CN113642732A - Data optimization method, system, device and medium for co-evolution and covariance - Google Patents

Data optimization method, system, device and medium for co-evolution and covariance Download PDF

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CN113642732A
CN113642732A CN202110780834.9A CN202110780834A CN113642732A CN 113642732 A CN113642732 A CN 113642732A CN 202110780834 A CN202110780834 A CN 202110780834A CN 113642732 A CN113642732 A CN 113642732A
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王彬
任露
江巧永
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Abstract

The invention discloses a data optimization method, a system, equipment and a medium based on co-evolution and covariance, and belongs to the technical field of single-target optimization in evolution calculation. The function evaluation times are generated in the evolution process, such as the function evaluation times are increased when the fitness is evaluated; the relation between the function evaluation times and the maximum function evaluation times is a circulation condition set in the evolution process; the problem that variables can be separated can be solved through co-evolution, the optimization problem that the variables cannot be separated can be solved by adding covariance analysis into an optimizer, finally, the population is evolved towards a direction with a good fitness value, the global search capability of the algorithm is enhanced, and the convergence speed of the algorithm is accelerated.

Description

Data optimization method, system, device and medium for co-evolution and covariance
Technical Field
The invention belongs to the technical field of single-target optimization in evolution calculation, and relates to a data optimization method, a system, equipment and a medium based on co-evolution and covariance.
Background
Differential Evolution (DE) is a random search algorithm for numerical optimization problems. Since the years that the DE algorithm was proposed, it has had some influence in the field of evolution, but the search performance of DE depends on the settings of the control parameters, i.e. population size, scaling factor F, crossover rate CR, which in turn depend on practical issues. In many practical problems, it is difficult to set optimal parameters for problem optimization under unknown conditions, especially for large-scale problems, and it is difficult to find optimal parameter settings in a short time, so that more and more researchers have made a lot of improvements on the basis of DE.
Co-evolution (CC) is used to solve large-scale optimization problems that are decomposed into multiple independent sub-components and then optimized simultaneously in finding the optimal solution. The CC genetic algorithm proposed in Potter et al can solve the separable optimization problem, but is ineffective in the inseparable optimization problem. This is because the complexity of the correlation between variables affects the performance of the algorithm during co-evolution.
Disclosure of Invention
The invention aims to overcome the defects that differential evolution cannot be applied to large-scale practice and co-evolution cannot be applied to an inseparable optimization situation in the prior art, and provides a data optimization method and system based on co-evolution and covariance.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
a data optimization method based on co-evolution and covariance comprises the following steps:
step 1) initializing a data population to obtain an initial population;
step 2) carrying out differential grouping on the initial population to obtain a correlation variable group and a non-correlation variable group;
step 3) adopting a differential evolution mechanism, randomly selecting parent individuals based on target vectors of the relevant variable group and the non-relevant variable group, and breeding to obtain offspring individuals; carrying out fitness evaluation on the parent individuals and the offspring individuals, and keeping the individuals with smaller objective function values in the next generation;
step 4) grouping the initial population in the step 1) by using covariance analysis, randomly selecting parent individuals based on the target vector of each group after grouping, and obtaining offspring individuals after breeding; carrying out fitness evaluation on the parent individuals and the child individuals, and keeping the parent individuals and the child individuals with smaller objective function values in the next generation;
step 5) obtaining a fitness function according to the fitness value of the population, and further adaptively selecting an evolution method; if the fitness of the co-evolution is good, returning to the step 2), otherwise returning to the step 4);
step 6) judging the relation between the function evaluation times and the maximum function evaluation times;
if the function evaluation times are less than the maximum function evaluation times, returning to the step 2) to continue the circular evolution; and stopping the evolution if the evaluation times of the functions are more than or equal to the maximum evaluation times of the functions.
Preferably, the specific process of initialization is as follows: and generating a plurality of individuals as an initialization population by using a random key coding mode, and obtaining the population dimension, the individual number, the initial individual dimension and the maximum evaluation times of an initialization function of the initialization population.
Preferably, the specific process of step 2) is:
based on a preset test problem, dividing decision variables in the initial population into two groups by utilizing the correlation between the decision variables, wherein the two groups are a correlation variable group and a non-correlation variable group respectively;
the set of correlated variables contains separable decision variables and the set of uncorrelated variables contains inseparable decision variables.
Preferably, the propagation process of step 3) specifically comprises mutation operation and crossover operation which are sequentially performed;
the specific process of mutation operation is to generate a new individual by using the mutation strategy of DE/rand/1/bin;
the specific process of the crossover operation is to generate an experimental vector by the mutation vector and the target vector.
