WO2020063690A1 - Electrical power system prediction method and apparatus - Google Patents
Electrical power system prediction method and apparatus Download PDFInfo
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- the invention relates to the technical field of computer algorithms, and in particular, to a method and device for power system prediction.
- Load forecasting is a traditional research problem in the field of power systems. It refers to starting from known power system, economic, social, and meteorological conditions, and analyzing and researching historical data to explore the internal relationship between things and the development and change laws , Make advance estimates and inferences about load development. Load forecasting is the basic work of power system planning, planning, power consumption, and dispatching departments, and its importance has long been recognized.
- Load forecasting essentially fits and regresses the power curve. Since the real-time power curve is affected by many factors such as power system, economy, society, weather and so on, it generally shows complex non-linear characteristics. A predictive model of learning ability.
- SVM Support Vector Machine
- SVM parameter optimization algorithms include a grid search algorithm, a particle swarm algorithm, and the like. Although the SVM parameters can be selected using these algorithms, they cannot obtain particularly suitable parameter values, and the speed of searching for optimal or satisfactory solutions is too slow, and the efficiency of load prediction based on the selected parameters is low.
- the embodiments of the present invention provide a method and a device for power system prediction, which can not only obtain more optimized parameter values, but also solve the problem that the support vector machine searches for the optimal solution or the satisfactory solution is too slow and causes low load prediction efficiency. .
- an embodiment of the present invention provides a method for predicting a power system.
- the method includes:
- S2 Assign the parameters in S1 to the support vector machine to calculate the fitness of each individual in the population
- S3 Calculate the selection probability of the individuals in the population according to the individual fitness, and use the selection probability to perform individual selection;
- step S2 is specifically assigning the parameters in S1 to the least squares support vector machine, obtaining the predicted value, and calculating the fitness of each individual, the calculation formula is:
- f i is the fitness of the i-th individual; Is the predicted value; y i is the real value.
- the formula for calculating the selection probability of the population individual in step S3 is:
- P i is the selection probability of the i-th individual.
- the probability that the population individuals cross in step S4 is:
- f c is the highest fitness among the two individuals before the parents cross the individual;
- f max is the maximum fitness among the population of the parents before the individuals cross;
- k 1 and k 2 are constants.
- the probability of mutation of the individual population in step S4 is:
- f m is the fitness of the individual to be mutated; k 3 and k 4 are constants.
- the training sample in step S6 is a filtered training sample
- the screening process includes:
- M1 Determine the time of the day and obtain the feature vector of the day
- M2 Calculate whether the similarity between the feature vector of the historical day that meets the preset conditions and the feature vector of the day meets the preset threshold, and if so, select the current historical day as the training sample; otherwise, exclude the current historical day.
- an embodiment of the present invention provides a device for predicting a power system.
- the device includes an initial module, an assignment module, a selection module, an alternating module, a judgment module, and a training module.
- the initial module is configured to initialize a population parameter and generate a population individual
- the assignment module is configured to assign parameters initialized by the initial module to a support vector machine to calculate the fitness of each individual in the population;
- the selection module is configured to calculate a selection probability of a population individual according to the individual fitness obtained by the assignment module, and perform individual selection with the selection probability;
- the alternation module is configured to cross and mutate the individuals of the population selected by the selection module;
- the judging module is configured to judge whether the current population reaches the training termination condition, and if yes, obtain an optimized support vector machine and trigger the training module; otherwise, trigger a selection module;
- the training module is configured to input training samples to an optimized support vector machine for training to obtain a prediction model.
- the assignment module is specifically configured to assign parameters initialized by the initial module to a least squares support vector machine, obtain prediction values, calculate the fitness of each individual, and modify the fitness of the individual, where:
- the formula for calculating the selection probability of the population by the selection module is:
- P i is the selection probability of the i-th individual.
- the probability that the alternating module performs population individual crossover is:
- f c is the highest fitness among the two individuals before the parents cross the individual;
- f max is the maximum fitness among the population of the parents before the individuals cross;
- k 1 and k 2 are constants.
- the probability that the alternating module performs individual mutation of the population is:
- f m is the fitness of the individual to be mutated; k 3 and k 4 are constants.
- the present invention has at least the following beneficial effects:
- the invention effectively improves the speed of searching for an optimal solution or a satisfactory solution, thereby improving the efficiency of load prediction by a support vector machine configured with selected parameters, and in the process of selecting parameters, the load data similar to the prediction date is obtained
- the algorithm optimizes the algorithm based on similar daily load data and minimizes the error value after optimization to improve the accuracy of the selected parameters, thereby reducing the prediction error of the support vector machine model during actual prediction and improving the accuracy of load prediction.
- FIG. 1 is a flowchart of a power system prediction method according to an embodiment of the present invention
- FIG. 2 is a flowchart of a filtered training sample provided by an embodiment of the present invention.
- FIG. 3 is a block diagram of a power system prediction apparatus according to an embodiment of the present invention.
- an embodiment of the present invention provides a method for predicting a power system.
- the method may include the following steps:
- S2 Assign the parameters in S1 to the support vector machine to calculate the fitness of each individual in the population
- S3 Calculate the selection probability of the individuals in the population according to the individual fitness, and use the selection probability to perform individual selection;
- step S1 may be to generate parameters such as an initial kernel function parameter and a penalty factor, and use an 8-bit binary code for encoding, and set the population size and the number of iterations.
- Each individual in the population is a parameter Encoding form, and the initial value of the individual is randomly generated.
- the training termination condition is whether the number of iterations reaches a preset number of iterations or whether the error is less than a preset threshold. If the number of iterations is less than a preset number of iterations, step S3 is performed; or, if the error is greater than a preset threshold, step S3 is performed.
- step S2 is specifically assigning the parameters in S1 to the least squares support vector machine, obtaining the predicted value, and calculating the fitness of each individual, the calculation formula is:
- f i is the fitness of the i-th individual; Is the predicted value; y i is the real value.
- the parameter of step S1 is used to assign the least squares support vector machine, and then the fitness value of each individual is calculated according to the prediction result.
- the formula for calculating the selection probability of the population by the selection module is:
- P i is the selection probability of the i-th individual.
- the individuals are selected with the individual selection probability when calculating the selection probability of the population individuals according to the obtained fitness values.
