CN111178621A - Parameter optimization method of electric heating load prediction support vector regression model - Google Patents
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Abstract
The invention provides a parameter optimization method of an electric heating load prediction support vector regression model, which comprises the following steps: firstly, analyzing and preprocessing relevant factors influencing the electric heating load, and dividing preprocessed data into training data and testing data; secondly, by utilizing the good nonlinear mapping characteristic of the support vector regression machine, a method for establishing a support vector regression model for short-term electric heating load prediction is provided; and finally, carrying out SVR model parameter analysis and selection, and designing an electric heating load SVR prediction model based on PSO optimization. The optimization method can remarkably improve the prediction precision of the SVR model and greatly shorten the modeling time. Meanwhile, compared with a common electric heating load linear prediction model, the model established by the method has higher efficiency and higher accuracy, and can be used for effectively guiding the fine management of electric heating equipment.
Description
Technical Field
The invention relates to a method for predicting load trend of an electric heating user under the operation of resident heating coal-to-electricity conversion, in particular to a parameter optimization method of an electric heating load prediction support vector regression model.
Background
The accurate prediction of the electric heating load is the premise of realizing 'heat supply on demand' and also the premise of realizing 'energy conservation and emission reduction'. Establishing an outdoor temperature-load linear model cannot realize accurate prediction, nor "on-demand heating" of a central heating system. In addition, the thermal load is affected by a variety of factors. Therefore, other influencing factors need to be considered and analyzed, and a nonlinear model is established to meet the prediction accuracy of the scheduling requirement and realize the quantitative management of the heat supply industry. With the development of informatization, heat supply enterprises can store heat supply data in real time, accurately acquire meteorological conditions and provide conditions for related research of heat load prediction.
In addition, the current load operation condition of the electric heating user cannot be monitored in real time. The emergency safety event can not be early warned in advance, and can only be remedied afterwards, so that the requirement of safe and reliable heating of the user can not be ensured. Therefore, it is necessary to analyze the relevant data of the electric heating users in each marketing service system, construct an electric heating user load prediction model by combining the relevant information of the electric heating equipment, monitor the use condition of the electric heating of the users on line in real time, early warn the possible hidden dangers, assist and promote the heating of enterprises and public institutions and residents to change coal into electricity, and reduce the pollution to the atmosphere caused by the direct-fired scattered coal heating mode.
In recent years, a large amount of research on electric heating load prediction is carried out by scholars at home and abroad. The traditional electric heating load prediction method comprises regression prediction, time series and the like, mainly carries out research and analysis based on mathematical statistics, and has a relatively simple structure. Furthermore, predictions with non-linear characteristics are difficult to implement. With the development of artificial intelligence, methods such as a neural network and a support vector machine are introduced into the thermal load prediction. The neural network can be used for obtaining a heat load prediction model, but the neural network is easy to fall into local optimization. The support vector regression has better nonlinear mapping characteristics, so that in recent years, many scholars apply the support vector regression to the field of load prediction, but the model parameter optimization of the support vector regression is still to be further researched because the selection of SVR model parameters directly influences the prediction accuracy of the model, and the currently adopted methods mainly comprise a trial and error method, a traversal method, a random algorithm and the like. The trial and error method is actually an empirical method, and is dependent on abundant experience, so that the optimal value cannot be obtained frequently. The conventional traversal method is a grid search method, which takes a long time and cannot achieve good effect.
Disclosure of Invention
In order to make up for the defects, the invention provides a parameter optimization method of an electric heating load prediction support vector regression model based on a particle swarm optimization, which introduces a PSO algorithm with global optimization capability to improve model parameters of an SVR model, improves the solving efficiency and obtains a more accurate solution, thereby achieving the purpose of improving the accuracy and stability of the SVR prediction model for electric heating load prediction.