Preferably, the specific process of step 3) is as follows:
for each target individual i involved in the evolution, a new individual was generated using the DE/rand/1/bin mutation strategy:
Vi,G＝Xr1,G+F·(Xr2.G-Xr3,G) (1)
in formula (1), the subscript Xr1,G,Xr2.G,Xr3,GIs at P ═ x1,x2,…,xNRandomly selected from (C); vi,GIs a new individual generated, parameter F is a positive mutation factor;
then passing through the mutation vector Vj,i,GAnd the target vector Xj,i,GGenerating an experiment vector Uj,i,G：
Figure BDA0003156847680000031
In formula (2), rand (0,1) represents a uniform random number between (0, 1); j is a function ofrandIs from [1, D ]]Uniformly and randomly selecting decision variable subscripts; CR is a crossover operating parameter; d represents the dimension of the decision variable;
then for the target vector Xi,GAnd experiment vector Ui,GAnd evaluating the fitness, selecting an individual with a better fitness value based on a greedy selection method, wherein the selection process comprises the following steps:
Figure BDA0003156847680000032
in formula (3), if f (U)i,G)<f(Xi,G) Then choose the experimental vector Ui,GEntering the next generation, otherwise selecting the target vector Xi,GAnd entering the next generation.
Preferably, the specific process of step 4) is:
step 4.1), selecting the first N/2 individuals according to the population after differential evolution to calculate a covariance matrix:
Figure BDA0003156847680000041
wherein the content of the first and second substances,
Figure BDA0003156847680000042
is the covariance matrix of the first N/2 individuals, and is calculated from cov (i, j), which is the covariance of the ith and jth dimensions of the first N/2 individuals in the current population as:
Figure BDA0003156847680000043
k＝1，2，…，D；j＝1，2，…，D；
in formulae (4) to (5), xi,kIs the firstK-dimension, x, of i individualsi,jIs the jth dimension of the ith individual,
Figure BDA0003156847680000044
and
Figure BDA0003156847680000045
respectively are the average values of the k-th dimension and the j-th dimension of the first N/2 individuals of the current population.
Step 4.1), covariance matrix cov (P) for the first N/2 individuals in step 4.1) based on data characteristics1:N/2) The decomposition is carried out as follows:
Figure BDA0003156847680000046
in the formula (6), R is a D × D orthogonal matrix coordinate system representing the feature, and each row of R is a covariance matrix cov (P)1:N/2) R' represents the transformation from the eigen-coordinate system to the natural coordinate system, Λ is a diagonal matrix consisting of eigenvalues;
step 4.3), according to the characteristic vector of the covariance matrix in the step 4.2), the target vector x in the natural coordinate system is processediAnd xkExpressed in the characteristic coordinate system as:
xi′＝xiR (7)
xk′＝xkR (8)
step 4.4) obtaining the target vector X in the step 4.3)r1,j,Xr2,j,Xr3,jExpressed as X in the characteristic coordinate systemr1,j′,Xr2,j′,Xr3,j' generating candidate solutions v in a characteristic coordinate system using a search equation of differential evolutionj′，
vj′＝Xr1,j′+F·(Xr2,j′-Xr3,j′) (9)
Step 4.5), candidate solution v in the characteristic coordinate system obtained in the step 4.4) is processedj' conversion to v in the Natural coordinate Systemj，
vj＝vj′R′ (10)
Wherein v isjIs a solution candidate v in the characteristic coordinate systemj' converting to a natural coordinate system to obtain a candidate solution;
for target vector Xi,GAnd experiment vector Ui,GAnd (3) carrying out fitness evaluation, and selecting individuals with better fitness values by greedy, namely, keeping the individuals with smaller objective function values in the next generation, wherein the selection process comprises the following steps:
Figure BDA0003156847680000051
wherein if f (U)i,G)＜f(Xi,G) Then choose the experimental vector Ui,GEntering the next generation, otherwise selecting the target vector Xi,GAnd entering the next generation.
Preferably, the adaptive selection evolution method of step 5) comprises the following specific processes:
after each generation, the probability p is calculated as follows:
Figure BDA0003156847680000052
in formula (12), p represents the probability that CCDE is selected for the next generation, and the overall success rates of CCDE and codde are described as p1 and p2, respectively;
if p is greater than 0.5 when a generation starts, the success rate of CCDE is greater than CODDE, and CCDE is an optimizer of the generation; otherwise, the self-adaptive selection evolution method is continued.
