i,j Ex is the current population individual that uses the i-th parent individual to produce the j-th mutant individual; k represents an individual randomly selected from the elite individual set, where k is the index value of the randomly selected individual in the elite individual set; Px r1 With Px r2 Individuals with index values ​​r1 and r2 are randomly selected from the high potential database; F 1 With F 2 are scaling factors;

[0039] (44) All candidate offspring individuals generated by each parent individual are used to construct the corresponding global candidate offspring pool. The specific expression is as follows:

[0040] VV i ={vv i,j,m |j=1,...N 1 ,m=1,...,n},i=1,...ND 2

[0041] Where VV i N represents the global candidate offspring pool generated for the i-th parent individual; 1 Represents the number of candidate offspring individuals in the global candidate offspring pool; ND 2 Represents the current population size; j represents the jth candidate offspring individual generated for the ith parent individual; m represents the mth dimension component of the jth candidate offspring individual generated for the ith parent individual.

[0042] Furthermore, the construction of a high potential database adapted to iterative information comprises the following specific steps:

[0043] (411) Calculate the trend function TF that adapts to the iterative information. The specific expression is as follows:

[0044]

[0045] Where FEs is the number of true function evaluations consumed by the optimization so far; MaxFEs is the maximum number of true function evaluations allowed for the overall optimization;

[0046] (412) Calculate the cutoff parameter GF of the high potential ratio. The specific expression is as follows:

[0047] GF=0.5TF+0.1(1-TF)

[0048] (413) Sort all the target values ​​of the individuals in the database from small to large and select the first individuals are used to construct a high potential database, where NData is the number of individuals in the database.

[0049] Furthermore, the above-mentioned high-potential population and elite individual screening strategy for building a balance between target greed and spatial distribution characteristics has the following specific steps:

[0050] (421) using the method described in the above steps (21), (22) and (23) to calculate the distribution density scores of all individuals in the database that can measure the individual distribution characteristics, and determining the optimal non-dominated individual set by a fast non-dominated sorting method, which is the obtained high-potential population;

[0051] (422) All individuals in the high-potential population are sorted from small to large according to the target value, and the top 15% of individuals are selected to form a set of elite individuals.

[0052] Furthermore, the two-layer real offspring individual screening mechanism is constructed based on the global radial basis function prediction value and the candidate offspring individual distribution characteristics, and the specific steps are as follows:

[0053] (51) Select all the individuals evaluated so far to construct a global radial basis function proxy model, and use the global proxy model to predict all individuals in the corresponding global candidate offspring pool to obtain the optimization target prediction value of the candidate offspring;

[0054] (54) For each global candidate offspring pool, select the candidate offspring with the smallest optimization target prediction value as the optimal candidate offspring individual of the candidate offspring pool, and combine the optimal candidate offspring of all candidate offspring pools to form a global temporary offspring set;

[0055] (55) using the method described in the above steps (21), (22) and (23) to calculate the distribution density scores of all offspring individuals in the global temporary offspring set that can measure the individual distribution characteristics, and determining the optimal non-dominated temporary offspring individual set by a fast non-dominated sorting method;

[0056] (56) Select two individuals with the smallest predicted value of the optimization objective from the optimal set of non-dominated temporary offspring individuals as the real offspring.

[0057] Furthermore, the construction of the local radial basis function training sample selection strategy based on space partitioning comprises the following specific steps:

[0058] (61) Taking the current best individual as the center, calculate the Euclidean distance of all evaluated individuals from the current best individual;

[0059] (62) According to the Euclidean distance, the first κ individuals are selected to construct the optimal local space currently explored. These individuals become the training samples of the local radial basis function constructed for the optimal local space currently explored, where κ = max(50, (n+1)(n+2) / 2), n is the number of design variables;

[0060] (63) All evaluated individuals are sorted from small to large according to the target value, and the first individual is selected to construct the historical high potential space explored by the optimization so far. These individuals become the training samples of the local radial basis function constructed for the historical high potential space explored by the optimization so far, where κ = max(50, (n+1)(n+2) / 2), and n is the number of design variables.

[0061] Furthermore, the specific steps of designing an efficient local search strategy based on local radial basis functions in the two constructed local design spaces are as follows:

[0062] (64) Using the JADE algorithm as the optimization operator and the hyper-rectangular regions composed of individuals in each space as the optimization upper and lower bounds, the optimal value of the local radial basis function corresponding to each space is solved to obtain the corresponding optimal individual;

[0063] (65) The optimal individual is evaluated using the true function.

[0064] Furthermore, the updating of the population and key iteration parameter information comprises the following specific steps:

[0065] (71) All evaluated individuals in the current iteration are merged with the individuals in the current population, and the first NP better individuals are selected from small to large according to the target value to form the updated current population;

[0066] (72) adding all evaluated individuals in the current iteration to the current global database to form an updated global database;

[0067] (73) Update the current number of iterations and the current optimal individual to prepare for the next generation.

[0068] In summary, compared with the prior art, the above technical solution conceived by the present invention, the parallel collaborative method assisted by the proxy model for high-dimensional expensive optimization problems provided by the present invention mainly has the following beneficial effects:

[0069] 1. In a parallel framework, multiple dimensional perturbation and mutation operations are performed simultaneously to generate a diverse local candidate offspring pool, which effectively enhances the diversity of local candidate offspring and avoids the excessive tendency of a single greedy information in a single candidate offspring pool. This improves local rapid convergence while preventing the algorithm from falling into local optimality.