The technical scheme provided by the invention is as follows:
a parameter optimization method of an electric heating load prediction support vector regression model comprises the following steps:
s1, analyzing and preprocessing relevant factors influencing the electric heating load, and dividing the preprocessed data into training data and testing data;
s2 is a method for establishing a support vector regression model for electric heating load prediction by utilizing the good nonlinear mapping characteristic of the support vector regression machine;
s3, carrying out SVR model parameter analysis and selection, identifying the processed training data by using a particle swarm algorithm to obtain optimal parameters (C, g), executing the SVR algorithm to output a predicted value, and finally comparing the predicted value with SVR and other methods to verify the effectiveness of the method.
Preferably, the relevant factors influencing the electric heating load in step S1 are divided into two categories: random and non-random factors;
the non-random factors are determinacy factors influencing the change of the electric heating load, and comprise meteorological factors, date factors and social factors;
the random factors are special conditions such as equipment faults and the like which may occur in the heating process of the electric heating equipment, and have great influence on heating; some special cases occur during heating, including equipment failure, site specific activity, due to random error terms.
Preferably, the data preprocessing described in step S1 includes correlation analysis and outlier rejection.
Preferably, the meteorological factors comprise outdoor temperature, humidity, solar radiation intensity, weather conditions and wind direction and wind speed; the weather condition value represents a humidity and solar radiation intensity parameter in addition to the outdoor temperature; taking the outdoor temperature and the weather condition as input variables, obtaining the outdoor temperature through weather forecast to obtain a specific quantitative value, and quantifying the weather condition value through qualitative classification; the weather conditions are fine, cloudy, light rain, light snow, medium snow and heavy snow, and the quantized values are 1, 0.9, 0.8, 0.7, 0.6, 0.3, 0.2 and 0.1 respectively;
the date factors comprise working days, weekends and holidays, and the quantized values are 1, 1.5 and 2 respectively;
the social factor prediction does not take its influence into account.
Preferably, the basic idea of the method for establishing the support vector regression model described in step S2 is to introduce a kernel function K (x)i,xj) Converting the nonlinear problem of the low-dimensional space into the linear problem of the high-dimensional space;
let a given set of training samples T { (x)1,y1),...,(xn,yn)}，xi,yiE.g. R, constructing a regression function in a high-dimensional space H as
F＝{f|f(x)＝ωTφ(x)+b,ω∈Rn}
Omega is weight vector, b is intercept; t is a given training set; phi (x) is RnA spatial to Hilbert space transformation; n is RnThe spatial dimension.
Preferably, the structural risk function is introduced as:
in the formula (I), the compound is shown in the specification,
||ω||2is a term describing the complexity of the model, RempIs an empirical risk function, C is a penalty factor, n is the number of training samples, and epsilon is a relaxation variable.
Preferably, the regression problem is converted into a convex quadratic programming problem with respect to the variables ω, b:
in the formula (I), the compound is shown in the specification,
is a relaxation variable;
for nonlinear support regression, by introducing a kernel function
And transforming by using Lagrange function and dual principle to obtain the following formula:
in the formula (I), the compound is shown in the specification,
is the lagrange factor;
the final SVR regression function f (x) is expressed as:
preferably, the SVR model parameters in step S3 are selected according to the support vector regression model by the kernel function exp (-g | | x)i-xj||2) The radial basis function of (a);
the punishment coefficient C and the width coefficient g directly influence the modeling process and the model property, the parameter C reflects the punishment degree of the algorithm to the sample data, and the parameter g reflects the correlation degree between the support vector machines.
Preferably, the SVR algorithm in step S3 includes the following steps:
s301: and preprocessing the acquired data.
S302: recognizing the processed training data by utilizing a particle swarm algorithm to obtain optimal parameters (C, g);
s303: obtaining an optimal solution, executing an SVR algorithm, and outputting a predicted value;
s304: compared with SVR and other methods, the validity of the model is verified.