A co-evolution and covariance based data optimization system comprising:
the initialization module is used for initializing the data population to obtain an initial population;
the grouping module is interacted with the initialization module and is used for grouping the initial population to obtain a correlation variable group and a non-correlation variable group;
the evolution module is interacted with the grouping module, carries out differential evolution and propagation on the relevant variable group and the non-relevant variable group respectively according to the adaptive selection evolution method of the population fitness value to obtain corresponding parent individuals and offspring individuals, and carries out fitness evaluation on the parent individuals and the offspring individuals;
and the evaluation decision module is interacted with the evolution module, judges the relationship between the function evaluation times and the maximum function evaluation times, and selects whether to carry out continuous evolution or not based on the judgment result.
A terminal device comprising a memory, a processor and a computer program stored in said memory and executable on said processor, said processor implementing the steps of said data optimization method when executing said computer program.
A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of a method for data optimization
Compared with the prior art, the invention has the following beneficial effects:
the invention discloses a data optimization method based on co-evolution and covariance, which comprises the steps of initializing a data population, grouping by using covariance, selecting an evolution method through co-evolution, evaluating fitness, and judging the relationship between the evaluation times of a function and the evaluation times of a maximum function so as to judge whether to continue to evolve or not. The function evaluation times are generated in the evolution process, such as the function evaluation times are increased when the fitness is evaluated; the relation between the function evaluation times and the maximum function evaluation times is a circulation condition set in the evolution process; the problem that variables can be separated can be solved through co-evolution, the optimization problem that the variables cannot be separated can be solved by adding covariance analysis into an optimizer, finally, the population is evolved towards a direction with a good fitness value, the global search capability of the algorithm is enhanced, and the convergence speed of the algorithm is accelerated.
The invention also discloses a data optimization system based on co-evolution and covariance, which comprises an initialization module, a data population generation module and a data population optimization module, wherein the initialization module is used for initializing the data population to obtain an initial population; the grouping module is interacted with the initialization module and is used for grouping the initial population to obtain a correlation variable group and a non-correlation variable group; the evolution module is interacted with the grouping module, carries out differential evolution and propagation on the relevant variable group and the non-relevant variable group respectively according to the adaptive selection evolution method of the population fitness value to obtain corresponding parent individuals and offspring individuals, and carries out fitness evaluation on the parent individuals and the offspring individuals; and the evaluation decision module is interacted with the evolution module, judges the relationship between the function evaluation times and the maximum function evaluation times, and selects whether to carry out continuous evolution or not based on the judgment result.
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FIG. 1 is a graph comparing convergence on a test function F1 of an evolutionary algorithm based on co-evolution and covariance according to the present invention;
FIG. 2 is a graph comparing convergence on a test function F8 of an evolutionary algorithm based on co-evolution and covariance according to the present invention;
FIG. 3 is a graph comparing convergence on a test function F9 of an evolutionary algorithm based on co-evolution and covariance according to the present invention;
FIG. 4 is a graph comparing convergence on a test function F10 of an evolutionary algorithm based on co-evolution and covariance according to the present invention;
FIG. 5 is a graph comparing convergence on a test function F14 of an evolutionary algorithm based on co-evolution and covariance according to the present invention;
FIG. 6 is a graph comparing convergence on a test function F15 of an evolutionary algorithm based on co-evolution and covariance according to the present invention;
FIG. 7 is a graph comparing convergence on a test function F16 of an evolutionary algorithm based on co-evolution and covariance according to the present invention;
FIG. 8 is a graph comparing convergence on a test function F17 of an evolutionary algorithm based on co-evolution and covariance according to the present invention;
FIG. 9 is a graph comparing convergence on a test function F18 of an evolutionary algorithm based on co-evolution and covariance according to the present invention;
FIG. 10 is a graph comparing convergence on a test function F19 of an evolutionary algorithm based on co-evolution and covariance according to the present invention;
FIG. 11 is a graph of the convergence comparison of the evolutionary algorithm based on co-evolution and covariance on the test function F20.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
example 1
A data optimization method based on co-evolution and covariance comprises the following steps:
step 1) initializing a data population to obtain an initial population;
step 2) carrying out differential grouping on the initial population to obtain a correlation variable group and a non-correlation variable group;
step 3) adopting a differential evolution mechanism, randomly selecting parent individuals based on target vectors of the relevant variable group and the non-relevant variable group, and breeding to obtain offspring individuals; carrying out fitness evaluation on the parent individuals and the child individuals, and keeping the individuals with smaller objective function values in the next generation;
step 4) grouping the initial population in the step 1) by using covariance analysis, randomly selecting parent individuals based on the target vector of each group after grouping, and obtaining offspring individuals after breeding; carrying out fitness evaluation on the parent individuals and the child individuals, and keeping the parent individuals and the child individuals with smaller objective function values in the next generation;
step 5) selecting an evolution method in a self-adaptive manner according to the fitness value of the population; if the CCDE has good fitness, returning to the step 2), otherwise returning to the step 4);
step 6) judging the relation between the function evaluation times and the maximum function evaluation times, and returning to the step 2) to continue the circular evolution if the function evaluation times are smaller than the maximum function evaluation times; and stopping the evolution if the evaluation times of the functions are more than or equal to the maximum evaluation times of the functions.