[0070] 2. Through differential evolution collaborative mutation, the high-value information of elite individuals in the optimization process and the diverse information of all individuals are coordinated, which effectively accelerates the information interaction and collaboration capabilities in the algorithm search process, improves the potential of global candidate offspring, significantly reduces the pre-screening pressure of the agent model, and improves the optimization efficiency of the algorithm.

[0071] 3. With the help of the space division method, two local spaces are constructed, one for the current optimal local area of ​​the algorithm and the other for the high potential area optimized so far. An adaptive local radial basis function proxy model is constructed in the corresponding local space, which improves the predictive adaptability of the proxy model for the local space.

[0072] 4. Designing efficient local search strategies based on local and global radial basis function proxy models in two local spaces effectively alleviates the difficulty of exploring the huge design space faced by local search in the original high-dimensional space, improves the optimization efficiency of local search, and accelerates the local exploration capability of the algorithm.

[0073] 5. The present invention can accurately predict and search high-dimensional design spaces, improve the accuracy of the optimization solution, and can be widely used in the design optimization of expensive problems, which is conducive to promotion and application. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 A flow chart of a parallel collaborative method assisted by an agent model for high-dimensional expensive optimization problems provided by the present invention. DETAILED DESCRIPTION

[0075] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0076] See also Figure 1 The present invention provides a proxy model-assisted parallel collaborative method for high-dimensional expensive optimization problems, which is applicable to engineering optimization problems. Specifically, the method mainly includes the following steps:

[0077] Step 1: Determine the design space and optimization target evaluation function of the optimization problem according to the actual engineering problem to be optimized, sample within the upper and lower bounds of the design space to obtain the initial population sample points, and evaluate through the optimization target function to form the initial population. All evaluated individuals in the initial population are used to build a database. Convergence conditions are designed according to the actual engineering design cycle and optimization accuracy requirements, and key iteration parameters in the algorithm iteration process are initialized.

[0078] The initial population is obtained by Latin hypercube sampling, and the specific steps are as follows:

[0079] (11) Each dimension of the design space is evenly divided into NP intervals, where NP is the initial population size;

[0080] (12) For each dimension, randomly select an interval and generate a uniformly distributed random number in the selected interval according to a uniform distribution;

[0081] (13) The random numbers of all dimensions are combined to form a vector, which is the individual of the current population;

[0082] (14) Repeat steps (12)-(13) for NP-1 times until NP population individuals are obtained.

[0083] Step 2: Determine the set of non-dominated individuals through the multi-objective non-dominated sorting method, and perform parallel dimensional perturbation and mutation operations on all non-dominated individuals to generate multiple local candidate offspring pools.

[0084] The method of determining the non-dominated individual set by the multi-objective non-dominated sorting method specifically includes the following steps:

[0085] (21) For each individual in the database, calculate the minimum Euclidean distance from the individual to the rest of the individuals in the database, and take the negative value of the minimum Euclidean distance as the distribution density score of the individual;

[0086] (22) Taking the optimization objective function value and distribution density score of the individual as two separate objectives, the non-dominated hierarchy of all individuals in the database is obtained according to the efficient fast non-dominated sorting method;

[0087] (23) All individuals with non-dominated level 1 are combined to form the final optimal non-dominated individual set.

[0088] The parallel dimensional perturbation and mutation operation is performed on all non-dominated individuals to generate multiple local candidate offspring pools. The specific steps are as follows:

[0089] (24) A dimensional perturbation mutation operation is performed on each individual in the non-dominated individual set. The specific expression is as follows:

[0090]

[0091] In the formula, v i,j,m Nx represents the m-th dimension component of the j-th variant individual generated for the i-th non-dominated individual; i,j,m is the m-th dimension component of the i-th non-dominated individual used to generate the j-th variant individual; Z m means the mean is 0 and the standard deviation is 0.2 (ub m -lb m )'s normally distributed random number; ub m With lb m are the upper and lower bounds of the design space in the mth dimension; rand is a uniformly distributed random number in the interval [0,1]; n is the dimension of the design space of the current optimization problem; FEs is the number of true function evaluations consumed so far in the optimization; MaxFEs is the maximum number of true function evaluations allowed for the overall optimization; NP is the current population size.

[0092] (25) All candidate offspring individuals generated by each non-dominated individual are used to construct the corresponding local candidate offspring pool. The specific expression is as follows:

[0093] V i = {v i,j,m |j=1,...N 1 ,m=1,...,n},i=1,...ND 1

[0094] Where V i represents the local candidate offspring pool generated for the i-th non-dominated individual; N 1 Represents the number of candidate offspring individuals in the local candidate offspring pool; ND 1 represents the number of non-dominated individuals; j represents the j-th candidate offspring individual generated for the ith non-dominated individual; m represents the m-th dimension component of the j-th candidate offspring individual generated for the ith non-dominated individual.

[0095] Step three, based on the local radial basis function prediction value and the distribution characteristics of candidate offspring individuals, a two-layer real offspring individual screening mechanism is constructed to evaluate the real offspring and update the population and key iteration information.