- the probability that the alternating module performs population individual crossover is:
- f c is the highest fitness among the two individuals before the parents cross the individual;
- f max is the maximum fitness among the population of the parents before the individuals cross;
- k 1 and k 2 are constants.
- the probability of mutation of the individual population in step S4 is:
- f m is the fitness of the individual to be mutated; k 3 and k 4 are constants.
- the individual parameters are converted into binary codes
- the crossover operation uses a single-point fork
- the mutation strategy uses multipoint mutation.
- k 1 and k 2 are taken as 1
- k 3 and k 4 are taken as 0.5.
- the training sample in step S6 is a filtered training sample
- the screening process includes:
- M1 Determine the time of the day and obtain the feature vector of the day
- M2 Calculate whether the similarity between the feature vector of the historical day that meets the preset conditions and the feature vector of the day meets the preset threshold, and if so, select the current historical day as the training sample; otherwise, exclude the current historical day.
- similar historical day data can be selected to improve the selected Parameter accuracy.
- the process of selecting similar historical day data is also the process of screening training samples.
- the day to be predicted that is, the current day
- the month of the day are not more than 2 months or the same month of the previous year
- the working characteristics of the prediction day are the same, that is, the same working day, or weekend, or holiday
- Given a similarity threshold 4) Calculate the feature vector of the day to be predicted and the historical day that simultaneously meets the conditions 1), 2) Similarity (Euclidean distance can be used for similarity calculation); 5)
- the similarity value is less than a given threshold
- the day is used as a training sample.
- the filtered training samples are input to the least squares support vector machine. After the training is completed, a prediction model is obtained.
- the model can be used to obtain the prediction value in the next 24 hours.
- the thermal load forecast value for the next 24 hours can be obtained.
- the conditions of the historical day of the constituency can be appropriately modified, and the training samples can be screened on the future day.
- the heat load forecast value of 30 days (24 hours, corresponding to one heat load value per hour) was selected for comparison.
- the test data is 24 points a day.
- Three algorithms are compared:
- Root Mean Square Error RMSE Root Mean Square Error RMSE
- step S2 the individual fitness calculated in step S2 may be modified, and the specific process of the modification is:
- N1 Get the average fitness of the current population Maximum fitness in the current population
- f ′ i is the i-th modified individual fitness
- f i is the i-th unmodified individual fitness
- c is a constant.
- the modified individual fitness can be used to calculate the selection probability of the population individuals, the probability of crossover of the population individuals, and the probability of mutation of the population individuals.
- an embodiment of the present invention provides a device for predicting a power system.
- the device includes an initial module, an assignment module, a selection module, an alternating module, a judgment module, and a training module.
- An assignment module configured to assign parameters initialized by the initial module to a support vector machine to calculate the fitness of each individual in the population
- a selection module configured to calculate a selection probability of a population individual based on the individual fitness obtained by the assignment module, and perform individual selection with the selection probability
- An alternation module configured to cross and mutate the individuals of the population selected by the selection module
- a judging module for judging whether the current population reaches the training termination condition; if so, obtaining an optimized support vector machine and triggering the training module; otherwise, triggering a selection module;
- a training module is used to input training samples to an optimized support vector machine for training to obtain a prediction model.
- the assignment module may be specifically configured to assign a parameter initialized by the initial module to a least squares support vector machine, obtain a predicted value, and calculate the fitness of each individual, where:
- the formula for calculating the selection probability of the population by the selection module is:
- P i is the selection probability of the i-th individual.
- the probability that the alternating module performs population individual crossover is:
- f c is the highest fitness among the two individuals before the parents cross the individual;
- f max is the maximum fitness among the population of the parents before the individuals cross;
- k 1 and k 2 are constants.
- the probability that the alternation module performs individual mutation of the population is:
- f m is the fitness of the individual to be mutated; k 3 and k 4 are constants.
- the individual fitness calculated by the assignment module can be modified.
- the specific process of the modification is:
- N1 Get the average fitness of the current population Maximum fitness in the current population
- f ′ i is the i-th modified individual fitness
- f i is the i-th unmodified individual fitness
- c is a constant.
- the modified individual fitness can be used for calculating the selection probability of the population individuals, the probability of the population individuals crossing, and the probability of the population individuals being mutated.
- the foregoing program may be stored in a computer-readable storage medium.
- the method includes the steps of the foregoing method embodiment.
- the foregoing storage medium includes: a ROM, a RAM, a magnetic disk, or an optical disc, which can store program codes in various media.
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Abstract
An electrical power system prediction method and apparatus, the method comprising: S1: initialising population parameters to generate population individuals; S2: assigning the parameters in S1 to a support vector machine and calculating the degree of adaption of each individual in the population; S3: on the basis of the degree of adaption of the individuals, calculating the selection probability of the individuals in the population and performing individual selection using said selection probability; S4: crossing and mutating the population individuals selected in S3; S5: determining whether the current population has reached a training termination condition and, if so, then acquiring an optimised support vector machine and executing S6; and if not, then executing S3; and S6: inputting a training sample into the optimised support vector machine for training to acquire a prediction model. The present method effectively increases the efficiency of load prediction performed by a support vector machine and increases the accuracy of the selected parameters, thereby reducing prediction error during actual prediction by the support vector machine model, and increasing the precision of load prediction.
Description
本发明涉及计算机算法技术领域,特别涉及一种电力系统预测的方法和装置。The invention relates to the technical field of computer algorithms, and in particular, to a method and device for power system prediction.
科学的预测是正确决策的依据和保证。负荷预测是电力系统领域的一个传统研究问题,是指从已知的电力系统、经济、社会、气象等情况出发,通过对历史数据的分析和研究,探索事物之间的内在联系和发展变化规律,对负荷发展做出预先估计和推测。负荷预测是电力系统规划、计划、用电、调度等部门的基础工作,其重要性早已被人们所认识。Scientific prediction is the basis and guarantee for correct decisions. Load forecasting is a traditional research problem in the field of power systems. It refers to starting from known power system, economic, social, and meteorological conditions, and analyzing and researching historical data to explore the internal relationship between things and the development and change laws , Make advance estimates and inferences about load development. Load forecasting is the basic work of power system planning, planning, power consumption, and dispatching departments, and its importance has long been recognized.
