CN116579371A - Double-layer optimization heterogeneous proxy model assisted multi-objective evolutionary optimization computing method - Google Patents
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Abstract
The invention discloses a double-layer optimization heterogeneous proxy model assisted multi-objective evolutionary optimization calculation method, which relates to the technical field of multi-objective optimization, and comprises the steps of firstly, generating an initialization sample from a design space by using Latin hypercube sampling and evaluating the fitness value of the initialization sample, establishing a global quick Kriging model by using current optimal data, generating a global candidate solution by using ARNSGA-3 of a self-adaptive entropy difference selection reference point as an optimizer, and judging whether to transition an evaluation stage; constructing a local SVM classifier, searching a promising local area by using the MOEA/D-iDE as an optimizer to explore a local optimal candidate solution, selecting an ideal solution set from the candidate solutions by using a filling sampling criterion based on convergence and diversity indexes, updating a proxy model to improve the prediction precision, and judging whether the preset evaluation times are reached; finally outputting an optimization result; thus, the complex expensive constraint multi-objective optimization problem can be efficiently processed.
Description
Technical Field
The invention relates to the technical field of multi-objective optimization, in particular to a double-layer optimization heterogeneous proxy model assisted multi-objective evolutionary optimization computing method.
Background
Many practical optimization problems have multiple conflicting objectives requiring simultaneous optimization, which is referred to as a multi-objective optimization problem. In most evolutionary algorithms it is assumed that there are objective or constraint functions that are inexpensive to analyze and calculate, however in practical applications it may happen that each function is difficult to evaluate and extremely time consuming. Expensive optimization problems are just those where the computational overhead or physical experiment costs of those targets are high, for example in the case of multi-target neural architecture searches, GPU-based evaluations can be computationally and economically expensive, with only a small number of function evaluations being affordable. Thus, the main objective of solving the expensive constraint multi-objective optimization problem is to find the optimal solution within the feasible region in a limited time. In recent years, with the development of the automatic machine learning field, the problem of expensive multi-objective optimization with constraint conditions is ubiquitous in the engineering application field, and the importance of the problem is increasing, so that the problem is very important in scientific research value and practical significance.
At present, the agent assisted evolutionary algorithm combines the traditional evolutionary algorithm with the agent modeling technology, and is a mainstream method for solving the problem of high-cost optimization, and the general concept is to pre-screen candidate solutions. Specifically, the proxy assisted evolution algorithm utilizes the output of the surrogate model to evaluate the high quality solution to be evaluated. To improve its predictive performance, new samples need to be determined, and the prediction accuracy is improved by updating the proxy model through the evaluation of the original real objective function. The use of proxy models to replace the evaluation of the candidate solution by the original objective function reduces the number of expensive evaluations and thus reduces the computational cost. When there is little prior knowledge about the target, using a set of different proxy models is a popular way to increase the approximate robustness.
For the proxy model, proxy assisted evolutionary algorithms can be broadly divided into approximation-based and classification-based. The proxy assisted evolution algorithm based on approximation constructs a proxy model of the approximation objective function or constraint function. For example, in ParEGO, a single Kriging model is built to approximate each generation of aggregation functions, where the aggregation functions are constructed with randomly selected vectors in a set of uniform weight vectors; in EDN-armea, the more computationally efficient Dropout neural network replaces the gaussian process model to reduce the variable dimension time consumption of the approximation model construction. In general, approximation-based proxy-assisted evolutionary algorithms have rich pre-screening capabilities to estimate high quality solutions because an approximation model can rank any candidate solution with the real-valued output that its model obtains. However, when such approximation-based proxy-assisted evolutionary algorithms are used to solve high-dimensional problems, approximation errors will accumulate as the number of targets increases, the computational effort will also increase dramatically, and obtaining adequate model accuracy may be hampered by a limited number of high-dimensional training samples.