Preferably, the identifying the processed training data by using the particle swarm algorithm in step S302 to obtain the optimal parameters (C, g), specifically includes the following steps:
a) an initial population;
b) calculating the particle fitness;
c) if the current adaptation value of the particle is better than the previous best position best pbestOr better than global gbestThe best location experienced is then replaced with the current best location.
d) The particle velocity and position are updated according to the following equations:
Vi＝ωv×Vi+c1×rand()×(pBest[i]-Xi)+c2×Rand()×(pBest[g]-Xi)
Xi＝Xi-1+Vi
in the formula, c1，c2Rand () is a constant and Rand () is 0,1]A random number of (a) < omega >vIs the inertial weight controlling the effect of the previous speed on the current speed; xiIs the particle position; viIs the particle velocity; and p isBest[i]Is an individual's optimal solution; p is a radical ofbest[g]Is a global optimal solution gbest；
e) If the iteration times are reached, stopping iteration and outputting an optimal solution; otherwise, jumping to step b.
Compared with the closest prior art, the invention has the following remarkable progress:
the invention provides a parameter optimization method of an electric heating load prediction support vector regression model, which comprises the following steps: relevant factors influencing the electric heating load are preprocessed to be divided into training data and testing data, a support vector regression model for electric heating load prediction is established, the support vector regression model has good nonlinear mapping characteristics, compared with an artificial neural network method and the like, the support vector regression model can solve the problems of small samples, nonlinearity and local optimization, and the prediction accuracy is higher than that of a common linear prediction model;
the training data after the processing is identified by the particle swarm algorithm to obtain the optimal parameters (C, g), compared with the traditional optimization algorithm, the particle swarm algorithm has higher searching speed, can avoid being trapped in local optimization, particularly avoids complicated steps such as crossing and variation compared with a similar genetic algorithm, has simple algorithm, effectively solves the problem that the optimal solution can not be reached depending on manual experience during the selection of SVR model parameters, and improves the model prediction precision;
the PSO-SVR model is used for electric heating load prediction, the prediction accuracy is high, the production scheduling requirement of a centralized heating system is basically met, the refined and scientific management of the heating industry can be promoted, the on-demand heating is realized, the deep development of the coal-to-electricity work in the Hebei area is assisted, and the demand-side management is deepened.
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FIG. 1 is a flow chart of a method provided in an embodiment of the present invention;
FIG. 2 is a flow chart of the PSO-SVR algorithm provided in the embodiment of the present invention.
Detailed Description
For a better understanding of the present invention, reference is made to the following description taken in conjunction with the accompanying drawings and examples.
At present, the load operation condition of an electric heating user cannot be monitored in real time. The emergency safety event can not be early warned in advance, and can only be remedied afterwards, so that the requirement of safe and reliable heating of the user can not be ensured. Therefore, it is necessary to analyze the relevant data of the electric heating users in each marketing service system, construct an electric heating user load prediction model by combining the relevant information of the electric heating equipment, monitor the use condition of the electric heating of the users on line in real time, early warn the possible hidden dangers, assist and promote the heating of enterprises and public institutions and residents to work in a coal-to-electricity mode and a coal-to-gas mode, so as to reduce the pollution to the atmosphere caused by the direct-combustion scattered coal heating mode. In view of the above situation, how to predict electric heating user load potential and electric energy substitution potential based on a machine learning method to grasp heating load growth situation and influence relationship on load of the whole network is an important key point for improving demand side management at present.
Aiming at the problems in the related art, the patent provides a parameter optimization method of an electric heating load prediction support vector regression model; according to the scheme, under the condition of fully utilizing electric heating user data in a marketing service system, an electric heating load support vector regression machine prediction model is constructed by means of quantized weather, date and other information with the aim of realizing maximum 'heat supply on demand', and the prediction precision is improved by utilizing particle swarm optimization parameters; necessary theoretical support is provided for improving the optimal configuration of electric heating resources and realizing the fine control of the load of electric heating users in the future.