负荷预测本质上是对功率曲线进行拟合与回归,由于实时功率曲线受电力系统、经济、社会、气象等诸多因素影响,一般表现为复杂非线性特点,宜采用对复杂非线性特性具备较强学习能力的预测模型。Load forecasting essentially fits and regresses the power curve. Since the real-time power curve is affected by many factors such as power system, economy, society, weather and so on, it generally shows complex non-linear characteristics. A predictive model of learning ability.
目前应用较多且比较成熟的预测方法,主要为支持向量机(Support VectorMachine,SVM)等。SVM同时考虑经验风险最小和结构风险最小,使模型具有较强的推广性,在小样本识别方面有较大优势,且SVM有严格的数学理论基础,其决策为全局最优。At present, there are more and more mature prediction methods, mainly Support Vector Machine (SVM) and so on. SVM considers both empirical risk and structural risk at the same time, which makes the model have a strong generalization and has a great advantage in small sample recognition. SVM has a strict mathematical theoretical foundation and its decision is globally optimal.
SVM参数的选取策略目前尚没有统一的方法,SVM参数选取的优劣将直接影响模型的拟合和回归能力。现有技术中,较为常用的SVM参数优化算法包括网格搜索算法、粒子群算法等。利用这些算法虽然可以选取SVM参数,但并不能得到特别合适的参数值,并且搜索到最优解或满意解的速度太慢,依据选取的参数进行负荷预测的效率低。There is currently no unified method for selecting SVM parameters. The pros and cons of selecting SVM parameters will directly affect the model's fitting and regression capabilities. In the prior art, more commonly used SVM parameter optimization algorithms include a grid search algorithm, a particle swarm algorithm, and the like. Although the SVM parameters can be selected using these algorithms, they cannot obtain particularly suitable parameter values, and the speed of searching for optimal or satisfactory solutions is too slow, and the efficiency of load prediction based on the selected parameters is low.
发明内容Summary of the Invention
本发明实施例提供了一种电力系统预测的方法和装置,不仅能够获得更 加优化的参数值,并且解决了支持向量机搜索到最优解或满意解的速度太慢导致负荷预测效率低的问题。The embodiments of the present invention provide a method and a device for power system prediction, which can not only obtain more optimized parameter values, but also solve the problem that the support vector machine searches for the optimal solution or the satisfactory solution is too slow and causes low load prediction efficiency. .
第一方面,本发明实施例提供了一种电力系统预测的方法,该方法包括:In a first aspect, an embodiment of the present invention provides a method for predicting a power system. The method includes:
S1:初始化种群参数,生成种群个体;S1: Initialize population parameters to generate population individuals;
S2:将S1中的参数赋值给支持向量机,计算种群中每个个体的适应度;S2: Assign the parameters in S1 to the support vector machine to calculate the fitness of each individual in the population;
S3:根据个体适应度,计算种群个体的选择概率,并以该选择概率进行个体选择;S3: Calculate the selection probability of the individuals in the population according to the individual fitness, and use the selection probability to perform individual selection;
S4:对S3选择的种群个体进行交叉、变异;S4: cross and mutate the individuals selected in S3;
S5:判断当前种群是否达到训练终止条件,若是,则获得优化后的支持向量机,并执行S6;否则,执行S3;S5: determine whether the current population meets the training termination condition, and if so, obtain an optimized support vector machine and execute S6; otherwise, execute S3;
S6:将训练样本输入到优化后的支持向量机进行训练获得预测模型。S6: The training samples are input to an optimized support vector machine for training to obtain a prediction model.
优选地,步骤S2具体为将S1中的参数赋值给最小二乘机支持向量机,获得预测值,并计算每个个体的适应度,计算公式为:Preferably, step S2 is specifically assigning the parameters in S1 to the least squares support vector machine, obtaining the predicted value, and calculating the fitness of each individual, the calculation formula is:
其中,f
i为第i个个体的适应度;
为预测值;y
i为真实值。
Where f i is the fitness of the i-th individual; Is the predicted value; y i is the real value.
优选地,步骤S3中计算种群个体的选择概率的公式为:Preferably, the formula for calculating the selection probability of the population individual in step S3 is:
其中,P
i为第i个个体的选择概率。
Among them, P i is the selection probability of the i-th individual.
优选地,步骤S4中种群个体进行交叉的概率为:Preferably, the probability that the population individuals cross in step S4 is:
其中,f
c为个体进行交叉前父代两个个体中适应度大者;f
max为个体进行交叉前父代种群中的最大适应度;
为个体进行交叉前父代 种群中所有个体的平均适应度;k
1和k
2为常数。
Among them, f c is the highest fitness among the two individuals before the parents cross the individual; f max is the maximum fitness among the population of the parents before the individuals cross; The average fitness of all individuals in the parent population before crossing the individuals; k 1 and k 2 are constants.
优选地,步骤S4中种群个体进行变异的概率为:Preferably, the probability of mutation of the individual population in step S4 is:
其中,f
m为需要变异个体的适应度;k
3和k
4为常数。
Among them, f m is the fitness of the individual to be mutated; k 3 and k 4 are constants.
优选地,步骤S6中的训练样本是经过筛选的训练样本,该筛选过程包括:Preferably, the training sample in step S6 is a filtered training sample, and the screening process includes:
M1:确定当日时间,获取当日特征向量;M1: Determine the time of the day and obtain the feature vector of the day;
M2:分别计算符合预设条件的历史日的特征向量与当日特征向量的相似度是否符合预设阈值,若是,则选择当前历史日为训练样本;否则,排除当前历史日。M2: Calculate whether the similarity between the feature vector of the historical day that meets the preset conditions and the feature vector of the day meets the preset threshold, and if so, select the current historical day as the training sample; otherwise, exclude the current historical day.
第二方面,本发明实施例提供了一种电力系统预测的装置,该装置包括:初始模块、赋值模块、选择模块、交变模块、判断模块和训练模块,其中,In a second aspect, an embodiment of the present invention provides a device for predicting a power system. The device includes an initial module, an assignment module, a selection module, an alternating module, a judgment module, and a training module.