The classification-based proxy assisted evolutionary algorithm builds a classification model to predict the reasonable class of candidate solutions without building an accurate proxy model for approximating each objective function. When a new individual is predicted by such a proxy model, a specific fitness value is not obtained, but a simple label is used to determine whether the individual is good or bad. For example, a multi-objective evolutionary algorithm (CPS-MOEA) based on classification and pareto dominance, individuals are labeled as positive and negative categories, and classification regression trees are used to predict newly generated child categories to reduce the number of child evaluations; classification-based CSEA uses a feed-forward neural network to predict the dominance relationship between candidate individuals and reference individuals. Compared with an approximate model, the classification model does not need to accurately fit the real values of the target and the sample, can save the approximate time and improve the prediction efficiency, and returns less information to cause poorer screening capability.
The high evaluation cost is needed to be solved as a real problem, and the classification and regression models have advantages and disadvantages, and no algorithm is used for taking the classification and regression models into consideration in a proper method. Furthermore, when the problem dimension is high, it is often difficult to build an accurate global model using a limited number of training points due to "curse of dimension", and the use of local proxy models is often used to enhance the local search capability of proxy-assisted evolutionary algorithms and further speed convergence. The existing agent assisted evolution algorithm is limited to the problem of expensive multi-objective optimization with small scale, and the high-dimensional decision space and objective space bring great pressure to the efficiency and precision required for constructing the model.
Disclosure of Invention
In order to solve the technical problems, the invention provides a double-layer optimization heterogeneous proxy model assisted multi-objective evolutionary optimization computing method, which comprises the following steps of
S1, initializing a population through Latin hypercube sampling, and evaluating individual fitness in the population;
s2, establishing a global quick Kriging model by adopting current optimal data;
s3, using the self-adaptive entropy difference to select an AR-NSGA-III of a reference point as an optimizer to generate a global search candidate solution;
s4, judging whether a feasible solution exists in the feasible region, and returning to the step S2 if the feasible solution exists; if a feasible solution exists, executing a step S5;
s5, dividing a possible sub-area according to a possible depolymerization strategy;
s6, constructing a local support vector machine classifier;
s7, searching a promising local area by using the MOEA/D-iDE with the improved differential evolution operator as an optimizer;
s8, selecting an ideal solution set from candidate solutions through a filling sampling criterion based on convergence and diversity indexes to update the proxy model;
s9, judging whether the current evaluation times reach preset evaluation times, if not, returning to the step S5; if yes, outputting a final optimization result.
The technical scheme of the invention is as follows:
further, in step S1, an initial sample is generated from the design space according to the latin hypercube sampling, and the individual fitness value is calculated as an original objective function and stored in the database DB.
The aforementioned method for calculating the multi-objective evolutionary optimization assisted by the double-layer optimization heterogeneous proxy model specifically comprises the following sub-steps of
S2.1, constructing a Kriging approximate model for each original objective function, wherein the Kriging approximate model is shown in the following formula
y(x)＝μ(x)+ε(x),ε(x)～N(0,σ 2 )
Wherein μ is the predictive value of the regression model, i.e., μ=fβ and ε (x) are gaussian distributions with mean 0 and standard deviation σ; the correlation function selects a Gaussian kernel function
Wherein i, j represents the row and column positions of the variables in the matrix, θ i Expressed as a super-parameter, the value of θ is obtained by the following maximum likelihood function
wherein ,N1 Representing population, y being the real objective function value, det (R) being the determinant of matrix R; after obtaining the super parameter theta, respectively calculating the coefficient beta and the variance sigma 2 Further approximating the objective function value;
s2.2, using the initial model learned super parameters for an incremental model to accelerate the approximation of the original Kriging model; from R -1 Calculate and calculateNew correlation matrix writing
Wherein the matrix is divided by n, qPartitioning, wherein R is a correlation matrix of an original Kriging model; inversion calculation of the partition matrix is as follows
Wherein c=b-ase:Sub>A T R -1 A。
In the aforementioned method for calculating multi-objective evolutionary optimization assisted by the double-layer optimized heterogeneous agent model, in step S3, the difference between entropy values of the population in each evolutionary iteration is adopted for determining the AR-NSGA-III, wherein the method for calculating the entropy values is as follows:
wherein inf is a normalized value, mid is a normalized median difference, t is the number of iterations, and the entropy difference between two iterations is Δe t ＝|e t -e t-1 I, Δe when population updates t The value of (a) is positively correlated with the individual variation amplitude in the decision space, i.e. Δe t The larger the value, the larger the population change, indicating that the population is undergoing an exploration phase, will tend towards an uncertainty region; conversely, Δe t The smaller the value, the smaller the population variation, and the population tends to converge and stabilize.