[0096] The two-layer real offspring individual screening mechanism is constructed based on the local radial basis function prediction value and the candidate offspring individual distribution characteristics, and the specific steps are as follows:

[0097] (31) For each candidate offspring pool, calculate the maximum and minimum values ​​of all candidate offspring individuals in each dimension;

[0098] (32) Combining the maximum and minimum values ​​of all dimensions in the order of the dimensions to form the upper and lower bounds of the local region containing all candidate offspring individuals in each candidate offspring pool;

[0099] (33) Select all the individuals evaluated so far in the optimization within the upper and lower bounds of the local region to construct a local radial basis function proxy model, and use the local proxy model to predict all individuals in the corresponding candidate offspring pool to obtain the optimization target prediction value of the candidate offspring;

[0100] (34) For each candidate offspring pool, select the candidate offspring with the smallest optimization target prediction value as the optimal candidate offspring individual of the candidate offspring pool, and combine the optimal candidate offspring of all candidate offspring pools to form a temporary offspring set;

[0101] (35) using the method described in the above steps (21), (22) and (23) to calculate the distribution density scores of all offspring individuals in the temporary offspring set that can measure the individual distribution characteristics, and determining the optimal non-dominated temporary offspring individual set by a fast non-dominated sorting method;

[0102] (36) Select two individuals with the smallest predicted value of the optimization objective from the optimal set of non-dominated temporary offspring individuals as the real offspring.

[0103] The specific steps of evaluating the real offspring and updating the population and key iteration information are as follows:

[0104] (37) Use the true objective function to evaluate the offspring individuals, merge the evaluated offspring individuals with the current population individuals, select the first NP better individuals from small to large according to the target value, and form an updated population;

[0105] (38) All evaluated individuals in the current iteration are added to the current global database to form an updated global database, and key iteration information such as the number of iterations and the current optimal individual are updated.

[0106] Step 4: DE / current-to-pbest / 2 / bin is used to perform collaborative mutation guided by high-potential individuals to generate multiple global candidate offspring pools.

[0107] The DE / current-to-pbest / 2 / bin is used to perform collaborative mutation guided by high-potential individuals to generate multiple global candidate progeny pools. The specific steps are as follows:

[0108] (41) Construct a high-potential database that adapts to iterative information and provides diverse high-potential parent individual position information for collaborative mutation;

[0109] (42) Construct a high-potential population and elite individual screening strategy that balances target greed and spatial distribution characteristics, providing effective elite guiding individuals for collaborative mutation;

[0110] (43) For each parent individual in the high-potential population, the corresponding global candidate offspring pool is generated by realizing the coordinated variation between the elite individuals and the diverse individuals in the high-potential database. The specific expression is as follows:

[0111] vv i,j =Gx i,j +F 1 (Ex k -Gx i,j )+F 2 (Px r1 -Px r2 )

[0112] In the formula, vv i,j Gx represents the jth mutant individual generated for the i-th parent individual; i,j Ex is the current population individual that uses the i-th parent individual to produce the j-th mutant individual; k represents an individual randomly selected from the elite individual set, where k is the index value of the randomly selected individual in the elite individual set; Px r1 With Px r2 Individuals with index values ​​r1 and r2 are randomly selected from the high potential database; F 1 With F 2 are scaling factors.

[0113] (44) All candidate offspring individuals generated by each parent individual are used to construct the corresponding global candidate offspring pool. The specific expression is as follows:

[0114] VV i ={vv i,j,m |j=1,...N 1 ,m=1,...,n},i=1,...ND 2

[0115] Where VV i N represents the global candidate offspring pool generated for the i-th parent individual; 1 Represents the number of candidate offspring individuals in the global candidate offspring pool; ND 2 Represents the current population size; j represents the jth candidate offspring individual generated for the ith parent individual; m represents the mth dimension component of the jth candidate offspring individual generated for the ith parent individual.

[0116] The specific steps of constructing a high potential database that adapts to iterative information are as follows:

[0117] (411) Calculate the trend function TF that adapts to the iterative information. The specific expression is as follows:

[0118]

[0119] Where FEs is the number of true function evaluations consumed by the optimization so far; MaxFEs is the maximum number of true function evaluations allowed for the overall optimization;

[0120] (412) Calculate the cutoff parameter GF of the high potential ratio. The specific expression is as follows:

[0121] GF=0.5TF+0.1(1-TF)

[0122] (413) Sort all the target values ​​of the individuals in the database from small to large and select the first individuals are used to construct a high potential database, where NData is the number of individuals in the database.

[0123] The above-mentioned strategy for constructing a high-potential population and elite individual screening strategy that balances target greed and spatial distribution characteristics has the following specific steps:

[0124] (421) using the method described in the above steps (21), (22) and (23) to calculate the distribution density scores of all individuals in the database that can measure the individual distribution characteristics, and determining the optimal non-dominated individual set by a fast non-dominated sorting method, which is the obtained high-potential population;

[0125] (422) All individuals in the high-potential population are sorted from small to large according to the target value, and the top 15% of individuals are selected to form a set of elite individuals.

[0126] Step 5: Based on the global radial basis function prediction value and the distribution characteristics of candidate offspring individuals, a two-layer real offspring individual screening mechanism is constructed to evaluate the real offspring and update the population and key iteration information.

[0127] The two-layer real offspring individual screening mechanism is constructed based on the global radial basis function prediction value and the distribution characteristics of the candidate offspring individuals. The specific steps are as follows:

[0128] (51) Select all the individuals evaluated so far to construct a global radial basis function proxy model, and use the global proxy model to predict all individuals in the corresponding global candidate offspring pool to obtain the optimization target prediction value of the candidate offspring;

[0129] (54) For each global candidate offspring pool, select the candidate offspring with the smallest optimization target prediction value as the optimal candidate offspring individual of the candidate offspring pool, and combine the optimal candidate offspring of all candidate offspring pools to form a global temporary offspring set;

[0130] (55) using the method described in the above steps (21), (22) and (23) to calculate the distribution density scores of all offspring individuals in the global temporary offspring set that can measure the individual distribution characteristics, and determining the optimal non-dominated temporary offspring individual set by a fast non-dominated sorting method;

[0131] (56) Select two individuals with the smallest predicted value of the optimization objective from the optimal set of non-dominated temporary offspring individuals as the real offspring.