所述初始模块,用于初始化种群参数,生成种群个体;The initial module is configured to initialize a population parameter and generate a population individual;
所述赋值模块,用于将所述初始模块初始化的参数赋值给支持向量机,计算种群中每个个体的适应度;The assignment module is configured to assign parameters initialized by the initial module to a support vector machine to calculate the fitness of each individual in the population;
所述选择模块,用于根据所述赋值模块获得的个体适应度,计算种群个体的选择概率,并以该选择概率进行个体选择;The selection module is configured to calculate a selection probability of a population individual according to the individual fitness obtained by the assignment module, and perform individual selection with the selection probability;
所述交变模块,用于对所述选择模块选择的种群个体进行交叉、变异;The alternation module is configured to cross and mutate the individuals of the population selected by the selection module;
所述判断模块,用于判断当前种群是否达到训练终止条件,若是,则获得优化后的支持向量机,并触发所述训练模块;否则,触发选择模块;The judging module is configured to judge whether the current population reaches the training termination condition, and if yes, obtain an optimized support vector machine and trigger the training module; otherwise, trigger a selection module;
所述训练模块,用于将训练样本输入到优化后的支持向量机进行训练获得预测模型。The training module is configured to input training samples to an optimized support vector machine for training to obtain a prediction model.
优选地,所述赋值模块具体用于将所述初始模块初始化的参数赋值给最小二乘机支持向量机,获得预测值,计算每个个体的适应度,并对个体的适应度进行修正,其中,Preferably, the assignment module is specifically configured to assign parameters initialized by the initial module to a least squares support vector machine, obtain prediction values, calculate the fitness of each individual, and modify the fitness of the individual, where:
个体的适应度计算公式为:The calculation formula of individual fitness is:
其中,
为预测值;y
i为真实值;f
i为第i个个体的适应度;c为常数。
among them, Is the predicted value; y i is the true value; f i is the fitness of the i-th individual; c is a constant.
优选地,所述选择模块计算种群个体的选择概率的公式为:Preferably, the formula for calculating the selection probability of the population by the selection module is:
其中,P
i为第i个个体的选择概率。
Among them, P i is the selection probability of the i-th individual.
优选地,所述交变模块进行种群个体交叉的概率为:Preferably, the probability that the alternating module performs population individual crossover is:
其中,f
c为个体进行交叉前父代两个个体中适应度大者;f
max为个体进行交叉前父代种群中的最大适应度;
为个体进行交叉前父代种群中所有个体的平均适应度;k
1和k
2为常数。
Among them, f c is the highest fitness among the two individuals before the parents cross the individual; f max is the maximum fitness among the population of the parents before the individuals cross; The average fitness of all individuals in the parent population before crossing the individuals; k 1 and k 2 are constants.
优选地,所述交变模块进行种群个体变异的概率为:Preferably, the probability that the alternating module performs individual mutation of the population is:
其中,f
m为需要变异个体的适应度;k
3和k
4为常数。
Among them, f m is the fitness of the individual to be mutated; k 3 and k 4 are constants.
与现有技术相比,本发明至少具有以下有益效果:Compared with the prior art, the present invention has at least the following beneficial effects:
本发明有效地提高了搜索到最优解或满意解的速度,从而提高以选取的参数配置的支持向量机进行负荷预测的效率,而且在选取参数过程中,获取了与预测日的负荷数据相似的相似日负荷数据对算法进行优化,优化后使误差值将至最低,以此提高选取的参数的准确性,从而降低支持向量机模型在实际预测时的预测误差,提高负荷预测的精度。The invention effectively improves the speed of searching for an optimal solution or a satisfactory solution, thereby improving the efficiency of load prediction by a support vector machine configured with selected parameters, and in the process of selecting parameters, the load data similar to the prediction date is obtained The algorithm optimizes the algorithm based on similar daily load data and minimizes the error value after optimization to improve the accuracy of the selected parameters, thereby reducing the prediction error of the support vector machine model during actual prediction and improving the accuracy of load prediction.
为了更清楚地说明本发明实施例或现有技术中的技术方案,下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍,显而易见地,下面描述中的附图是本发明的一些实施例,对于本领域普通技术人员来讲,在不付出创造性劳动的前提下,还可以根据这些附图获得其他的附图。In order to more clearly explain the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are Some embodiments of the present invention, for those skilled in the art, can obtain other drawings according to these drawings without paying creative labor.
图1是本发明一个实施例提供的一种电力系统预测的方法的流程图;FIG. 1 is a flowchart of a power system prediction method according to an embodiment of the present invention; FIG.
图2是本发明一个实施例提供的一种筛选的训练样本的流程图。FIG. 2 is a flowchart of a filtered training sample provided by an embodiment of the present invention.
图3是本发明一个实施例提供的一种电力系统预测的装置的框图。FIG. 3 is a block diagram of a power system prediction apparatus according to an embodiment of the present invention.
为使本发明实施例的目的、技术方案和优点更加清楚,下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例是本发明一部分实施例,而不是全部的实施例,基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动的前提下所获得的所有其他实施例,都属于本发明保护的范围。In order to make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments These embodiments are part of, but not all of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by a person of ordinary skill in the art without creative efforts belong to the protection of the present invention. range.
如图1所示,本发明实施例提供了一种电力系统预测的方法,该方法可以包括以下步骤:As shown in FIG. 1, an embodiment of the present invention provides a method for predicting a power system. The method may include the following steps:
S1:初始化种群参数,生成种群个体;S1: Initialize population parameters to generate population individuals;
S2:将S1中的参数赋值给支持向量机,计算种群中每个个体的适应度;S2: Assign the parameters in S1 to the support vector machine to calculate the fitness of each individual in the population;
S3:根据个体适应度,计算种群个体的选择概率,并以该选择概率进行个体选择;S3: Calculate the selection probability of the individuals in the population according to the individual fitness, and use the selection probability to perform individual selection;
S4:对S3选择的种群个体进行交叉、变异;S4: cross and mutate the individuals selected in S3;
S5:判断当前种群是否达到训练终止条件,若是,则获得优化后的支持向量机,并执行S6;否则,执行S3;S5: determine whether the current population meets the training termination condition, and if so, obtain an optimized support vector machine and execute S6; otherwise, execute S3;
S6:将训练样本输入到优化后的支持向量机进行训练获得预测模型。S6: The training samples are input to an optimized support vector machine for training to obtain a prediction model.