In the aforementioned method for calculating multi-objective evolutionary optimization assisted by the double-layer optimized heterogeneous proxy model, in step S4, it is determined whether there is a feasible solution in the feasible region, if so, the optimization stage is shifted, and local optimization is performed according to the region where the feasible solution is located; if no feasible solution exists, adopting a repair strategy to guide the evolution of the infeasible solution to a feasible region until the feasible solution is generated, and specifically, the method comprises the following steps of:
s4.1, real evaluation solutions stored in all databases are used for establishing a Kriging model for the constraint function;
s4.2, give the solution x of population P i And calculate x i Is constrained by VC (x) i )＝(max{0,g 1 (x i )},...,max{0,g m (x i )}) T, wherein g(xi ) Is x i Each constraint value;
s4.3, the constructed Kriging modeling is used for approximating x i +e j Expressed as
Where j=1, …, d, m is the constraint number,is the adaptation value of the Kriging model approximation of the kth constraint, e j Is a vector in which the j-th element is an extremely small positive constant and the remaining constants are all 0;
s4.4, calculating a gradient matrix
wherein ,C(xi )＝(g 1 (x i ),...,g m (x i )) T ；
S4.5 thusI.e. a repair solution, if the constraint violates the condition G (x' i )<G(x i ) Then x 'is' i Added to the evolved population.
The aforementioned method for calculating the multi-objective evolutionary optimization assisted by the double-layer optimization heterogeneous proxy model specifically comprises the following sub-steps of
S5.1, carrying out ascending order on all feasible solutions stored in the steps S2 to S4, wherein the order is based on the shortest Euclidean distance between the feasible solutions and the infeasible solutions:
wherein ,is the i < th > feasible solution, <>Is the j-th infeasible solution, |ip| represents the number of infeasible solutions; if it isThen the two feasible solutions are assigned to the same cluster; if->The single feasible solution and the nearest infeasible solution form a cluster until all the feasible solutions are distributed into the respective clusters;
s5.2, forming a promising feasible local area by the minimum lower bound and the maximum upper bound of the decision variables of all solutions in the cluster according to the clusters formed by the respective components, and further searching for the optimal solution.
In the aforementioned method for performing multi-objective evolutionary optimization calculation assisted by the two-layer optimized heterogeneous proxy model, in step S6, the support vector machine constructs a decision function c (x) =sgn (w) T φ(x)+w 0 ) As a classifier, for a classification problem, inputWill be divided into positive or negative classes denoted c ε { +1, -1}, where φ (x) is a +_ from the input space to the high-dimensional feature space>Mapping function of (2), weight vector->And offset->Parameters to be optimized;
will be based on training samplesBuilding an SVM model is considered as an optimization problem:
s.t.ci(wTφ(x)+w0)≥1-ξi,ξi≥0
wherein ,c1 Is of the positive and negative type, xi i Is a relaxation variable, C is a hyper-parameter; the SVM estimates a new sampling point by the following equation
wherein ,ai Is Lagrangian multiplier, K (x i ,x)＝exp(-γ||x i -x|) is an RBF kernel function, gamma>0 controls the complexity of the decision boundary.