Example 2
A data optimization method based on co-evolution and covariance comprises the following steps:
step 1, initializing a population, and randomly generating N (N is 100) individuals in a search space as an initial population;
step 1.1, initializing a population: encoding method using random keyThe formula generates N (N ═ 100) individuals as an initialization population, and the initialization population P ═ x1,x2,…,xNThe initial individual dimension is max { D }, where x1,x2,…,xNN individuals, D is the population dimension (D50);
step 1.2, initializing the maximum evaluation times of the function: set FESMAX 10000;
step 2, aiming at the initial population generated in the step 1, grouping variables according to the correlation between the variables by using the expanded differential grouping, and grouping the correlation variables into a group;
step 2.1, aiming at the initial population generated in the step 1, dividing decision variables by utilizing the correlation among the decision variables by combining the test problem CEC 2014;
2.2, dividing separable variables into the same group, and dividing inseparable variables into the same group;
step 3, generating offspring individuals aiming at the target vectors in each group in the population by adopting a differential evolution mechanism;
the propagation process comprises mutation operation and then cross operation;
the specific process of mutation operation is as follows:
for each target individual i involved in the evolution, a new individual was generated using the DE/rand/1/bin mutation strategy:
Vi,G＝Xr1,G+F·(Xr2.G-Xr3，G) (1)；
wherein the subscript Xr1，G，Xr2.G,Xr3,GIs at P ═ x1,x2,…,xNRandomly selected but different individuals from the subscript i, Vi,GIs a new individual generated, parameter F is a positive mutation factor;
the specific process of the cross operation is as follows:
the operation is carried out by mutating the vector Vj,i,GAnd the target vector Xj,i,GGenerating an experiment vector Uj，i，G，
Figure BDA0003156847680000101
Wherein rand (0,1) represents a uniform random number between (0,1), jrandIs from [1, D ]]Uniformly randomly selected decision variable subscripts, CR is a crossover operating parameter.
Step 4, evaluating the fitness of parent individuals and child individuals in the coevolution, and keeping the parent individuals and the child individuals with smaller objective function values in the next generation;
for target vector Xi，GAnd experiment vector Ui，GAnd (3) carrying out fitness evaluation, and selecting individuals with better fitness values by greedy, namely, keeping the individuals with smaller objective function values in the next generation, wherein the selection process comprises the following steps:
Figure BDA0003156847680000102
wherein if f (U)i，G)＜f(Xi，G) Then choose the experimental vector Ui，GEntering the next generation, otherwise selecting the target vector Xi，GAnd entering the next generation.
Step 5, adding covariance analysis in an optimizer (differential evolution) aiming at the initial population generated in the step 1, and generating offspring individuals aiming at target vectors in each group in the population;
step 5.1, selecting the first N/2 individuals according to the population after differential evolution to calculate a covariance matrix:
Figure BDA0003156847680000103
wherein the content of the first and second substances,
Figure BDA0003156847680000104
is the covariance matrix of the first N/2 individuals, and is calculated from cov (i, j), which is the covariance of the ith and jth dimensions of the first N/2 individuals in the current population as:
Figure BDA0003156847680000105
k＝1,2,…,D，j＝1,2,…,D；
wherein x isi,kIs the k dimension, x, of the ith individuali,jIs the jth dimension of the ith individual,
Figure BDA0003156847680000106
and
Figure BDA0003156847680000107
respectively are the average values of the k-th dimension and the j-th dimension of the first N/2 individuals of the current population.
