CN116468181A - Improved whale-based optimization method - Google Patents

Improved whale-based optimization method Download PDF

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CN116468181A
CN116468181A CN202310463413.2A CN202310463413A CN116468181A CN 116468181 A CN116468181 A CN 116468181A CN 202310463413 A CN202310463413 A CN 202310463413A CN 116468181 A CN116468181 A CN 116468181A
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王佐勋
库杨杨
隋金雪
刘健
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Shandong Technology and Business University
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Abstract

An improved whale optimization method belongs to the technical field of big data. S1, collecting sample data and normalizing the sample data, and dividing the data into a training set and a testing set; s2, optimizing the nuclear parameters and the penalty factors of the support vector machine by using an improved whale optimization algorithm, and establishing a support vector machine prediction model based on the improved whale optimization algorithm; s3, training the support vector machine prediction model by using a training set sample to obtain an optimal kernel parameter and a penalty factor support vector machine prediction model; s4, importing the sample characteristics of the test set into a support vector machine prediction model based on the optimal nuclear parameters and penalty factors to obtain a predicted value of the data; s5, evaluating the model prediction effect by using RMSE, MAE and MAPE. The invention improves the optimizing speed and optimizing precision of the algorithm; the firefly disturbance strategy is added in the whale algorithm, so that the capability of the algorithm to jump out of local optimum is further improved, and the optimizing precision of the algorithm is greatly improved.