[0132] The specific steps of evaluating the real offspring and updating the population and key iteration information are as follows:

[0133] (57) Use the true objective function to evaluate the offspring individuals, merge the evaluated offspring individuals with the current population individuals, select the first NP better individuals from small to large according to the target value, and form an updated population;

[0134] (58) All evaluated individuals in the current iteration are added to the current global database to form an updated global database, and key iteration information such as the number of iterations and the current optimal individual are updated.

[0135] Step six, construct a local radial basis function training sample selection strategy based on space partitioning, and design an efficient local search strategy based on local radial basis function in the two constructed local design spaces.

[0136] The specific steps of constructing the local radial basis function training sample selection strategy based on space partitioning are as follows:

[0137] (61) Taking the current best individual as the center, calculate the Euclidean distance of all evaluated individuals from the current best individual;

[0138] (62) According to the Euclidean distance, the first κ individuals are selected to construct the optimal local space currently explored. These individuals become the training samples of the local radial basis function constructed for the optimal local space currently explored, where κ = max(50, (n+1)(n+2) / 2), n is the number of design variables;

[0139] (63) All evaluated individuals are sorted from small to large according to the target value, and the first κ individuals are selected to construct the historical high potential space explored by the optimization so far. These individuals become the training samples of the local radial basis function constructed for the historical high potential space explored by the optimization so far, where κ = max(50, (n+1)(n+2) / 2), and n is the number of design variables.

[0140] The specific steps of designing an efficient local search strategy based on local radial basis functions in the two constructed local design spaces are as follows:

[0141] (64) Using the JADE algorithm as the optimization operator and the hyper-rectangular regions composed of individuals in each space as the optimization upper and lower bounds, the optimal value of the local radial basis function corresponding to each space is solved to obtain the corresponding optimal individual;

[0142] (65) The optimal individual is evaluated using the true function.

[0143] Step 7: Update the population and key iteration parameter information to determine whether the algorithm has reached the convergence condition. If it has converged, output the optimized solution obtained by the algorithm. Otherwise, go to step 2 until the algorithm reaches the convergence condition.

[0144] The specific steps of updating the population and key iteration parameter information are as follows:

[0145] (71) All evaluated individuals in the current iteration are merged with the individuals in the current population, and the first NP better individuals are selected from small to large according to the target value to form the updated current population;

[0146] (72) adding all evaluated individuals in the current iteration to the current global database to form an updated global database;

[0147] (73) Update the current number of iterations and the current optimal individual to prepare for the next generation.

[0148] Example

[0149] See also Figure 1 In this embodiment, the parallel collaborative method assisted by the proxy model for high-dimensional expensive optimization problems provided by this embodiment is described by using the classic test function Ackley of high-dimensional expensive optimization problems. The optimization problem expression of Ackley in this embodiment is as follows:

[0150] Find X=(x 1 ,x 2 ,...,x 50 )

[0151]

[0152] In the formula, x i is the i-th design variable; F(X) is the optimization objective function.

[0153] See also Figure 1 The proxy model-assisted parallel collaborative method for high-dimensional expensive optimization problems (abbreviated as SAPCDE) provided in this embodiment mainly includes the following steps:

[0154] Step 1: Determine the design space and optimization target evaluation function of the optimization problem according to the actual engineering problem to be optimized, sample within the upper and lower bounds of the design space to obtain the initial population sample points, and evaluate through the optimization target function to form the initial population. All evaluated individuals in the initial population are used to build a database. Convergence conditions are designed according to the actual engineering design cycle and optimization accuracy requirements, and key iteration parameters in the algorithm iteration process are initialized.

[0155] The initial population is obtained by Latin hypercube sampling, and the specific steps are as follows:

[0156] (11) Each dimension of the design space is evenly divided into NP intervals, where NP is the initial population size;

[0157] (12) For each dimension, randomly select an interval and generate a uniformly distributed random number in the selected interval according to a uniform distribution;

[0158] (13) The random numbers of all dimensions are combined to form a vector, which is the individual of the current population;

[0159] (14) Repeat steps (12)-(13) for NP-1 times until NP population individuals are obtained.

[0160] Step 2: Determine the set of non-dominated individuals through the multi-objective non-dominated sorting method, and perform parallel dimensional perturbation and mutation operations on all non-dominated individuals to generate multiple local candidate offspring pools.

[0161] The method of determining the non-dominated individual set by the multi-objective non-dominated sorting method specifically includes the following steps:

[0162] (21) For each individual in the database, calculate the minimum Euclidean distance from the individual to the rest of the individuals in the database, and take the negative value of the minimum Euclidean distance as the distribution density score of the individual;

[0163] (22) Taking the optimization objective function value and distribution density score of the individual as two separate objectives, the non-dominated hierarchy of all individuals in the database is obtained according to the efficient fast non-dominated sorting method;

[0164] (23) All individuals with non-dominated level 1 are combined to form the final optimal non-dominated individual set.

[0165] The parallel dimensional perturbation and mutation operation is performed on all non-dominated individuals to generate multiple local candidate offspring pools. The specific steps are as follows:

[0166] (24) A dimensional perturbation mutation operation is performed on each individual in the non-dominated individual set. The specific expression is as follows:

[0167]

[0168] In the formula, v i,j,m Nx represents the m-th dimension component of the j-th variant individual generated for the i-th non-dominated individual; i,j,m is the m-th dimension component of the i-th non-dominated individual used to generate the j-th variant individual; Z m means the mean is 0 and the standard deviation is 0.2 (ub m -lb m )'s normally distributed random number; ub m With lb m are the upper and lower bounds of the design space in the mth dimension; rand is a uniformly distributed random number in the interval [0,1]; n is the dimension of the design space of the current optimization problem; FEs is the number of true function evaluations consumed so far in the optimization; MaxFEs is the maximum number of true function evaluations allowed for the overall optimization; NP is the current population size.