In the aforementioned method for optimizing and calculating the multi-objective evolutionary process assisted by the double-layer optimized heterogeneous agent model, in step S7, the population is first divided by using a layering technology in a vector difference generating strategy, and a vector difference is obtained by matching with a reference individual to simulate different evolutionary directions of the population according to different periods, so as to explicitly guide the random search with the direction of the evolution of the population; then dynamically adjusting the DE scaling factor by mining evolutionary information of a deeper level of the decision space;
MOEA/D-iDE decomposes a multi-objective problem into multiple single-objective sub-problems, for the ith sub-problem, building a datasetAll solutions are included in the archive for training input and +.> Classified as wherein />For all evaluated solutions, < >>Is the current best solution set for the adjacent sub-problem;
wherein g (x|lambda) k Z) is chebyshev decomposition, and B (i) is the index set of adjacent sub-questions of the ith question.
The aforementioned double-layer optimization heterogeneous proxy model assisted multi-objective evolutionary optimization computing method, step S8 specifically comprises the following sub-steps
S8.1, carrying out normalization treatment on the test solution of the agent auxiliary evaluation;
s8.2, regarding the minimum value in the decision variables of the parent and the offspring of the population as an ideal point;
s8.3 several individuals x which will be furthest from the parent * Stored in the diversity metric Dvs file, x * The method meets the following conditions:
Dvs(x * )＝max p＝1:N {|x * ,x p | 2 }
wherein ,xp Traversing from 1 to N for the current individuals in the population;
s8.4, calculating Euclidean distance between the test solution and the ideal point, storing the Euclidean distance in a convergence metric Cvg file, and merging the individuals stored in Cvg and Dvs into a new set newObj;
s8.5, applying a solution of a first front edge in the non-dominant sorting screening set newObj;
and S8.6, evaluating the screening solution through the original expensive function to update the model.
The beneficial effects of the invention are as follows:
(1) According to the invention, according to the inherent consistency of the regression and classification models, unlike the traditional single model agent assisted evolution algorithm, the algorithm convergence and distribution are improved under the condition of high calculation cost by cooperating with global and local optimization;
(2) According to the invention, based on a clustering strategy of the feasible solution, the feasible solution is adaptively clustered into a plurality of clusters according to the current population and historical search information, each cluster can form a promising feasible local area, and the optimization convergence performance of the current population can be further improved by utilizing the local areas;
(3) In the invention, a simple index filling sampling criterion is provided, convergence and diversity indexes are used for determining a proper sampling strategy for re-evaluating an expensive objective function, and the method not only can accelerate convergence and improve the optimization efficiency, but also can prevent searching from falling into local optimum to a certain extent;
(4) The invention can efficiently process the expensive multi-objective optimization problem with constraint on the premise of not reducing the performance of the evolutionary algorithm.
Drawings
FIG. 1 is a schematic overall flow chart of the present invention;
FIG. 2 is a schematic diagram of a module and data flow according to the present invention;
FIG. 3 is a schematic diagram of an effect evaluation for obtaining final solution set convergence in an embodiment of the present invention;
FIG. 4 is a schematic diagram of evaluation of the effect of obtaining the final solution set diversity in the embodiment of the present invention.
Detailed Description
The method for assisting multi-objective evolutionary optimization calculation by using the double-layer optimization heterogeneous proxy model provided by the embodiment, as shown in fig. 1 to 2, comprises the following steps of
S1, initializing a population through Latin hypercube sampling, and evaluating individual fitness in the population; initial samples are generated from the design space according to Latin hypercube sampling, individual fitness values are calculated as original objective functions and stored in a database DB.