Step 5.2, covariance matrix cov (P) for the first N/2 individuals in step 5.1 based on data characteristics1:N/2) The decomposition is carried out as follows:
Figure BDA0003156847680000111
where R is a D × D orthogonal matrix coordinate system representing the feature, and each row of R is a covariance matrix cov (P)1:N/2) R' represents the transformation from the eigen-coordinate system to the natural coordinate system, Λ is a diagonal matrix consisting of eigenvalues;
step 5.3, according to the characteristic vector of the covariance matrix in the step 5.2, the target vector x in the natural coordinate system is processediAnd xkExpressed in the characteristic coordinate system as:
xi′＝xiR (7)；
xk′＝xkR (8)；
step 5.4, obtaining the target vector X in the step 5.3r1,j,Xr2,j,Xr3,jExpressed as X in the characteristic coordinate systemr1,j′,Xr2,j′,r3,j' generating candidate solutions v in a characteristic coordinate system using a search equation of differential evolutionj′：
vj′＝Xr1,j′+F·(Xr2，j′-Xr3，j′) (9)；
Step (ii) of5.5, solving the candidate solution v in the characteristic coordinate system obtained in the step 5.4j' conversion to v in the Natural coordinate Systemj：
vj＝vj′R′ (10)；
Wherein v isjIs a solution candidate v in the characteristic coordinate systemj' candidate solution obtained after conversion to natural coordinate system.
Step 6, carrying out fitness evaluation on parent individuals and child individuals which are added into the optimizer and evolved by covariance analysis, and keeping the parent individuals and child individuals with smaller objective function values in the next generation;
for target vector Xi，GAnd experiment vector Ui，GAnd (3) carrying out fitness evaluation, and selecting individuals with better fitness values by greedy, namely, keeping the individuals with smaller objective function values in the next generation, wherein the selection process comprises the following steps:
Figure BDA0003156847680000121
wherein if f (U)i,G)＜f(Xi,G) Then choose the experimental vector Ui,GEntering the next generation, otherwise selecting the target vector Xi,GAnd entering the next generation.
Step 7, selecting an evolutionary method in a self-adaptive manner according to the fitness value of the population;
in order to improve the performance of the algorithm, adaptive selection is performed between CCDE and CODDE. After each generation, the probability p is calculated as follows:
Figure BDA0003156847680000122
where p represents the probability that CCDE is selected for the next generation. The overall success rates of CCDE and CODDE are described as p1 and p2, respectively. If p >0.5 at the beginning of a generation, then the success rate of CCDE is greater than CODDE, and therefore CCDE will be the optimizer for that generation. Otherwise, the evolution will continue with COVDE. The method has the advantage that a better optimization result can be obtained no matter whether the optimization problem can be separated or not.
And 8, judging whether the termination condition is met, returning to the step 3 to continue the circular evolution if the function evaluation frequency FES is less than MAXFES, and stopping the evolution if the function evaluation frequency FES is more than or equal to MAXFES. Wherein MAXFES is the maximum function evaluation time.
Example 3
First, a test function is given: the performance of the proposed algorithm was tested using CEC2014, as shown in table 1 in particular, where the second column is the dimension of the decision variable. Then, algorithm parameters are initialized: in this simulation, the population size of the test function is D50, the population size N is 2 × D (i.e., 100), and the maximum function evaluation number MAXFES is D × 10000.
TABLE 1 test set of functions
Figure BDA0003156847680000123
Figure BDA0003156847680000131
And carrying out simulation experiments on the test functions according to the specific flow of the A-CC/COV-DE, thereby obtaining test results corresponding to the test functions. To better illustrate the effect of the present invention, original DE, CODDE and CCDE were also selected to perform simulation experiments on the test functions, and compared with the algorithm performance of the A-CC/COV-DE of the present invention, and the results are shown in Table 2. The p-value was obtained using the Kruskal-Wallis rank sum test and compared pairwise using the Wilcoxon rank sum test, comparing the median in the samples mainly, the median that the comparison algorithm compares significantly with A-CC/COV-DE is marked in bold, and the conventional font indicates that the median has similar algorithm performance as A-CC/COV-DE. As a result of the rank sum test, the signs +, -and ≈ following the result of each algorithm run indicate that the performance of A-CC/COV-DE is better than, worse than, and similar to that of the current algorithm, respectively.