[0169] (25) All candidate offspring individuals generated by each non-dominated individual are used to construct the corresponding local candidate offspring pool. The specific expression is as follows:

[0170] V i = {v i,j,m |j=1,...N 1 ,m=1,...,n},i=1,...ND 1

[0171] Where V i represents the local candidate offspring pool generated for the i-th non-dominated individual; N 1 Represents the number of candidate offspring individuals in the local candidate offspring pool; ND 1represents the number of non-dominated individuals; j represents the j-th candidate offspring individual generated for the ith non-dominated individual; m represents the m-th dimension component of the j-th candidate offspring individual generated for the ith non-dominated individual.

[0172] Step three, based on the local radial basis function prediction value and the distribution characteristics of candidate offspring individuals, a two-layer real offspring individual screening mechanism is constructed to evaluate the real offspring and update the population and key iteration information.

[0173] The two-layer real offspring individual screening mechanism is constructed based on the local radial basis function prediction value and the candidate offspring individual distribution characteristics, and the specific steps are as follows:

[0174] (31) For each candidate offspring pool, calculate the maximum and minimum values ​​of all candidate offspring individuals in each dimension;

[0175] (32) Combining the maximum and minimum values ​​of all dimensions in the order of the dimensions to form the upper and lower bounds of the local region containing all candidate offspring individuals in each candidate offspring pool;

[0176] (33) Select all the individuals evaluated so far in the optimization within the upper and lower bounds of the local region to construct a local radial basis function proxy model, and use the local proxy model to predict all individuals in the corresponding candidate offspring pool to obtain the optimization target prediction value of the candidate offspring;

[0177] (34) For each candidate offspring pool, select the candidate offspring with the smallest optimization target prediction value as the optimal candidate offspring individual of the candidate offspring pool, and combine the optimal candidate offspring of all candidate offspring pools to form a temporary offspring set;

[0178] (35) using the method described in the above steps (21), (22) and (23) to calculate the distribution density scores of all offspring individuals in the temporary offspring set that can measure the individual distribution characteristics, and determining the optimal non-dominated temporary offspring individual set by a fast non-dominated sorting method;

[0179] (36) Select two individuals with the smallest predicted value of the optimization objective from the optimal set of non-dominated temporary offspring individuals as the real offspring.

[0180] The specific steps of evaluating the real offspring and updating the population and key iteration information are as follows:

[0181] (37) Use the true objective function to evaluate the offspring individuals, merge the evaluated offspring individuals with the current population individuals, select the first NP better individuals from small to large according to the target value, and form an updated population;

[0182] (38) All evaluated individuals in the current iteration are added to the current global database to form an updated global database, and key iteration information such as the number of iterations and the current optimal individual are updated.

[0183] Step 4: DE / current-to-pbest / 2 / bin is used to perform collaborative mutation guided by high-potential individuals to generate multiple global candidate offspring pools.

[0184] The DE / current-to-pbest / 2 / bin is used to perform collaborative mutation guided by high-potential individuals to generate multiple global candidate progeny pools. The specific steps are as follows:

[0185] (41) Construct a high-potential database that adapts to iterative information and provides diverse high-potential parent individual position information for collaborative mutation;

[0186] (42) Construct a high-potential population and elite individual screening strategy that balances target greed and spatial distribution characteristics, providing effective elite guiding individuals for collaborative mutation;

[0187] (43) For each parent individual in the high-potential population, the corresponding global candidate offspring pool is generated by realizing the coordinated variation between the elite individuals and the diverse individuals in the high-potential database. The specific expression is as follows:

[0188] vv i,j =Gx i,j +F 1 (Ex k -Gx i,j )+F 2 (Px r1 -Px r2 )

[0189] In the formula, vv i,j Gx represents the jth mutant individual generated for the i-th parent individual; i,j Ex is the current population individual that uses the i-th parent individual to produce the j-th mutant individual; k represents an individual randomly selected from the elite individual set, where k is the index value of the randomly selected individual in the elite individual set; Px r1 With Px r2 Individuals with index values ​​r1 and r2 are randomly selected from the high potential database; F 1 With F 2 are scaling factors.

[0190] (44) All candidate offspring individuals generated by each parent individual are used to construct the corresponding global candidate offspring pool. The specific expression is as follows:

[0191] VVi ={vv i,j,m |j=1,...N 1 ,m=1,...,n},i=1,...ND 2

[0192] Where VV i N represents the global candidate offspring pool generated for the i-th parent individual; 1 Represents the number of candidate offspring individuals in the global candidate offspring pool; ND 2 Represents the current population size; j represents the jth candidate offspring individual generated for the ith parent individual; m represents the mth dimension component of the jth candidate offspring individual generated for the ith parent individual.

[0193] The specific steps of constructing a high potential database that adapts to iterative information are as follows:

[0194] (411) Calculate the trend function TF that adapts to the iterative information. The specific expression is as follows:

[0195]

[0196] Where FEs is the number of true function evaluations consumed by the optimization so far; MaxFEs is the maximum number of true function evaluations allowed for the overall optimization;

[0197] (412) Calculate the cutoff parameter GF of the high potential ratio. The specific expression is as follows:

[0198] GF=0.5TF+0.1(1-TF)

[0199] (413) Sort all the target values ​​of the individuals in the database from small to large and select the first individuals are used to construct a high potential database, where NData is the number of individuals in the database.