S2, establishing a global quick Kriging model by adopting current optimal data, which comprises the following steps of
S2.1, constructing a Kriging approximate model for each original objective function, wherein the Kriging approximate model is shown in the following formula
y(x)＝μ(x)+ε(x),ε(x)～N(0,σ 2 )
Wherein μ is the predictive value of the regression model, i.e., μ=fβ and ε (x) are gaussian distributions with mean 0 and standard deviation σ; the correlation function selects a Gaussian kernel function
Wherein i, j represents the row and column positions of the variables in the matrix, θ i Expressed as a super-parameter, the value of θ is obtained by the following maximum likelihood function
wherein ,N1 Representing population, y being the real objective function value, det (R) being the determinant of matrix R; after obtaining the super parameter theta, respectively calculating the coefficient beta and the variance sigma 2 Further approximating the objective function value;
s2.2, using the initial model learned super parameters for an incremental model to accelerate the approximation of the original Kriging model; from R -1 Calculate and calculateNew correlation matrix writing
Wherein the matrix is divided by n, qPartitioning, wherein R is a correlation matrix of an original Kriging model; inversion calculation of the partition matrix is as follows
Wherein c=b-ase:Sub>A T R -1 A。
S3, using the self-adaptive entropy difference to select an AR-NSGA-III of a reference point as an optimizer to generate a global search candidate solution;
AR-NSGA-III provides individual selection pressure for the population, promoting the population to converge better to the pareto front; in addition, the improved reference point selection strategy is helpful for better guiding the spatial distribution of the population, and provides convergence and diversity support for the overall rapid Kriging model management;
in order to judge the evolution stage of the population, the AR-NSGA-III is determined by adopting the difference of entropy values of the population in each evolution iteration, wherein the entropy value calculation method comprises the following steps:
wherein inf is a normalized value, mid is a normalized median difference, t is the number of iterations, and the entropy difference between two iterations is Δe t ＝|e t -e t-1 I, Δe when population updates t The value of (a) is positively correlated with the individual variation amplitude in the decision space, i.e. Δe t The larger the value, the larger the population change, indicating that the population is undergoing an exploration phase, will tend towards an uncertainty region; conversely, Δe t The smaller the value, the smaller the population variation, and the population tends to converge and stabilize.
S4, judging whether a feasible solution exists in the feasible region, and returning to the step S2 if the feasible solution exists; if a feasible solution exists, executing a step S5;
judging whether a feasible solution exists in the feasible region, if so, converting to an optimization stage, and performing local optimization according to the region where the feasible solution exists;
if no feasible solution exists, adopting a repair strategy to guide the evolution of the infeasible solution to a feasible region until the feasible solution is generated, and specifically, the method comprises the following steps of:
s4.1, real evaluation solutions stored in all databases are used for establishing a Kriging model for the constraint function;
s4.2, give the solution x of population P i And calculate x i Is constrained by VC (x) i )＝(max{0,g 1 (x i )},...,max{0,g m (x i )}) T, wherein g(xi ) Is x i Each constraint value;
s4.3, the constructed Kriging modeling is used for approximating x i +e j Expressed as
Where j=1, …, d, m is the constraint number,is the adaptation value of the Kriging model approximation of the kth constraint, e j Is a vector in which the j-th element is an extremely small positive constant and the remaining constants are all 0;
s4.4, calculating a gradient matrix
wherein ,C(xi )＝(g 1 (x i ),...,g m (x i )) T ；
S4.5 thusI.e. a repair solution, if the constraint violates the condition G (x' i )<G(x i ) Then x 'is' i Added to the evolved population.
S5, dividing the possible sub-areas according to the possible depolymerization strategies, wherein the method specifically comprises the following sub-steps of
S5.1, carrying out ascending order on all feasible solutions stored in the steps S2 to S4, wherein the order is based on the shortest Euclidean distance between the feasible solutions and the infeasible solutions:
wherein ,is the i < th > feasible solution, <>Is the j-th infeasible solution, |ip| represents the number of infeasible solutions; if it isThen the two feasible solutions are assigned to the same cluster; if->The single feasible solution and the nearest infeasible solution form a cluster until all the feasible solutions are distributed into the respective clusters;
s5.2, forming a promising feasible local area by the minimum lower bound and the maximum upper bound of the decision variables of all solutions in the cluster according to the clusters formed by the respective components, so as to further search the optimal solution in the local search stage.