在该实施例中,步骤S1可以为生成初始核函数参数和惩罚因子等参数, 并采用长度为8位的二进制码来进行编码,并设置种群大小以及迭代次数,种群中每个个体均为参数编码形式,且随机生成个体的初始值。训练终止条件为迭代次数是否达到预设的迭代次数或者误差是否小于预设阈值,若迭代次数小于预设的迭代次数,则执行步骤S3;或者,若误差大于预设阈值,则执行步骤S3。In this embodiment, step S1 may be to generate parameters such as an initial kernel function parameter and a penalty factor, and use an 8-bit binary code for encoding, and set the population size and the number of iterations. Each individual in the population is a parameter Encoding form, and the initial value of the individual is randomly generated. The training termination condition is whether the number of iterations reaches a preset number of iterations or whether the error is less than a preset threshold. If the number of iterations is less than a preset number of iterations, step S3 is performed; or, if the error is greater than a preset threshold, step S3 is performed.
在本发明一个实施例中,步骤S2具体为将S1中的参数赋值给最小二乘机支持向量机,获得预测值,并计算每个个体的适应度,计算公式为:In an embodiment of the present invention, step S2 is specifically assigning the parameters in S1 to the least squares support vector machine, obtaining the predicted value, and calculating the fitness of each individual, the calculation formula is:
其中,f
i为第i个个体的适应度;
为预测值;y
i为真实值。
Where f i is the fitness of the i-th individual; Is the predicted value; y i is the real value.
在该实施例中,利用步骤S1的参数赋值给最小二乘支持向量机,然后根据预测结果,计算各个个体的适应度值。In this embodiment, the parameter of step S1 is used to assign the least squares support vector machine, and then the fitness value of each individual is calculated according to the prediction result.
在本发明一个实施例中,所述选择模块计算种群个体的选择概率的公式为:In an embodiment of the present invention, the formula for calculating the selection probability of the population by the selection module is:
其中,P
i为第i个个体的选择概率。
Among them, P i is the selection probability of the i-th individual.
在该实施例中,在获得个体适应度之后,根据所获得的适应度值,计算种群个体的选择概率时以个体选择概率选择个体。In this embodiment, after the individual fitness is obtained, the individuals are selected with the individual selection probability when calculating the selection probability of the population individuals according to the obtained fitness values.
在本发明一个实施例中,所述交变模块进行种群个体交叉的概率为:In an embodiment of the present invention, the probability that the alternating module performs population individual crossover is:
其中,f
c为个体进行交叉前父代两个个体中适应度大者;f
max为个体进行交叉前父代种群中的最大适应度;
为个体进行交叉前父代种群中所有个体的平均适应度;k
1和k
2为常数。
Among them, f c is the highest fitness among the two individuals before the parents cross the individual; f max is the maximum fitness among the population of the parents before the individuals cross; The average fitness of all individuals in the parent population before crossing the individuals; k 1 and k 2 are constants.
步骤S4中种群个体进行变异的概率为:The probability of mutation of the individual population in step S4 is:
其中,f
m为需要变异个体的适应度;k
3和k
4为常数。
Among them, f m is the fitness of the individual to be mutated; k 3 and k 4 are constants.
在该实施例中,将个体参量转化为二进制编码,交叉运算采用单点叉,变异策略采用多点变异。一般取k
1和k
2为1,k
3和k
4为0.5。通过以上方法的调整,使遗传算法在搜索过程中,对于优质个体(即适应度高于种群的平均适应度值),交叉概率P
c,变异概率P
m取小一些,促进遗传算法快速收敛,对于适应度值低于种群平均适应度值的个体,交叉概率P
c,变异概率P
m取大一些,避免陷入遗传算法局部极值点,发生早期收敛现象。
In this embodiment, the individual parameters are converted into binary codes, the crossover operation uses a single-point fork, and the mutation strategy uses multipoint mutation. Generally, k 1 and k 2 are taken as 1, k 3 and k 4 are taken as 0.5. Through the adjustment of the above methods, during the search process of the genetic algorithm, for high-quality individuals (that is, the fitness is higher than the average fitness value of the population), the crossover probability P c and the mutation probability P m are smaller, which promotes the rapid convergence of the genetic algorithm. For individuals whose fitness value is lower than the average fitness value of the population, the crossover probability P c and the mutation probability P m should be larger to avoid falling into the local extreme point of the genetic algorithm and causing early convergence.
如图2所示,在本发明一个实施例中,步骤S6中的训练样本是经过筛选的训练样本,该筛选过程包括:As shown in FIG. 2, in an embodiment of the present invention, the training sample in step S6 is a filtered training sample, and the screening process includes:
M1:确定当日时间,获取当日特征向量;M1: Determine the time of the day and obtain the feature vector of the day;
M2:分别计算符合预设条件的历史日的特征向量与当日特征向量的相似度是否符合预设阈值,若是,则选择当前历史日为训练样本;否则,排除当前历史日。M2: Calculate whether the similarity between the feature vector of the historical day that meets the preset conditions and the feature vector of the day meets the preset threshold, and if so, select the current historical day as the training sample; otherwise, exclude the current historical day.
在该实施例中,由于每日数据的特征有天气(晴、阴、多云、雨)、最高温度,最低温度、平均温度、湿度等等,所以可以选取相似的历史日数据,以提高选取的参数的准确性。选取相似的历史日数据的过程也就是筛选训练样本的过程,可以为:1)待预测日(也就是当日)与当日的月份相差不超过2个月或上一年的同月;2)与待预测日的工作特性相同,即同为工作日,或周末,或节假日;3)给定一个相似度阈值;4)计算待预测日和同时满足条件1),2)的历史日的特征向量的相似度(相似度计算可以采用欧式距离);5)当相似度值小于给定的阈值时,该日就作为训练样本。将经过筛选的训练样本输入给最小二乘支持向量机,训练完成得到预测模型,调用该模型便可 以得到未来24小时的预测值。在电力系统中应用,便可以得到未来24小时的热负载预测值。除此之外,可以根据天气预报给出的未来某日的天气特征,适当修改选区历史日的条件,可以对未来某日进行训练样本的筛选。In this embodiment, since the characteristics of daily data are weather (clear, overcast, cloudy, rain), maximum temperature, minimum temperature, average temperature, humidity, etc., similar historical day data can be selected to improve the selected Parameter accuracy. The process of selecting similar historical day data is also the process of screening training samples. It can be: 1) the day to be predicted (that is, the current day) and the month of the day are not more than 2 months or the same month of the previous year; 2) and The working characteristics of the prediction day are the same, that is, the same working day, or weekend, or holiday; 3) Given a similarity threshold; 4) Calculate the feature vector of the day to be predicted and the historical day that simultaneously meets the conditions 1), 2) Similarity (Euclidean distance can be used for similarity calculation); 5) When the similarity value is less than a given threshold, the day is used as a training sample. The filtered training samples are input to the least squares support vector machine. After the training is completed, a prediction model is obtained. The model can be used to obtain the prediction value in the next 24 hours. When applied to the power system, the thermal load forecast value for the next 24 hours can be obtained. In addition, according to the weather characteristics of the future day given by the weather forecast, the conditions of the historical day of the constituency can be appropriately modified, and the training samples can be screened on the future day.