[0200] The above-mentioned strategy for constructing a high-potential population and elite individual screening strategy that balances target greed and spatial distribution characteristics has the following specific steps:

[0201] (421) using the method described in the above steps (21), (22) and (23) to calculate the distribution density scores of all individuals in the database that can measure the individual distribution characteristics, and determining the optimal non-dominated individual set by a fast non-dominated sorting method, which is the obtained high-potential population;

[0202] (422) All individuals in the high-potential population are sorted from small to large according to the target value, and the top 15% of individuals are selected to form a set of elite individuals.

[0203] Step 5: Based on the global radial basis function prediction value and the distribution characteristics of candidate offspring individuals, a two-layer real offspring individual screening mechanism is constructed to evaluate the real offspring and update the population and key iteration information.

[0204] The two-layer real offspring individual screening mechanism is constructed based on the global radial basis function prediction value and the distribution characteristics of the candidate offspring individuals. The specific steps are as follows:

[0205] (51) Select all the individuals evaluated so far to construct a global radial basis function proxy model, and use the global proxy model to predict all individuals in the corresponding global candidate offspring pool to obtain the optimization target prediction value of the candidate offspring;

[0206] (54) For each global candidate offspring pool, select the candidate offspring with the smallest optimization target prediction value as the optimal candidate offspring individual of the candidate offspring pool, and combine the optimal candidate offspring of all candidate offspring pools to form a global temporary offspring set;

[0207] (55) The methods described in (21), (22) and (23) above are used to calculate the distribution density scores of all offspring individuals in the global temporary offspring set that can measure the individual distribution characteristics, and the optimal non-dominated temporary offspring individual set is determined by a fast non-dominated sorting method;

[0208] (56) Select two individuals with the smallest predicted value of the optimization objective from the optimal set of non-dominated temporary offspring individuals as the real offspring.

[0209] The specific steps of evaluating the real offspring and updating the population and key iteration information are as follows:

[0210] (57) Use the true objective function to evaluate the offspring individuals, merge the evaluated offspring individuals with the current population individuals, select the first NP better individuals from small to large according to the target value, and form an updated population;

[0211] (58) All evaluated individuals in the current iteration are added to the current global database to form an updated global database, and key iteration information such as the number of iterations and the current optimal individual are updated.

[0212] Step six, construct a local radial basis function training sample selection strategy based on space partitioning, and design an efficient local search strategy based on local radial basis function in the two constructed local design spaces.

[0213] The specific steps of constructing the local radial basis function training sample selection strategy based on space partitioning are as follows:

[0214] (61) Taking the current best individual as the center, calculate the Euclidean distance of all evaluated individuals from the current best individual;

[0215] (62) According to the Euclidean distance, the first κ individuals are selected to construct the optimal local space currently explored. These individuals become the training samples of the local radial basis function constructed for the optimal local space currently explored, where κ = max(50, (n+1)(n+2) / 2), n is the number of design variables;

[0216] (63) All evaluated individuals are sorted from small to large according to the target value, and the first individual is selected to construct the historical high potential space explored by the optimization so far. These individuals become the training samples of the local radial basis function constructed for the historical high potential space explored by the optimization so far, where κ = max(50, (n+1)(n+2) / 2), and n is the number of design variables.

[0217] The specific steps of designing an efficient local search strategy based on local radial basis functions in the two constructed local design spaces are as follows:

[0218] (64) Using the JADE algorithm as the optimization operator and the hyper-rectangular regions composed of individuals in each space as the optimization upper and lower bounds, the optimal value of the local radial basis function corresponding to each space is solved to obtain the corresponding optimal individual;

[0219] (65) The optimal individual is evaluated using the true function.

[0220] Step 7: Update the population and key iteration parameter information to determine whether the algorithm has reached the convergence condition. If it has converged, output the optimized solution obtained by the algorithm. Otherwise, go to step 2 until the algorithm reaches the convergence condition.

[0221] The specific steps of updating the population and key iteration parameter information are as follows:

[0222] (71) All evaluated individuals in the current iteration are merged with the individuals in the current population, and the first NP better individuals are selected from small to large according to the target value to form the updated current population;

[0223] (72) adding all evaluated individuals in the current iteration to the current global database to form an updated global database;

[0224] (73) Update the current number of iterations and the current optimal individual to prepare for the next generation.

[0225] In order to further illustrate this embodiment, the method of this embodiment is compared with the SA-COSO, SHPSO, and ESAO algorithms, the maximum number of calls of the real simulation model is set to 1000, and each algorithm is independently run 25 times. The experimental results are shown in Table 1. It can be seen from the results in Table 1 that within the same time cost limit, the method of this embodiment obtains the minimum mean of the target value, which reflects that the method has a faster convergence speed and optimization accuracy when solving high-dimensional problems, and the method of this embodiment obtains the minimum standard deviation of the target value in 25 independent runs, which reflects that the method has stronger robustness when solving high-dimensional problems. Therefore, it can be considered that the method of this embodiment has good performance in high-dimensional expensive optimization problems.