S6, constructing a local support vector machine SVM classifier, and constructing a decision function c (x) =sgn (w) by using a support vector machine T φ(x)+w 0 ) As a classifier, for a classification problem, inputWill be divided into positive or negative classes denoted c ε { +1, -1}, where φ (x) is a +_ from the input space to the high-dimensional feature space>Mapping function of (2), weight vector->And offset->Parameters to be optimized;
will be based on training samplesBuilding an SVM model is considered as an optimization problem:
s.t.ci(wTφ(x)+w0)≥1-ξi,ξi≥0
wherein ,c1 Is of the positive and negative type, xi i Is a relaxation variable, C is a hyper-parameter; the SVM estimates a new sampling point by the following equation
wherein ,ai Is Lagrangian multiplier, K (x i ,x)＝exp(-γ||x i -x|) is an RBF kernel function, gamma>0 controls the complexity of the decision boundary.
S7, searching a promising local area by using the MOEA/D-iDE with the improved differential evolution operator as an optimizer;
firstly, dividing a population by using a layering technology in a vector difference generation strategy, simulating different evolution directions of the population according to different periods by matching with a reference individual to further obtain a vector difference, enhancing convergence speed in the early stage, focusing on diversity in the later stage, and carrying out explicit guidance on random search with direction of population evolution; then dynamically adjusting the DE scaling factor by mining evolutionary information of a deeper level of a decision space, thereby realizing implicit guidance of population evolution in the aspect of improving convergence precision;
MOEA/D-iDE decomposes a multi-objective problem into multiple single-objective sub-problems, for the ith sub-problem, building a datasetAll solutions are included in the archive for training input and +.> Classified as wherein />For all evaluated solutions, < >>Is the current best solution set for the adjacent sub-problem;
wherein g (x|lambda) k Z) is chebyshev decomposition, and B (i) is the index set of adjacent sub-questions of the ith question.
S8, selecting an ideal solution set from candidate solutions through a filling sampling criterion based on convergence and diversity indexes to update the proxy model, wherein the method specifically comprises the following substeps
S8.1, carrying out normalization treatment on the test solution of the agent auxiliary evaluation;
s8.2, regarding the minimum value in the decision variables of the parent and the offspring of the population as an ideal point;
s8.3 several individuals x which will be furthest from the parent * Stored in the diversity metric Dvs file, x * The method meets the following conditions:
Dvs(x * )＝max p＝1:N {|x * ,x p | 2 }
wherein ,xp Traversing from 1 to N for the current individuals in the population;
s8.4, calculating Euclidean distance between the test solution and the ideal point, storing the Euclidean distance in a convergence metric Cvg file, and merging the individuals stored in Cvg and Dvs into a new set newObj;
s8.5, applying a solution of a first front edge in the non-dominant sorting screening set newObj;
and S8.6, evaluating the screening solution through the original expensive function to update the model.
S9, judging whether the current evaluation times reach preset evaluation times, if not, returning to the step S5; if yes, outputting a final optimization result.
As shown in fig. 3, in the algorithm of this embodiment, a trend chart of convergence of the population to the Pareto front in 300 times of function evaluation is shown, a gray grid represents the real Pareto front of the WFG8 test problem, gray points represent individuals of the population, and solutions optimized by the algorithm of this embodiment are shown to be continuously converged to the Pareto front.
As shown in fig. 4, the effect of the algorithm of the embodiment on the front surface of the WFG8 test problem is intuitively shown, and in combination with fig. 3, the algorithm of the embodiment can converge on the real Pareto front of the test problem and can still keep the uniform distribution of the population non-dominant solution diversity.
In addition to the embodiments described above, other embodiments of the invention are possible. All technical schemes formed by equivalent substitution or equivalent transformation fall within the protection scope of the invention.
Claims (9)
1. A double-layer optimization heterogeneous proxy model assisted multi-objective evolutionary optimization computing method is characterized by comprising the following steps of: comprises the following steps
S1, initializing a population through Latin hypercube sampling, and evaluating individual fitness in the population;
s2, establishing a global quick Kriging model by adopting current optimal data;
s3, using the self-adaptive entropy difference to select an AR-NSGA-III of a reference point as an optimizer to generate a global search candidate solution;
s4, judging whether a feasible solution exists in the feasible region, and returning to the step S2 if the feasible solution exists; if a feasible solution exists, executing a step S5;
s5, dividing a possible sub-area according to a possible depolymerization strategy;
s6, constructing a local support vector machine classifier;
s7, searching a promising local area by using the MOEA/D-iDE with the improved differential evolution operator as an optimizer;
s8, selecting an ideal solution set from candidate solutions through a filling sampling criterion based on convergence and diversity indexes to update the proxy model;
s9, judging whether the current evaluation times reach preset evaluation times, if not, returning to the step S5; if yes, outputting a final optimization result.