对此利用实验对本发明的优越性进行验证。选取了30天的热负荷预测值(24小时,每小时对应一个热负荷值)来进行对比。测试数据为一天,24个点。分别对比了三种算法:In this regard, the superiority of the present invention was verified by experiments. The heat load forecast value of 30 days (24 hours, corresponding to one heat load value per hour) was selected for comparison. The test data is 24 points a day. Three algorithms are compared:
(1)用网格搜索选取参数的最小二乘支持向量机算法;(1) Least squares support vector machine algorithm with parameters selected by grid search;
(2)用相似日选取的训练集训练最小二乘支持向量机算法(最小二乘支持向量机的参数用网格搜索获取);(2) Training the least squares support vector machine algorithm with the training set selected on similar days (the parameters of the least squares support vector machine are obtained by grid search);
(3)本发明算法,即:用相似日选取的训练集训练最小二乘支持向量机算法,最小二乘支持向量机参数使用改进的遗传算法得到;(3) The algorithm of the present invention, that is, training the least squares support vector machine algorithm with the training set selected on similar days, and the parameters of the least squares support vector machine are obtained using an improved genetic algorithm;
通过对比三种方法的均方根误差RMSE和平均相对误差MAPE指标进行说明,数据如下:By comparing the root mean square error RMSE and average relative error MAPE indicators of the three methods to illustrate, the data is as follows:
平均相对误差MAPE:Average relative error MAPE:
均方根误差RMSE:Root Mean Square Error RMSE:
计算结果如下表1所示:The calculation results are shown in Table 1 below:
表1Table 1
指标index | SVM算法SVM algorithm | 相似日+SVM算法Similar Day + SVM Algorithm | 本发明算法Algorithm of the invention |
RMSERMSE | 0.960.96 | 0.720.72 | 0.490.49 |
MAPEMAPE | 8.2%8.2% | 6.7%6.7% | 5.9%5.9% |
通过实验数据的对比,可以看出本文提出的方法在热负荷的预测上能够达到更好的效果。By comparing the experimental data, it can be seen that the method proposed in this paper can achieve better results in predicting the heat load.
值得说明的是,在本发明一个实施例中,可以对步骤S2计算出的个体适应度进行修正,修正的具体过程为:It is worth noting that in one embodiment of the present invention, the individual fitness calculated in step S2 may be modified, and the specific process of the modification is:
N1:获得当前种群的平均适应度
当前种群中的最大适应度
N1: Get the average fitness of the current population Maximum fitness in the current population
f
max和当前种群中的最小适应度f
min;
f max and the minimum fitness f min in the current population;
N5:获得修正后的个体适应度f′
i=af
i+b,i=1,2,3…,n;
N5: get the adjusted individual fitness f ′ i = af i + b, i = 1, 2, 3 ..., n;
其中,f′
i为第i个修正后的个体适应度;f
i为第i个未修正的个体适应度;c为常数。
Among them, f ′ i is the i-th modified individual fitness; f i is the i-th unmodified individual fitness; c is a constant.
在该实施例中,通过对个体适应度的修正,可以有效避免修正后的个体适应度小于0。而在以后步骤中,计算种群个体的选择概率、计算种群个体进行交叉的概率和计算种群个体进行变异的概率的时候可以采用修正后的个体适应度进行计算。In this embodiment, by modifying the individual fitness, it can be effectively avoided that the modified individual fitness is less than zero. In the subsequent steps, the modified individual fitness can be used to calculate the selection probability of the population individuals, the probability of crossover of the population individuals, and the probability of mutation of the population individuals.
如图3所示,本发明实施例提供了一种电力系统预测的装置,该装置包括:初始模块、赋值模块、选择模块、交变模块、判断模块和训练模块,其中,As shown in FIG. 3, an embodiment of the present invention provides a device for predicting a power system. The device includes an initial module, an assignment module, a selection module, an alternating module, a judgment module, and a training module.
初始模块,用于初始化种群参数,生成种群个体;An initial module for initializing population parameters and generating population individuals;
赋值模块,用于将所述初始模块初始化的参数赋值给支持向量机,计算种群中每个个体的适应度;An assignment module, configured to assign parameters initialized by the initial module to a support vector machine to calculate the fitness of each individual in the population;
选择模块,用于根据所述赋值模块获得的个体适应度,计算种群个体的选择概率,并以该选择概率进行个体选择;A selection module, configured to calculate a selection probability of a population individual based on the individual fitness obtained by the assignment module, and perform individual selection with the selection probability;
交变模块,用于对所述选择模块选择的种群个体进行交叉、变异;An alternation module, configured to cross and mutate the individuals of the population selected by the selection module;
判断模块,用于判断当前种群是否达到训练终止条件,若是,则获得优化后的支持向量机,并触发所述训练模块;否则,触发选择模块;A judging module for judging whether the current population reaches the training termination condition; if so, obtaining an optimized support vector machine and triggering the training module; otherwise, triggering a selection module;
训练模块,用于将训练样本输入到优化后的支持向量机进行训练获得预测模型。A training module is used to input training samples to an optimized support vector machine for training to obtain a prediction model.
优选地,赋值模块可以具体用于将所述初始模块初始化的参数赋值给最小二乘机支持向量机,获得预测值,计算每个个体的适应度,其中,Preferably, the assignment module may be specifically configured to assign a parameter initialized by the initial module to a least squares support vector machine, obtain a predicted value, and calculate the fitness of each individual, where:
个体的适应度计算公式为:The calculation formula of individual fitness is:
其中,
为预测值;y
i为真实值;f
i为第i个个体的适应度;c为常数。
among them, Is the predicted value; y i is the true value; f i is the fitness of the i-th individual; c is a constant.