A parameter optimization method for an electric heating load prediction support vector regression model is shown in figure 1, and comprises the following specific steps:
s1, analyzing and preprocessing relevant factors influencing the electric heating load, and dividing preprocessed data into training data and testing data;
s2, by using the good nonlinear mapping characteristic of the Support Vector regression Machine, providing a method for establishing a Support Vector Regression (SVR) model for electric heating load prediction;
s3, carrying out SVR model parameter analysis and selection, identifying the processed training data by using a particle swarm algorithm to obtain optimal parameters (C, g), executing the SVR algorithm to output a predicted value, and finally comparing the predicted value with SVR and other methods to verify the effectiveness of the method.
In step S1, the relevant factors affecting the electric heating load are mainly classified into two categories: random and non-random factors; wherein the content of the first and second substances,
the non-random factors are deterministic factors affecting the change in the electrical heating load, including meteorological factors, date factors, and social factors. The random factors are special conditions such as equipment faults and the like which may occur in the heating process of the electric heating equipment, and have great influence on heating. In particular, the present invention relates to a method for producing,
a. and (4) meteorological factors. Is the most important factor affecting the change of the heat load, including outdoor temperature, humidity, solar radiation intensity, weather conditions, wind direction and wind speed, etc. In addition to outdoor temperature, the weather condition value also represents parameters such as humidity and solar radiation intensity. The outdoor temperature and the weather condition are used as input variables, the outdoor temperature is obtained through weather forecast, a specific quantitative value is obtained, and the weather condition value is quantified through qualitative classification. The weather conditions were quantified according to literature. Thus, the weather conditions are classified into sunny, cloudy, light rain, light snow, medium snow, and heavy snow, and the quantified values are 1, 0.9, 0.8, 0.7, 0.6, 0.3, 0.2, and 0.1, respectively.
b. Date factor. Through studies on historical data, it has been found that loads are often affected by weekends and holidays, causing impacts of varying degrees. Different types of buildings, such as schools, residences, date factors, have different weights. And quantifying data factors of the residential building through expert consultation. Thus, the dates are divided into weekdays, weekends and holidays, with quantified values of 1, 1.5 and 2, respectively.
c. Social factors. The heat supply of the heat supply network is used for social production and resident life service of the area, and the economic development level and population distribution of the area have different restriction factors on the electric heating load. However, due to hidden social factors, and the relatively slow speed of change, there is no good quantification. Therefore, the influence thereof is not considered in the prediction.
d. A random factor. The heating device mainly means that special conditions such as equipment failure and the like can occur in the heating process, and the heating influence is large. Special situations may also occur during heating, such as equipment failure, specific activities at a specific location, etc., which may result in large fluctuations in the thermal load. This is due to the random error term.
Thus, in this model, outdoor maximum and minimum temperatures, quantification of weather conditions and date quantification are used as input variables to predict thermal load. Further, the simulation data was from the 10-day heating period of the heat supply company in north of Hebei province. The sampling period was 15 minutes. The entire sample was selected as test data and the first 7 days of the sample were used as training data.
In step S2, the method for establishing a Support Vector Regression (SVR) model for electric heating load prediction includes:
the basic idea behind vector regression is to introduce a kernel function K (x)i,xj) And converting the nonlinear problem of the low-dimensional space into the linear problem of the high-dimensional space. Wherein the content of the first and second substances,
assume a given set of training samples { (x)1,y1),...,(xn,yn)}，xi,yiE.g. R, constructing a regression function of
F＝{f|f(x)＝ωTφ(x)+b,ω∈Rn}
ω is the weight vector and b is the intercept.
Further, the introduced structural risk function is:
wherein the content of the first and second substances,
||ω||2is a term describing the complexity of the model, RempIs an empirical risk function, C is a penalty factor, N is the number of training samples, and epsilon is a relaxation variable.
The regression problem is converted into a convex quadratic programming problem with respect to the variables ω, b as follows:
in the formula (I), the compound is shown in the specification,
is the relaxation variable.