Table 2 shows experimental results obtained by running three algorithms 50 times on the test function CEC2014, and CCDE in table 2 shows a large-scale optimization problem solved by co-evolution; DE is differential evolution; COVDE means to add covariance analysis in the optimizer; A-CC/COV-DE represents an adaptive evolution algorithm based on co-evolution and covariance analysis;
table 2 experimental results obtained by running three algorithms 50 times on the test function CEC2014
CCDE COVDE DE A-CC/COV-DE
F1 8.01E+00 7.24E+05 1.43E+06 2.50E-01
F2 4.22E+06 1.63E+02 3.02E+00 3.41E+04
F3 1.71E+01 4.44E-12 2.75E-01 1.35E-05
F4 9.34E+01 8.24E+01 5.78E+01 8.13E+01
F5 2.12E+01 2.09E+01 2.11E+01 2.11E+01
F6 3.99E+00 4.44E+01 1.42E+00 4.13E+00
F7 6.79E-01 1.36E-13 1.27E-13 3.80E-01
F8 9.48E-13 1.37E+02 1.87E+02 9.35E-13
F9 8.98E+01 1.63E+02 3.53E+02 8.79E+01
F10 7.99E-03 6.64E+03 9.19E+03 6.50E-03
F11 4.03E+03 7.50E+03 1.30E+04 4.07E+03
F12 3.42E+00 1.58E+00 3.27E+00 1.76E+00
F13 5.50E-01 4.02E-01 4.61E-01 5.69E-01
F14 3.62E-01 2.61E-01 3.38E-01 2.79E-01
F15 3.25E+01 1.88E+01 3.10E+01 1.87E+01
F16 2.23E+01 2.12E+01 2.21E+01 2.12E+01
F17 7.72E+04 1.29E+03 1.58E+04 1.14E+03
F18 1.21E+02 8.91E+01 1.35E+02 3.30E+01
F19 6.89E+00 1.14E+01 1.22E+01 6.74E+00
F20 7.19E+01 6.04E+01 9.81E+01 3.58E+01
+/≈/- 17/3/0 13/2/5 15/5/0
From the data in table 2, one can see: over the 20 test functions of CEC2014, the performance of A-CC/COV-DE is similar to CCDE only over three test functions, is similar to COVDE only over two test functions, is worse than COVDE and DE over five test functions, and is better than CCDE, COVDE and DE over other test functions.
The convergence of the algorithm is compared as shown in fig. 1-11 over a 50-dimensional test function. As can be seen from FIG. 1, CCDE has better convergence than CODDE and DE and A-CC/COV-DE has better convergence than DE, CODDE and CCDE in the test function F1; from FIG. 2, it can be seen that the convergence of A-CC/COV-DE and the convergence of CCDE at the late stage of evolution are similar on the test function F8, but both have better convergence than DE and CODDE; from FIG. 3, it can be seen that the convergence of A-CC/COV-DE and that of CCDE are similar at the late stage of evolution on test function F9, but both have better convergence than DE and CODDE; from FIG. 4, it can be seen that the convergence of A-CC/COV-DE and the convergence of CCDE at the late stage of evolution are similar on the test function F10, but both have better convergence than DE and CODDE; from FIGS. 5 and 6, it can be seen that the convergence of A-CC/COV-DE, CCDE, CODDE and DE is similar in the late evolutionary stage on the test functions F14 and F15, but the convergence of A-CC/COV-DE is better; from FIGS. 7 and 8, it can be seen that the test functions F16 and F17 have better convergence of CODDE in the early stage of evolution, but the A-CC/COV-DE has better convergence than DE, CCDE and CODDE in the late stage of evolution; it can be seen from FIG. 9 that the test function F18 shows better convergence of CODDE and CODDE in the early stage of evolution, but the convergence of A-CC/COV-DE in the later stage of evolution is better than the convergence of DE, CCDE and CODDE; from FIG. 10, it can be seen that the convergence of A-CC/COV-DE and that of CCDE are similar at the late stage of evolution on test function F19, but both have better convergence than DE and CODDE; it can be seen from FIG. 11 that the convergence of A-CC/COV-DE on the test function F20 is better than the convergence of DE, CCDE, and CODDE during evolution.
Example 4
A co-evolution and covariance based data optimization system comprising:
the initialization module is used for initializing the data population to obtain an initial population;
the grouping module is interacted with the initialization module and is used for grouping the initial population to obtain a correlation variable group and a non-correlation variable group;
the evolution module is interacted with the grouping module, carries out differential evolution and propagation on the relevant variable group and the non-relevant variable group respectively according to the adaptive selection evolution method of the population fitness value to obtain corresponding parent individuals and offspring individuals, and carries out fitness evaluation on the parent individuals and the offspring individuals;
and the evaluation decision module is interacted with the evolution module, judges the relationship between the function evaluation times and the maximum function evaluation times, and selects whether to carry out continuous evolution or not based on the judgment result.