2. The method for assisting multi-objective evolutionary optimization computation by using a double-layer optimization heterogeneous proxy model according to claim 1, wherein the method comprises the following steps: in the step S1, an initial sample is generated from the design space according to the latin hypercube sampling, and the individual fitness value is calculated as an original objective function and stored in the database DB.
3. The method for assisting multi-objective evolutionary optimization computation by using a double-layer optimization heterogeneous proxy model according to claim 1, wherein the method comprises the following steps: the step S2 specifically comprises the following substeps
S2.1, constructing a Kriging approximate model for each original objective function, wherein the Kriging approximate model is shown in the following formula
y(x)＝μ(x)+ε(x),ε(x)～N(0,σ2)
Wherein μ is the predictive value of the regression model, i.e., μ=fβ and ε (x) are gaussian distributions with mean 0 and standard deviation σ; the correlation function selects a Gaussian kernel function
Wherein i, j represents the row and column positions of the variables in the matrix, θ i Expressed as a super-parameter, the value of θ is obtained by the following maximum likelihood function
wherein ,N1 Representing population, y being the real objective function value, det (R) being the determinant of matrix R; after obtaining the super parameter theta, respectively calculating the coefficient beta and the variance sigma 2 Further approximating the objective function value;
s2.2, using the initial model learned super parameters for an incremental model to accelerate the approximation of the original Kriging model; from R -1 Calculate and calculateNew correlation matrix writing
Wherein the matrix is divided by n, qPartitioning, wherein R is a correlation matrix of an original Kriging model; inversion calculation of the partition matrix is as follows
Wherein c=b-ase:Sub>A T R -1 A。
4. The method for assisting multi-objective evolutionary optimization computation by using a double-layer optimization heterogeneous proxy model according to claim 1, wherein the method comprises the following steps: in the step S3, the AR-NSGA-III is determined by adopting the difference of entropy values of the population in each evolutionary iteration, wherein the entropy value calculation method comprises the following steps:
wherein inf is a normalized value, mid is a normalized median difference, t is the number of iterations, and the entropy difference between two iterations is Δe t ＝|e t -e t-1 I, Δe when population updates t The value of (a) is positively correlated with the individual variation amplitude in the decision space, i.e. Δe t The larger the value, the larger the population change, indicating that the population is undergoing an exploration phase, will tend towards an uncertainty region; conversely, Δe t The smaller the value, the smaller the population variation, and the population tends to converge and stabilize.
5. The method for assisting multi-objective evolutionary optimization computation by using a double-layer optimization heterogeneous proxy model according to claim 1, wherein the method comprises the following steps: in the step S4, whether a feasible solution exists in the feasible region is judged, and if the feasible solution exists, the optimization stage is shifted, and local optimization is performed according to the region where the feasible solution exists; if no feasible solution exists, adopting a repair strategy to guide the evolution of the infeasible solution to a feasible region until the feasible solution is generated, and specifically, the method comprises the following steps of:
s4.1, real evaluation solutions stored in all databases are used for establishing a Kriging model for the constraint function;
s4.2, give the solution x of population P i And calculate x i Is constrained by VC (x) i )＝(max{0,g 1 (x i )},...,max{0,g m (x i )}) T, wherein g(xi ) Is x i Each constraint value;
s4.3, the constructed Kriging modeling is used for approximating x i +e j Expressed as
Where j=1, …, d, m is the constraint number,is the adaptation value of the Kriging model approximation of the kth constraint, e j Is a vector in which the j-th element is an extremely small positive constant and the remaining constants are all 0;
s4.4, calculating a gradient matrix
wherein ,C(xi )＝(g 1 (x i ),...,g m (x i )) T ；
S4.5 thusI.e. a repair solution, if the constraint violates the condition G (x' i )<G(x i ) Then x 'is' i Added to the evolved population.