For nonlinear support regression, the regression can be performed by introducing a kernel function
And transforming by using Lagrange function and dual principle to obtain the following formula:
in the formula (I), the compound is shown in the specification,
is the lagrange factor.
The final SVR regression function f (x) may be expressed as
In step S3, performing SVR model parameter analysis and selection, and recognizing the processed training data using a particle swarm algorithm to obtain optimal parameters (C, g), wherein,
the selection of the SVR model parameter mainly refers to the kernel function exp (-g | | | x) in the support vector regression modeli-xj||2) Is selected. The radial basis function can well map the sample set from the input space to the high-dimensional feature space in a nonlinear way, has good capability of processing the complex nonlinear relation between the input and the output of the sample, and has the advantages of less variable parameters, smaller calculation amount of selected parameters, high calculation efficiency and the like. In particular, the penalty coefficient C and the width coefficient g directly affect the modeling process and model properties. The parameter C reflects the punishment degree of the algorithm to the sample data, the parameter g reflects the correlation degree between the support vector machines, and the selection of the proper optimal parameters (C, g) is crucial to the prediction accuracy.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
The PSO-SVR algorithm flow can be seen with reference to FIG. 2, and includes the following steps
S301: and preprocessing the acquired data.
S302: recognizing the processed training data by utilizing a particle swarm algorithm to obtain optimal parameters (C, g);
a) an initial population;
b) calculating the particle fitness;
c) if the current adaptation value of the particle is better than the previous best position best pbestOr better than global gbestThe best location experienced is then replaced with the current best location.
d) The particle velocity and position are updated according to equations (7) - (8):
Vi＝ωv×Vi+c1×rand()×(pBest[i]-Xi)+c2×Rand()×(pBest[g]-Xi)
Xi＝Xi-1+Vi
wherein, c1，c2Rand () is a constant and Rand () is 0,1]A random number of (a) < omega >vIs the inertial weight controlling the effect of the previous speed on the current speed; xiIs the particle position; viIs the particle velocity; and p isBest[i]Is an individual's optimal solution; p is a radical ofbest[g]Is a global optimal solution gbest。
e) If the iteration times are reached, stopping iteration and outputting an optimal solution; otherwise, jumping to step b
S303: obtaining an optimal solution, executing an SVR algorithm, and outputting a predicted value;
s304: compared with SVR and other methods, the validity of the model is verified.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (10)
1. A parameter optimization method of an electric heating load prediction support vector regression model is characterized by comprising the following steps:
s1, analyzing and preprocessing relevant factors influencing the electric heating load, and dividing the preprocessed data into training data and testing data;
s2 is a method for establishing a support vector regression model for electric heating load prediction by utilizing the good nonlinear mapping characteristic of the support vector regression machine;
s3, carrying out SVR model parameter analysis and selection, identifying the processed training data by using a particle swarm algorithm to obtain optimal parameters (C, g), executing the SVR algorithm to output a predicted value, and finally comparing the predicted value with SVR and other methods to verify the effectiveness of the method.
2. The method for optimizing parameters of the electric heating load prediction support vector regression model according to claim 1, wherein the relevant factors influencing the electric heating load in step S1 are divided into two categories: random and non-random factors;
the non-random factors are determinacy factors influencing the change of the electric heating load, and comprise meteorological factors, date factors and social factors;
the random factors are special conditions such as equipment faults and the like which may occur in the heating process of the electric heating equipment, and have great influence on heating; some special cases occur during heating, including equipment failure, site specific activity, due to random error terms.
3. The method for optimizing parameters of the electric heating load prediction support vector regression model according to claim 1, wherein the data preprocessing in the step S1 comprises correlation analysis and outlier rejection.