在本发明一个实施例中,所述选择模块计算种群个体的选择概率的公式为:In an embodiment of the present invention, the formula for calculating the selection probability of the population by the selection module is:
其中,P
i为第i个个体的选择概率。
Among them, P i is the selection probability of the i-th individual.
在本发明一个实施例中,所述交变模块进行种群个体交叉的概率为:In an embodiment of the present invention, the probability that the alternating module performs population individual crossover is:
其中,f
c为个体进行交叉前父代两个个体中适应度大者;f
max为个体进行交叉前父代种群中的最大适应度;
为个体进行交叉前父代种群中所有个体的平均适应度;k
1和k
2为常数。
Among them, f c is the highest fitness among the two individuals before the parents cross the individual; f max is the maximum fitness among the population of the parents before the individuals cross; The average fitness of all individuals in the parent population before crossing the individuals; k 1 and k 2 are constants.
在本发明一个实施例中,所述交变模块进行种群个体变异的概率为:In an embodiment of the present invention, the probability that the alternation module performs individual mutation of the population is:
其中,f
m为需要变异个体的适应度;k
3和k
4为常数。
Among them, f m is the fitness of the individual to be mutated; k 3 and k 4 are constants.
值得说明的是,在本发明一个实施例中,可以对赋值模块计算出的个体 适应度进行修正,修正的具体过程为:It is worth noting that in one embodiment of the present invention, the individual fitness calculated by the assignment module can be modified. The specific process of the modification is:
修正个体的适应度的具体过程为:The specific process of modifying the fitness of an individual is:
N1:获得当前种群的平均适应度
当前种群中的最大适应度
N1: Get the average fitness of the current population Maximum fitness in the current population
f
max和当前种群中的最小适应度f
min;
f max and the minimum fitness f min in the current population;
N5:获得修正后的个体适应度f′
i=af
i+b,i=1,2,3…,n;
N5: get the adjusted individual fitness f ′ i = af i + b, i = 1, 2, 3 ..., n;
其中,f′
i为第i个修正后的个体适应度;f
i为第i个未修正的个体适应度;c为常数。
Among them, f ′ i is the i-th modified individual fitness; f i is the i-th unmodified individual fitness; c is a constant.
在该实施例中,通过对个体适应度的修正,可以有效避免修正后的个体适应度小于0。而在该装置的其他各模块中,计算种群个体的选择概率、计算种群个体进行交叉的概率和计算种群个体进行变异的概率的时候可以采用修正后的个体适应度进行计算。In this embodiment, by modifying the individual fitness, it can be effectively avoided that the modified individual fitness is less than zero. In the other modules of the device, the modified individual fitness can be used for calculating the selection probability of the population individuals, the probability of the population individuals crossing, and the probability of the population individuals being mutated.
上述装置内的各模块之间的信息交互、执行过程等内容,由于与本发明方法实施例基于同一构思,具体内容可参见本发明方法实施例中的叙述,此处不再赘述。The information exchange, execution process, and other content between the modules in the above device are based on the same concept as the method embodiment of the present invention. For specific content, refer to the description in the method embodiment of the present invention, and details are not described herein again.
需要说明的是,在本文中,诸如第一和第二之类的关系术语仅仅用来将一个实体或者操作与另一个实体或操作区分开来,而不一定要求或者暗示这些实体或操作之间存在任何这种实际的关系或者顺序。而且,术语“包括”、“包含”或者其任何其他变体意在涵盖非排他性的包含,从而使得包括一系列要素的过程、方法、物品或者设备不仅包括那些要素,而且还包括没有明确列出的其他要素,或者是还包括为这种过程、方法、物品或者设备所固有的要素。在没有更多限制的情况下,由语句“包括一个······”限定的要素,并不排除在包括所述要素的过程、方法、物品或者设备中还存在另 外的相同因素。It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that between these entities or operations There is any such actual relationship or order. Moreover, the terms "including", "comprising", or any other variation thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or device that includes a series of elements includes not only those elements but also those that are not explicitly listed Or other elements inherent to such a process, method, article, or device. Without more restrictions, the elements defined by the sentence "including a ..." do not exclude that the same factors exist in the process, method, article, or equipment that includes the elements.
本领域普通技术人员可以理解:实现上述方法实施例的全部或部分步骤可以通过程序指令相关的硬件来完成,前述的程序可以存储在计算机可读取的存储介质中,该程序在执行时,执行包括上述方法实施例的步骤;而前述的存储介质包括:ROM、RAM、磁碟或者光盘等各种可以存储程序代码的介质中。A person of ordinary skill in the art may understand that all or part of the steps of the foregoing method embodiments may be implemented by a program instructing related hardware. The foregoing program may be stored in a computer-readable storage medium. When the program is executed, the program is executed. The method includes the steps of the foregoing method embodiment. The foregoing storage medium includes: a ROM, a RAM, a magnetic disk, or an optical disc, which can store program codes in various media.
最后需要说明的是:以上所述仅为本发明的较佳实施例,仅用于说明本发明的技术方案,并非用于限定本发明的保护范围。凡在本发明的精神和原则之内所做的任何修改、等同替换、改进等,均包含在本发明的保护范围内。Finally, it should be noted that the above are only preferred embodiments of the present invention, and are only used to explain the technical solution of the present invention, and are not used to limit the protection scope of the present invention. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention are included in the protection scope of the present invention.
Claims (10)
- 一种电力系统预测的方法,其特征在于,该方法包括:A power system prediction method, characterized in that the method includes:S1:初始化种群参数,生成种群个体;S1: Initialize population parameters to generate population individuals;S2:将S1中的参数赋值给支持向量机,计算种群中每个个体的适应度;S2: Assign the parameters in S1 to the support vector machine to calculate the fitness of each individual in the population;S3:根据个体适应度,计算种群个体的选择概率,并以该选择概率进行个体选择;S3: Calculate the selection probability of the individuals in the population according to the individual fitness, and use the selection probability to perform individual selection;S4:对S3选择的种群个体进行交叉、变异;S4: cross and mutate the individuals selected in S3;S5:判断当前种群是否达到训练终止条件,若是,则获得优化后的支持向量机,并执行S6;否则,执行S3;S5: determine whether the current population meets the training termination condition, and if so, obtain an optimized support vector machine and execute S6; otherwise, execute S3;S6:将训练样本输入到优化后的支持向量机进行训练获得预测模型。S6: The training samples are input to an optimized support vector machine for training to obtain a prediction model.