6. The method for assisting multi-objective evolutionary optimization computation by using a double-layer optimization heterogeneous proxy model according to claim 1, wherein the method comprises the following steps: the step S5 specifically comprises the following substeps
S5.1, carrying out ascending order on all feasible solutions stored in the steps S2 to S4, wherein the order is based on the shortest Euclidean distance between the feasible solutions and the infeasible solutions:
wherein ,is the i < th > feasible solution, <>Is the j-th infeasible solution, |ip| represents the number of infeasible solutions; if it isThen the two feasible solutions are assigned to the same cluster; if it isThe single feasible solution and the nearest infeasible solution form a cluster until all the feasible solutions are distributed into the respective clusters;
s5.2, forming a promising feasible local area by the minimum lower bound and the maximum upper bound of the decision variables of all solutions in the cluster according to the clusters formed by the respective components, and further searching for the optimal solution.
7. The method for assisting multi-objective evolutionary optimization computation by using a double-layer optimization heterogeneous proxy model according to claim 1, wherein the method comprises the following steps: in the step S6, the support vector machine constructs a decision function c (x) =sgn (w) T φ(x)+w 0 ) As a classifier, for a classification problem, inputWill be divided into positive or negative classes denoted c ε { +1, -1}, where φ (x) is a +_ from the input space to the high-dimensional feature space>Mapping function of (2), weight vector->And offset->Parameters to be optimized;
will be based on training samplesBuilding an SVM model is considered as an optimization problem:
s.t.c i (w T φ(x)+w 0 )≥1-ξ i ,ξ i ≥0
wherein ,c1 Is of the positive and negative type, xi i Is a relaxation variable, C is a hyper-parameter; the SVM estimates a new sampling point by the following equation
wherein ,,i is Lagrangian multiplier, K (x i ,x)＝exp(-γ||x i -x|) is an RBF kernel function, gamma>0 controls the complexity of the decision boundary.
8. The method for assisting multi-objective evolutionary optimization computation by using a double-layer optimization heterogeneous proxy model according to claim 1, wherein the method comprises the following steps: in the step S7, firstly, a layering technology in a vector difference generation strategy is utilized to divide a population, and a reference individual is matched to simulate different evolution directions of the population according to different periods so as to obtain a vector difference, and the random search with the direction of the population evolution is conducted to be dominant; then dynamically adjusting the DE scaling factor by mining evolutionary information of a deeper level of the decision space;
MOEA/D-iDE decomposes a multi-objective problem into multiple single-objective sub-problems, for the ith sub-problem, building a datasetAll solutions are included in the archive for training input and +.> Classified as wherein />For all evaluated solutions, < >>Is the current best solution set for the adjacent sub-problem;
wherein g (x|lambda) k Z) is chebyshev decomposition, and B (i) is the index set of adjacent sub-questions of the ith question.
9. The method for assisting multi-objective evolutionary optimization computation by using a double-layer optimization heterogeneous proxy model according to claim 1, wherein the method comprises the following steps: the step S8 specifically comprises the following substeps
S8.1, carrying out normalization treatment on the test solution of the agent auxiliary evaluation;
s8.2, regarding the minimum value in the decision variables of the parent and the offspring of the population as an ideal point;
s8.3 several individuals x which will be furthest from the parent * Stored in the diversity metric Dvs file, x * The method meets the following conditions:
Dvs(x * )＝max p＝1:N {|x * ,x p | 2 }
wherein ,xp Traversing from 1 to N for the current individuals in the population;
s8.4, calculating Euclidean distance between the test solution and the ideal point, storing the Euclidean distance in a convergence metric Cvg file, and merging the individuals stored in Cvg and Dvs into a new set newObj;
s8.5, applying a solution of a first front edge in the non-dominant sorting screening set newObj;
and S8.6, evaluating the screening solution through the original expensive function to update the model.
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