[0226] Table 1 Comparison of optimization results of different algorithms

[0227] algorithm This algorithm (SAPCDE) SA-COSO SHPSO ESAO Target value mean 8.85E-01 8.93E+00 1.84E+00 1.43E+00 Target value standard deviation 5.60E-01 1.07E+00 5.64E-01 2.49E-01

[0228] The present invention provides a proxy model-assisted parallel collaboration method for high-dimensional expensive optimization problems. The method effectively enhances the rapid convergence ability of dimensional perturbation mutation operations under a parallel framework, improves the real-time collaboration and communication capabilities of the population through classical differential evolution collaborative mutation, and improves the algorithm's rapid search capability for high-dimensional space in a local search strategy based on space partitioning. In the entire optimization process, the algorithm's optimization accuracy and efficiency are improved, the time cost is reduced, and the applicability to high-dimensional problems is strong. It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A proxy model-assisted parallel collaborative method for high-dimensional expensive optimization problems, characterized in that: High-dimensional expensive optimization problems exist in the optimization design of vehicle body structures. Such problems usually involve a variety of complex and computationally time-consuming simulation analyses, which results in the inability of gradient optimization or evolutionary algorithms to effectively handle such high-dimensional expensive optimization problems involving time-consuming simulations. Therefore, a proxy model is constructed with the help of complex simulation analysis historical data to reduce the number of time-consuming simulations, and a parallel collaborative optimization method assisted by a proxy model is constructed to deal with the two major technical difficulties faced in the optimization process of the actual engineering optimization problem of vehicle body structure optimization design, namely, the high-dimensional design space composed of a large number of design variables in the vehicle body structure optimization problem leads to low algorithm optimization efficiency and poor optimization accuracy, so as to improve the optimization efficiency and accuracy of the high-dimensional expensive optimization problem involved in vehicle body structure optimization while reducing the number of expensive simulation evaluations. The specific steps are as follows: (1) According to the characteristics of the vehicle body structure optimization problem, the design space composed of vehicle body structure design variables and the vehicle body structure optimization objective evaluation function are determined. All vehicle body structure design variables are sampled within the upper and lower bounds of the design space to obtain the initial population sample points, which are evaluated through the vehicle body structure optimization objective function to form an initial population. All evaluated individuals in the initial population are used to construct a database. The convergence conditions are designed according to the actual engineering design cycle and optimization accuracy requirements, and the key iteration parameters in the algorithm iteration process are initialized. (2) In order to screen high-quality parent individuals to improve the quality of evolution, the non-dominated individual set is determined by the multi-objective non-dominated sorting method, and parallel dimensional perturbation mutation operations are performed on all non-dominated individuals to generate multiple local candidate offspring pools; (3) In order to select the best true offspring individuals, a two-layer true offspring individual screening mechanism is constructed based on the local radial basis function prediction value and the distribution characteristics of the candidate offspring individuals to evaluate the true offspring and update the population and key iteration information; (4) In order to enhance the evolutionary cooperation between excellent parent individuals to speed up the optimization efficiency, DE / current-to- p best / 2 / bin performs collaborative mutation guided by high-potential individuals to generate multiple global candidate offspring pools; (5) In order to screen the best offspring individuals and avoid wasting expensive simulation on evaluating low-quality offspring individuals, a two-layer real offspring individual screening mechanism is constructed based on the global radial basis function prediction value and the distribution characteristics of candidate offspring individuals to evaluate the real offspring and update the population and key iteration information; (6) In order to improve the prediction accuracy of the surrogate model for high-potential local spaces and improve the optimization accuracy through rapid local evolution of local areas, a local radial basis function training sample selection strategy based on space partitioning is constructed, and an efficient local search strategy based on local radial basis functions is designed in the two constructed local design spaces; (7) Update the population and key iteration parameter information to determine whether the convergence condition is met. If converged, output the optimized solution; otherwise, go to step (2) until the convergence condition is met. Determining the non-dominated individual set by the multi-objective non-dominated sorting method described in step (2) specifically includes the following steps: (21) For each individual in the database, calculate the minimum Euclidean distance from the individual to the rest of the individuals in the database, and take the negative value of the minimum Euclidean distance as the distribution density score of the individual; (22) Taking the individual optimization objective function value and distribution density score value as two separate objectives, the non-dominated hierarchy of all individuals in the database is obtained according to the efficient fast non-dominated sorting method; (23) All individuals with a non-dominated level of 1 are combined to form the final optimal non-dominated individual set; The parallel dimension perturbation mutation operation is performed on all non-dominated individuals in step (2) to generate multiple local candidate offspring pools. The specific steps are as follows: (24) A dimensional perturbation mutation operation is performed on each individual in the non-dominated individual set. The specific expression is as follows: In the formula, Indicates that for The first The variant individual Dimensional components; For the non-dominated individuals are used to produce The variant individual Dimensional components; means the mean is 0 and the standard deviation is Normally distributed random numbers; and The design space is Upper and lower bounds on dimensions; is a uniformly distributed random number in the interval [0,1]; is the dimension of the design space of the current optimization problem; is the number of real function evaluations consumed by the optimization so far; The maximum number of true function evaluations allowed to be consumed by the overall optimization; is the current population size; (25) All candidate offspring individuals generated by each non-dominated individual are used to construct the corresponding local candidate offspring pool. The specific expression is as follows: In the formula, Indicates that for A local candidate offspring pool generated by non-dominated individuals; Represents the number of candidate offspring individuals in the local candidate offspring pool; represents the number of non-dominated individuals; Indicates that for The first Candidate offspring individuals; Indicates that for The first The first candidate offspring individual Dimensional component; The two-layer real offspring individual screening mechanism described in step (3) is constructed based on the local radial basis function prediction value and the distribution characteristics of the candidate offspring individuals. The specific steps are as follows: (31) For each candidate offspring pool, calculate the maximum and minimum values ​​of all candidate offspring individuals in each dimension; (32) Combine the maximum and minimum values ​​of all dimensions in the order of the dimensions to form the upper and lower bounds of the local region containing all candidate offspring individuals in each candidate offspring pool; (33) Select all the individuals evaluated so far in the optimization within the upper and lower bounds of the local region to construct a local radial basis function proxy model, and use the local proxy model to predict all individuals in the corresponding candidate offspring pool to obtain the optimization target prediction value of the candidate offspring; (34) For each candidate offspring pool, select the candidate offspring with the smallest prediction value of the optimization target as the optimal candidate offspring individual of the candidate offspring pool, and combine the optimal candidate offspring of all candidate offspring pools to form a temporary offspring set; (35) using the methods described in steps (21), (22) and (23) to calculate the distribution density scores of all offspring individuals in the temporary offspring set that can measure the individual distribution characteristics, and determining the optimal non-dominated temporary offspring individual set by a fast non-dominated sorting method; (36) Select two individuals with the minimum optimization target prediction value from the optimal non-dominated temporary offspring individual set as the real offspring; Step (4) described in DE / current-to- p Best / 2 / bin conducts collaborative mutation guided by high-potential individuals to generate multiple global candidate offspring pools. The specific steps are as follows: (41) Construct a high-potential database that adapts to iterative information and provides diverse high-potential parent individual position information for collaborative mutation; (42) Construct a high-potential population and elite individual screening strategy that balances target greed and spatial distribution characteristics, providing effective elite guiding individuals for collaborative mutation; (43) For each parent individual in the high-potential population, the corresponding global candidate offspring pool is generated by realizing the coordinated variation between the elite individuals and the diverse individuals in the high-potential database. The specific expression is as follows: In the formula, Indicates that for The first generation of the parent individual variant individuals; To adopt the parent individuals to produce the The current population of mutant individuals; represents an individual randomly selected from the elite individual set, where is the index value of the randomly selected individual in the elite individual set; and The index values ​​randomly selected from the high potential database are and individuals; and are scaling factors; (44) All candidate offspring individuals generated by each parent individual are used to construct the corresponding global candidate offspring pool. The specific expression is as follows: In the formula, Indicates that for A global candidate offspring pool generated by each parent individual; Represents the number of candidate offspring individuals in the global candidate offspring pool; Indicates the current population size; Indicates that for The first generation of the parent individual Candidate offspring individuals; Indicates that for The first generation of the parent individual The first candidate offspring individual Dimensional component.