- 根据权利要求1所述的电力系统预测的方法,其特征在于,步骤S2具体为将S1中的参数赋值给最小二乘机支持向量机,获得预测值,并计算每个个体的适应度,计算公式为:The method for predicting a power system according to claim 1, wherein step S2 is specifically assigning the parameters in S1 to a least squares support vector machine to obtain a predicted value, and calculate the fitness of each individual, and calculate a formula for:
- 根据权利要求2所述的电力系统预测的方法,其特征在于,步骤S3中计算种群个体的选择概率的公式为:The method for predicting a power system according to claim 2, characterized in that the formula for calculating the selection probability of the population individual in step S3 is:其中,P i为第i个个体的选择概率。 Among them, P i is the selection probability of the i-th individual.
- 根据权利要求2所述的电力系统预测的方法,其特征在于,The method for predicting a power system according to claim 2, wherein:步骤S4中种群个体进行交叉的概率为:The probability that the individuals of the population cross in step S4 is:其中,f c为个体进行交叉前父代两个个体中适应度大者;f max 为个体进行交叉前父代种群中的最大适应度; 为个体进行交叉前父代种群中所有个体的平均适应度;k 1和k 2为常数。 Among them, f c is the highest fitness among the two individuals before the parents cross the individual; f max is the maximum fitness among the population of the parents before the individuals cross; The average fitness of all individuals in the parent population before crossing the individuals; k 1 and k 2 are constants.
- 根据权利要求2所述的电力系统预测的方法,其特征在于,The method for predicting a power system according to claim 2, wherein:步骤S4中种群个体进行变异的概率为:The probability of mutation of the individual population in step S4 is:其中,f m为需要变异个体的适应度;k 3和k 4为常数。 Among them, f m is the fitness of the individual to be mutated; k 3 and k 4 are constants.
- 根据权利要求1所述的电力系统预测的方法,其特征在于,步骤S6中的训练样本是经过筛选的训练样本,该筛选过程包括:The method for predicting a power system according to claim 1, wherein the training sample in step S6 is a filtered training sample, and the screening process includes:M1:确定当日时间,获取当日特征向量;M1: Determine the time of the day and obtain the feature vector of the day;M2:分别计算符合预设条件的历史日的特征向量与当日特征向量的相似度是否符合预设阈值,若是,则选择当前历史日为训练样本;否则,排除当前历史日。M2: Calculate whether the similarity between the feature vector of the historical day that meets the preset conditions and the feature vector of the day meets the preset threshold, and if so, select the current historical day as the training sample; otherwise, exclude the current historical day.
- 一种电力系统预测的装置,该装置包括:初始模块、赋值模块、选择模块、交变模块、判断模块和训练模块,其中,A power system prediction device includes an initial module, an assignment module, a selection module, an alternating module, a judgment module, and a training module. Among them,所述初始模块,用于初始化种群参数,生成种群个体;The initial module is configured to initialize a population parameter and generate a population individual;所述赋值模块,用于将所述初始模块初始化的参数赋值给支持向量机,计算种群中每个个体的适应度;The assignment module is configured to assign parameters initialized by the initial module to a support vector machine to calculate the fitness of each individual in the population;所述选择模块,用于根据所述赋值模块获得的个体适应度,计算种群个体的选择概率,并以该选择概率进行个体选择;The selection module is configured to calculate a selection probability of a population individual according to the individual fitness obtained by the assignment module, and perform individual selection with the selection probability;所述交变模块,用于对所述选择模块选择的种群个体进行交叉、变异;The alternation module is configured to cross and mutate the individuals of the population selected by the selection module;所述判断模块,用于判断当前种群是否达到训练终止条件,若是,则获得优化后的支持向量机,并触发所述训练模块;否则,触发选择模块;The judging module is configured to judge whether the current population reaches the training termination condition, and if yes, obtain an optimized support vector machine and trigger the training module; otherwise, trigger a selection module;所述训练模块,用于将训练样本输入到优化后的支持向量机进行训练获得预测模型。The training module is configured to input training samples to an optimized support vector machine for training to obtain a prediction model.
- 根据权利要求7所述的电力系统预测的装置,其特征在于,The apparatus for predicting a power system according to claim 7, wherein:所述赋值模块具体用于将所述初始模块初始化的参数赋值给最小二乘机支持向量机,获得预测值,计算每个个体的适应度,其中,The assignment module is specifically configured to assign a parameter initialized by the initial module to a least squares support vector machine, obtain a predicted value, and calculate the fitness of each individual, where:个体的适应度计算公式为:The calculation formula of individual fitness is:
- 根据权利要求8所述的电力系统预测的装置,其特征在于,The apparatus for predicting a power system according to claim 8, wherein:所述选择模块计算种群个体的选择概率的公式为:The formula for calculating the selection probability of the population by the selection module is:其中,P i为第i个个体的选择概率。 Among them, P i is the selection probability of the i-th individual.
- 根据权利要求8所述的电力系统预测的装置,其特征在于,The apparatus for predicting a power system according to claim 8, wherein:所述交变模块进行种群个体交叉的概率为:The probability that the alternating module performs population individual crossover is:其中,f c为个体进行交叉前父代两个个体中适应度大者;f max为个体进行交叉前父代种群中的最大适应度; 为个体进行交叉前父代种群中所有个体的平均适应度;k 1和k 2为常数; Among them, f c is the highest fitness among the two individuals before the parents cross the individual; f max is the maximum fitness among the population of the parents before the individuals cross; Average fitness of all individuals in the parent population before crossing the individuals; k 1 and k 2 are constants;所述交变模块进行种群个体变异的概率为:The probability that the alternating module performs individual mutation of the population is:其中,f m为需要变异个体的适应度;k 3和k 4为常数。 Among them, f m is the fitness of the individual to be mutated; k 3 and k 4 are constants.
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