Example 5
The method of the present invention, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, all or part of the flow of the method according to the embodiments of the present invention may also be implemented by a computer program, which may be stored in a computer-readable storage medium, and when the computer program is executed by a processor, the steps of the method embodiments may be implemented. Wherein the computer program comprises computer program code, which may be in the form of source code, object code, an executable file or some intermediate form, etc. Computer-readable storage media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. It should be noted that the computer readable medium may contain content that is subject to appropriate increase or decrease as required by legislation and patent practice in jurisdictions, for example, in some jurisdictions, computer readable media does not include electrical carrier signals and telecommunications signals as is required by legislation and patent practice. The computer storage medium may be any available medium or data storage device that can be accessed by a computer, including but not limited to magnetic memory (e.g., floppy disk, hard disk, magnetic tape, magneto-optical disk (MO), etc.), optical memory (e.g., CD, DVD, BD, HVD, etc.), and semiconductor memory (e.g., ROM, EPROM, EEPROM, nonvolatile memory (NANDFLASH), Solid State Disk (SSD)), etc.
Example 6
The invention also provides a computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, the processor implementing the steps of the method of the invention when executing the computer program. The Processor may be a Central Processing Unit (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable gate array (FPGA) or other Programmable logic device, discrete gate or transistor logic, discrete hardware components, etc.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (10)

1. A data optimization method based on co-evolution and covariance is characterized by comprising the following steps:
step 1) initializing a data population to obtain an initial population;
step 2) carrying out differential grouping on the initial population to obtain a correlation variable group and a non-correlation variable group;
step 3) adopting a differential evolution mechanism, randomly selecting parent individuals based on target vectors of the relevant variable group and the non-relevant variable group, and breeding to obtain offspring individuals; carrying out fitness evaluation on the parent individuals and the offspring individuals, and keeping the individuals with smaller objective function values in the next generation;
step 4) grouping the initial population in the step 1) by using covariance analysis, randomly selecting parent individuals based on the target vector of each group after grouping, and obtaining offspring individuals after breeding; carrying out fitness evaluation on the parent individuals and the child individuals, and keeping the parent individuals and the child individuals with smaller objective function values in the next generation;
step 5) obtaining a fitness function according to the fitness value of the population, and further adaptively selecting an evolution method; if the fitness of the co-evolution is good, returning to the step 2), otherwise returning to the step 4);
step 6) judging the relation between the function evaluation times and the maximum function evaluation times;
if the function evaluation times are less than the maximum function evaluation times, returning to the step 2) to continue the circular evolution; and stopping the evolution if the evaluation times of the functions are more than or equal to the maximum evaluation times of the functions.
2. The coevolution and covariance based data optimization method according to claim 1, wherein the specific process of initialization is as follows: and generating a plurality of individuals as an initialization population by using a random key coding mode, and obtaining the population dimension, the individual number, the initial individual dimension and the maximum evaluation times of an initialization function of the initialization population.
3. The coevolution and covariance based data optimization method according to claim 1, wherein the specific process of step 2) is as follows:
based on a preset test problem, dividing decision variables in the initial population into two groups by utilizing the correlation between the decision variables, wherein the two groups are a correlation variable group and a non-correlation variable group respectively;
the set of correlated variables contains separable decision variables and the set of uncorrelated variables contains inseparable decision variables.
4. The coevolution and covariance based data optimization method according to claim 1, wherein the propagation process of step 3) specifically comprises mutation operation and crossover operation performed in sequence;
the specific process of mutation operation is to generate a new individual by using the mutation strategy of DE/rand/1/bin;
the specific process of the crossover operation is to generate an experimental vector by the mutation vector and the target vector.
5. The coevolution and covariance based data optimization method according to claim 1, wherein the specific process in step 3) is as follows:
for each target individual i involved in the evolution, a new individual was generated using the DE/rand/1/bin mutation strategy:
Vi，G＝Xr1，G+F·(Xr2.G-Xr3，G) (1)
in formula (1), the subscript Xr1，G，Xr2.G，Xr3，GIs at P ═ x1，x2，...，xNRandomly selected from (C); vi，GIs a new individual generated, parameter F is a positive mutation factor;
then passing through the mutation vector Vj，i，GAnd the target vector Xj，i，GGenerating an experiment vector Uj，i，G：
Figure FDA0003156847670000021
In formula (2), rand (0,1) represents a uniform random number between (0, 1); j is a function ofrandIs from [1, D ]]Uniformly and randomly selecting decision variable subscripts; CR is a crossover operating parameter; d represents the dimension of the decision variable;
then for the target vector Xi，GAnd experiment vector Ui，GAnd evaluating the fitness, selecting an individual with a better fitness value based on a greedy selection method, wherein the selection process comprises the following steps:
Figure FDA0003156847670000031
in formula (3), if f (U)i，G)＜f(Xi，G) Then choose the experimental vector Ui，GEntering the next generation, otherwise selecting the target vector Xi，GAnd entering the next generation.