2. The method according to claim 1, characterized in that The high potential database for adapting the iterative information described in step (41) is constructed as follows: (411) Calculate the trend function adapted to the iterative information TF , the specific expression is as follows: In the formula, is the number of real function evaluations consumed by the optimization so far; The maximum number of true function evaluations allowed to be consumed by the overall optimization; (412) Calculate the cutoff parameter of the high potential ratio GF , the specific expression is as follows: (413) Sort all the target values ​​of the individuals in the database from small to large and select the first Individuals are used to build a high potential database, among which is the number of individuals in the database.

3. The method according to claim 1, characterized in that The high potential population and elite individual screening strategy described in step (42) that balances the greedy target and spatial distribution characteristics is as follows: (421) using the method described in steps (21), (22) and (23) to calculate the distribution density scores of all individuals in the database that can measure the individual distribution characteristics, and determining the optimal non-dominated individual set by a fast non-dominated sorting method, which is the obtained high potential population; (422) Sort all individuals in the high-potential population from small to large according to the target value, and select the top 15% of individuals to form a set of elite individuals.

4. The method according to claim 1, characterized in that The two-layer real offspring individual screening mechanism described in step (5) is constructed based on the global radial basis function prediction value and the distribution characteristics of the candidate offspring individuals. The specific steps are as follows: (51) Select all the individuals evaluated so far to construct a global radial basis function proxy model, and use the global proxy model to predict all individuals in the corresponding global candidate offspring pool to obtain the optimization target prediction value of the candidate offspring; (54) For each global candidate offspring pool, select the candidate offspring with the smallest optimization target prediction value as the optimal candidate offspring individual of the candidate offspring pool, and combine the optimal candidate offspring of all candidate offspring pools to form a global temporary offspring set; (55) using the method described in steps (21), (22) and (23) to calculate the distribution density scores of all offspring individuals in the global temporary offspring set that can measure the individual distribution characteristics, and determining the optimal non-dominated temporary offspring individual set by a fast non-dominated sorting method; (56) Select two individuals with the smallest predicted value of the optimization objective from the optimal set of non-dominated temporary offspring individuals as the real offspring.

5. The method according to claim 1, characterized in that The specific steps of constructing the local radial basis function training sample selection strategy based on space partitioning described in step (6) are as follows: (61) Taking the current best individual as the center, calculate the Euclidean distance of all evaluated individuals from the current best individual; (62) Sort by Euclidean distance from small to large and select the first Individuals are used to construct the optimal local space currently explored, and these individuals become training samples of the local radial basis function constructed for the optimal local space currently explored, where , n is the number of design variables; (63) Sort all evaluated individuals according to their target values ​​from small to large, and select the top Individuals are used to construct the historical high potential space explored by optimization so far, and these individuals become training samples of the local radial basis function constructed for the historical high potential space explored by optimization so far, where , n is the number of design variables.

6. The method according to claim 1, characterized in that The specific steps of designing an efficient local search strategy based on local radial basis functions in the two local design spaces constructed in step (6) are as follows: (64) Using the JADE algorithm as the optimization operator and the hyper-rectangular regions composed of individuals in each space as the optimization upper and lower bounds, the optimal value of the local radial basis function corresponding to each space is solved to obtain the corresponding optimal individual; (65) The optimal individual is obtained by evaluating the true function.

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