4. The parameter optimization method of the electric heating load prediction support vector regression model according to claim 2, wherein the meteorological factors comprise outdoor temperature, humidity, solar radiation intensity, weather conditions and wind direction and wind speed; weather conditions represent humidity and solar radiation intensity parameters in addition to outdoor temperature; taking the outdoor temperature and the weather condition as input variables, obtaining the outdoor temperature through weather forecast to obtain a specific quantitative value, and quantifying the weather condition value through qualitative classification; the weather conditions are fine, cloudy, light rain, light snow, medium snow and heavy snow, and the quantized values are 1, 0.9, 0.8, 0.7, 0.6, 0.3, 0.2 and 0.1 respectively;
the date factors comprise working days, weekends and holidays, and the quantized values are 1, 1.5 and 2 respectively;
the social factor prediction does not take its influence into account.
5. The method for optimizing parameters of an electric heating load prediction support vector regression model according to claim 1, wherein the method for establishing the support vector regression model in step S2 is to introduce a kernel function K (x)i,xj) Converting the nonlinear problem of the low-dimensional space into the linear problem of the high-dimensional space;
let a given set of training samples T { (x)1,y1),...,(xn,yn)}，xi,yiE.g. R, constructing a regression function in a high-dimensional space H as
F＝{f|f(x)＝ωTφ(x)+b,ω∈Rn}
Omega is weight vector, b is intercept; t is given trainingRefining; phi (x) is RnA spatial to Hilbert space transformation; n is RnThe spatial dimension.
6. The parameter optimization method of the electric heating load prediction support vector regression model according to claim 5, characterized in that the introduced structure risk function is:
in the formula (I), the compound is shown in the specification,
||ω||2is a term describing the complexity of the model, RempIs an empirical risk function, C is a penalty factor, n is the number of training samples, and epsilon is a relaxation variable.
7. The parameter optimization method of the electric heating load prediction support vector regression model according to claim 6, characterized by converting the regression problem into a convex quadratic programming problem about the variables ω, b:
in the formula, ξi,
Is a relaxation variable;
for nonlinear support regression, by introducing a kernel function
And transforming by using Lagrange function and dual principle to obtain the following formula:
in the formula, αi,
Is the lagrange factor;
the final SVR regression function f (x) is expressed as:
8. the parameter optimization method of the electric heating load prediction support vector regression model according to claim 7, wherein the selection of the SVR model parameters in the step S3 refers to the kernel function exp (-g | | x) in the support vector regression modeli-xj||2) The radial basis function of (a);
the punishment coefficient C and the width coefficient g directly influence the modeling process and the model property, the parameter C reflects the punishment degree of the algorithm to the sample data, and the parameter g reflects the correlation degree between the support vector machines.
9. The method for optimizing parameters of the electric heating load prediction support vector regression model according to claim 8, wherein the SVR algorithm in step S3 comprises the following steps:
s301: and preprocessing the acquired data.
S302: recognizing the processed training data by utilizing a particle swarm algorithm to obtain optimal parameters (C, g);
s303: obtaining an optimal solution, executing an SVR algorithm, and outputting a predicted value;
s304: compared with SVR and other methods, the validity of the model is verified.
10. The method for optimizing parameters of the electric heating load prediction support vector regression model according to claim 9, wherein the step S302 of identifying the processed training data by using the particle swarm algorithm to obtain the optimal parameters (C, g) specifically comprises the following steps:
a) an initial population;
b) calculating the particle fitness;
c) if the current adaptation value of the particle is better than the previous best position best pbestOr better than global gbestThe best location experienced is then replaced with the current best location.
d) The particle velocity and position are updated according to the following equations:
Vi＝ωv×Vi+c1×rand()×(pBest[i]-Xi)+c2×Rand()×(pBest[g]-Xi)
Xi＝Xi-1+Vi
in the formula, c1，c2Rand () is a constant and Rand () is 0,1]A random number of (a) < omega >vIs the inertial weight controlling the effect of the previous speed on the current speed; xiIs the particle position; viIs the particle velocity; and p isBest[i]Is an individual's optimal solution; p is a radical ofbest[g]Is a global optimal solution gbest；
e) If the iteration times are reached, stopping iteration and outputting an optimal solution; otherwise, jumping to step b.
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