6. The coevolution and covariance based data optimization method according to claim 5, wherein the specific process of step 4) is as follows:
step 4.1), selecting the first N/2 individuals according to the population after differential evolution to calculate a covariance matrix:
Figure FDA0003156847670000032
wherein the content of the first and second substances,
Figure FDA0003156847670000033
is the covariance matrix of the first N/2 individuals, and is calculated from cov (i, j), which is the covariance of the ith and jth dimensions of the first N/2 individuals in the current population as:
Figure FDA0003156847670000034
k＝1，2，...，D；j＝1，2，...，D；
in formulae (4) to (5), xi，kIs the k dimension, x, of the ith individuali，jIs the jth dimension of the ith individual,
Figure FDA0003156847670000036
and
Figure FDA0003156847670000037
respectively are the average values of the k-th dimension and the j-th dimension of the previous N/2 individuals of the current population;
step 4.1), covariance moments of the first N/2 individuals in step 4.1) according to data characteristicsArray cov (P)1：N/2) The decomposition is carried out as follows:
Figure FDA0003156847670000035
in the formula (6), R is a D × D orthogonal matrix coordinate system representing the feature, and each row of R is a covariance matrix cov (P)1：N/2) R' represents the transformation from the eigen-coordinate system to the natural coordinate system, Λ is a diagonal matrix consisting of eigenvalues;
step 4.3), according to the characteristic vector of the covariance matrix in the step 4.2), the target vector x in the natural coordinate system is processediAnd xkExpressed in the characteristic coordinate system as:
xi′＝xiR (7)
xk′＝xkR (8)
step 4.4) obtaining the target vector X in the step 4.3)r1，j，Xr2，j，Xr3，jExpressed as X in the characteristic coordinate systemr1，j′，Xr2，j′，Xr3，j' generating candidate solutions v in a characteristic coordinate system using a search equation of differential evolutionj′，
vj′＝Xr1，j′+F·(Xr2，j′-Xr3，j′) (9)
Step 4.5), candidate solution v in the characteristic coordinate system obtained in the step 4.4) is processedj' conversion to v in the Natural coordinate Systemj，
vj＝vj′R′ (10)0
Wherein v isjIs a solution candidate v in the characteristic coordinate systemj' converting to a natural coordinate system to obtain a candidate solution;
for target vector Xi，GAnd experiment vector Ui，GAnd (3) carrying out fitness evaluation, and selecting individuals with better fitness values by greedy, namely, keeping the individuals with smaller objective function values in the next generation, wherein the selection process comprises the following steps:
Figure FDA0003156847670000041
wherein if f (U)i，G)＜f(Xi，G) Then choose the experimental vector Ui，GEntering the next generation, otherwise selecting the target vector Xi，GAnd entering the next generation.
7. The coevolution and covariance based data optimization method according to claim 1, wherein the adaptive selection evolution method of step 5) comprises the following specific processes:
after each generation, the probability p is calculated as follows:
Figure FDA0003156847670000042
in formula (12), p represents the probability that CCDE is selected for the next generation, and the overall success rates of CCDE and codde are described as p1 and p2, respectively;
if p is more than 0.5 when a generation starts, the success rate of CCDE is more than CODDE, and CCDE is an optimizer of the generation; otherwise, the self-adaptive selection evolution method is continued.
8. A co-evolution and covariance based data optimization system, comprising:
the initialization module is used for initializing the data population to obtain an initial population;
the grouping module is interacted with the initialization module and is used for grouping the initial population to obtain a correlation variable group and a non-correlation variable group;
the evolution module is interacted with the grouping module, carries out differential evolution and propagation on the relevant variable group and the non-relevant variable group respectively according to the adaptive selection evolution method of the population fitness value to obtain corresponding parent individuals and offspring individuals, and carries out fitness evaluation on the parent individuals and the offspring individuals;
and the evaluation decision module is interacted with the evolution module, judges the relationship between the function evaluation times and the maximum function evaluation times, and selects whether to carry out continuous evolution or not based on the judgment result.
9. A terminal device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the steps of the data optimization method according to any one of claims 1 to 7 when executing the computer program.
10. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the data optimization method according to one of claims 1 to 7.
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CN117910410A (en) * 2024-03-19 2024-04-19 电子科技大学 Large-scale multi-target simulation chip circuit evolution optimization design method
CN117910410B (en) * 2024-03-19 2024-05-31 电子科技大学 Large-scale multi-target simulation chip circuit evolution optimization design method

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