Description

Improved whale-based optimization method
Technical Field
An improved whale optimization method belongs to the technical field of big data.
Background
With the development of intelligent optimization algorithms, students use some optimization algorithms to optimize parameters of some prediction models such as neural networks, support vector machines, extreme learning machines and the like. The common intelligent optimization algorithm comprises a particle swarm algorithm, an ant swarm optimization algorithm, a drosophila optimization algorithm, a whale optimization algorithm, a sparrow search algorithm and other novel optimization algorithms with good performances. The whale algorithm is a heuristic optimization algorithm for simulating whale population predation behavior, which is proposed by Mirjallii in 2016, and the predation behavior is called a bubble net predation method and is divided into 3 stages of hunting, surrounding hunting and bubble net attack. The algorithm is simple and easy to implement, and has loose requirements on the condition of the objective function and less parameter control.
The whale algorithm is the same as other intelligent swarm algorithms, and has the defects of low solving precision, easy sinking into local optimum and the like in solving the complex combination optimization problem.
Disclosure of Invention
The invention aims to solve the technical problems that: the improved whale optimizing method based on the improved precision of the load prediction can solve the problem of complex load sequences with high nonlinearity and randomness which are difficult to predict in the data prediction of a single prediction model and overcome the defects of the prior art.
The technical scheme adopted for solving the technical problems is as follows: the improved whale optimization method is characterized by comprising the following steps of: the method comprises the following steps:
s1, collecting sample data and normalizing the sample data, and dividing the data into a training set and a testing set;
s2, optimizing the nuclear parameters and the penalty factors of the support vector machine by using an improved whale optimization algorithm, and establishing a support vector machine prediction model based on the improved whale optimization algorithm;
s3, training the support vector machine prediction model by using a training set sample to obtain an optimal kernel parameter and a penalty factor support vector machine prediction model;
s4, importing the sample characteristics of the test set into a support vector machine prediction model based on the optimal nuclear parameters and penalty factors to obtain a predicted value of the data;
s5, evaluating the model prediction effect by using RMSE, MAE and MAPE.
Preferably, the normalization processing method is as follows:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,for normalized values, ++>For the original data +.>And->Representing the maximum and minimum values of the sample data.
Preferably, the method for optimizing the kernel parameters and penalty factors of the support vector machine by using the improved whale optimization algorithm comprises the following steps:
s3.1, initializing parameters;
s3.2, generating an initial position of an individual by using a chaotic mapping strategy;
s3.3, calculating the fitness of each individual, and finding out the individual with the optimal fitness;
s3.4, updating the position of the whale optimization algorithm;
s3.5 firefly disturbance strategy: calculating fitness, namely updating a current optimal position by utilizing a sine and cosine disturbance strategy, calculating the updated optimal individual fitness of the position, comparing the calculated optimal individual fitness with a current optimal fitness value of a prey, and taking the individual position with the better fitness value as a new optimal position if the updated individual fitness value is better than the prey;
s3.6, judging whether the maximum iteration times are reached, if so, going to the step S3.7, otherwise, going to the step S3.3;
and S3.7, deriving the optimal whale position to obtain the optimal kernel parameters and penalty factors of the support vector machine.
Preferably, the method further comprises the steps of:
；
where k is the current iteration number, in order to have randomness in the population initialization,。
preferably, the method further comprises calculating accuracy ACC of the extreme learning machine calculated by an internal K-fold cross validation method:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,representing the accuracy of the calculated results on each fold data.
Preferably, the method further comprises, in D-dimensional space, each whale being located:
。
preferably, the method further comprises swimming towards the optimal position whale, the position update formula is as follows:
；
；
the nonlinear convergence factor is:
；
；
wherein, the liquid crystal display device comprises a liquid crystal display device,for the current optimal whale position +.>、/>Is->T represents the current iteration number, T represents the maximum iteration number;
the position update of swimming the whale towards the position of a random whale is as follows:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,for the position of randomly selected whales in the current population, when |A<At 1|, whale chooses to swim toward the optimal individual, and when | (A.gtoreq.1) |, whale chooses to swim toward the random individual.
Preferably, the method further comprises, when using the bubble network, updating the position of whales as follows:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,is constant (I)>Is uniformly distributed in->A random number within; />；
Prior to each action, each whale uses an adaptive threshold to determine whether to choose to surround the prey or to use a bubble mesh to repel the prey, the location of which is updated as follows:
。
preferably, the relative fluorescence intensity of fireflies is:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,is the maximum fluorescence brightness of firefly, +.>Is the light intensity absorption coefficient>Is the Euclidean distance between firefly i and j;
the attractive force of fireflies is expressed as:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,is the maximum attraction.
Preferably, the firefly position is updated as:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,∈/>is a step factor; />Is->Random numbers obeying normal distribution.
Compared with the prior art, the invention has the following beneficial effects:
the improved whale optimization method is based on the fact that the nonlinear convergence factor, the self-adaptive threshold value and the self-adaptive weight are added in the optimizing process of the whale optimization algorithm, global searching and local searching of the algorithm are balanced, and optimizing speed and optimizing precision of the algorithm are improved; the firefly disturbance strategy is added in the whale algorithm, so that the capability of the algorithm to jump out of local optimum is further improved, and the optimizing precision of the algorithm is greatly improved.
Drawings
FIG. 1 is a flow chart of a method of improving a whale optimization algorithm to optimize data prediction;
FIG. 2 is a schematic diagram of a support vector machine prediction model based on an improved whale optimization algorithm;
FIG. 3 is a graph of raw experimental data trend for an algorithm for prediction;
fig. 4 is a box plot of seven data subsets of the original experimental data that the algorithm uses for prediction.
Detailed Description
The present invention will be further described with reference to specific embodiments, however, it will be appreciated by those skilled in the art that the detailed description herein with reference to the accompanying drawings is for better illustration, and that the invention is not necessarily limited to such embodiments, but rather is intended to cover various equivalent alternatives or modifications, as may be readily apparent to those skilled in the art.
Fig. 1 to 4 are diagrams illustrating preferred embodiments of the present invention, and the present invention is further described below with reference to fig. 1 to 4.
As shown in fig. 1-2: an improved whale-based optimization method comprises the following steps:
s1, collecting sample data and normalizing the sample data, and dividing the data into a training set and a testing set.
The specific process is that related historical data of the problem to be solved is obtained, the data is divided into a training set and a testing set, normalization processing is carried out, and standard normalization processing is carried out on the data by utilizing a formula (1);
； （1）
wherein, the liquid crystal display device comprises a liquid crystal display device,for normalized values, ++>For the original data +.>And->Representing the maximum and minimum values of the sample data.
And S2, optimizing the nuclear parameters and the penalty factors of the support vector machine by using an improved whale optimization algorithm, and establishing a support vector machine prediction model based on the improved whale optimization algorithm.
And S3, training the support vector machine prediction model by using the training set sample to obtain the support vector machine prediction model with optimal kernel parameters and penalty factors.
The method specifically comprises the following steps:
and S3.1, initializing parameters. The initialization parameters are: maximum iteration number, current iteration number, population number, search space upper and lower boundaries.
S3.2, population initialization is performed. The chaotic mapping strategy is used to generate the initial position of the individual.
And generating an initial position of the individual by using a chaotic mapping strategy, wherein the Tent chaotic mapping is shown as a formula (2).
； （2）
Where k is the current iteration number, in order to make the populationThe initialization is provided with a randomness of the initialization,。
and S3.3, calculating initial fitness. And calculating the fitness of each individual, and finding out the individual with the optimal fitness.
The fitness of each individual is based on the input layer weight and the threshold value of the current position, and the accuracy ACC of the extreme learning machine is calculated by an internal K-fold cross validation method according to a formula;
； （3）
wherein, the liquid crystal display device comprises a liquid crystal display device,representing the accuracy of the calculated results on each fold data.
S3.4, updating the position of the whale optimization algorithm.
The position of each whale in D-dimensional space is:
。 （4）
surrounding the prey: the whale moves towards the optimal position, and the position updating formula is as follows:
； （5）
； （6）
the nonlinear convergence factor is:
； （7）
； （8）
wherein, the liquid crystal display device comprises a liquid crystal display device,for the current optimal whale position +.>、/>Is->T represents the current iteration number, T represents the maximum iteration number.
The position update of swimming the whale towards the position of a random whale is as follows:
； （9）
wherein, the liquid crystal display device comprises a liquid crystal display device,for the position of randomly selected whales in the current population, when |A<At 1|, whale chooses to swim toward the optimal individual, and when | (A.gtoreq.1) |, whale chooses to swim toward the random individual.
Bubble net: whales can spray out of the steam drum to form a bubble net to drive the prey during hunting. Whales will also constantly update their position in order to use the bubble net to drive the prey. Using the bubble network, the whale's position update formula is as follows:
； （10）
wherein, the liquid crystal display device comprises a liquid crystal display device,is constant (I)>Is uniformly distributed in->A random number within;
； （11）
prior to each action, each whale uses an adaptive threshold to determine whether to choose to surround the prey or to use a net of bubbles to repel the prey. The formula is as follows:
。 （12）
s3.5 firefly disturbance strategy: calculating fitness, updating the current optimal position by using a sine and cosine disturbance strategy, calculating the updated optimal individual fitness of the position, comparing the calculated optimal individual fitness with the current optimal fitness value of the prey, and taking the individual position with the better fitness value as a new optimal position if the updated individual fitness value is better than the prey.
The relative fluorescence intensity of fireflies is:
； （13）
wherein, the liquid crystal display device comprises a liquid crystal display device,for the maximum fluorescence brightness of fireflies, the better the objective function value is, the higher the self brightness is; />Is the light intensity absorption coefficient; />Is the Euclidean distance between firefly i and j;
the attractive force of fireflies is expressed as:
； （14）
wherein, the liquid crystal display device comprises a liquid crystal display device,is the maximum attraction.
Firefly position updates are:
； （15）
wherein, the liquid crystal display device comprises a liquid crystal display device,∈/>is a step factor; />Is->Random numbers obeying normal distribution.
S3.6, judging whether the maximum iteration times are reached, if so, going to the step S3.7, otherwise, going to the step S3.3;
and S3.7, deriving the optimal whale position to obtain the optimal kernel parameters and penalty factors of the support vector machine.
S4, the sample characteristics of the test set are imported into a support vector machine prediction model based on the optimal nuclear parameters and the penalty factors, and the predicted value of the data is obtained.
S5, evaluating the model prediction effect by using RMSE, MAE and MAPE.
The support vector machine comprises the following specific steps: the Least Squares Support Vector Machine (LSSVM) is a model that can implement classification and regression, which can solve the problem as a problem of solving convex quadratic programming. The least squares support vector machine provides a clearer and more powerful way of learning complex nonlinear equations than other classification or regression models. The basic idea of the SVM is to infer the corresponding output value y from any one input sample x, for a given set of training data samplesWhere i=1, 2,3, …, l. Return of SVMThe theory is that a nonlinear mapping is performed on the sample data x to complete the conversion from the low-dimensional space to the high-dimensional space, and the regression problem is solved in the high-dimensional space. The expression of the prediction model is as follows:
； （16）
wherein, the liquid crystal display device comprises a liquid crystal display device,is a weight; b is a bias term, taking a constant; />As a kernel function, a nonlinear mapping of low-dimensional space to high-dimensional space is represented.
The expression and constraint conditions of the optimization target are as follows:
； （17）
； （18）
； （19）
； （20）
the dual form is as follows:
； （21）
wherein C is a penalty factor;and->Is a relaxation factor; />As a loss function.
In predicting nonlinear samples, data is generally converted from low dimension to high dimension by a kernel function, and kernel function selection is very important, and a common kernel function is shown in table 1.
TABLE 1 kernel function of support vector machine
After the determination of the kernel function, the penalty factor C and the kernel parameter g are determined, and the invention mainly uses an improved whale optimization algorithm to optimize the two parameters.
The invention discloses a support vector machine based on an improved whale optimization algorithm for a prediction model, and the effectiveness and superiority of the invention are described below with reference to specific embodiments. In this embodiment, the power load is predicted by taking the power load prediction as an example, and the power load has a certain change rule and is also influenced by factors such as air temperature and time, so that it is critical to obtain an accurate prediction result by considering the attribute of the load itself and the influence of other important factors when the load is predicted.
In order to test the reliability and stability of the prediction model provided by the invention, a region of 2009, 7 months and 6 days 0:00 to 2009 8 month 30 days 24: the actual power load data of 00 weeks at 8 weeks is taken as the data of a simulation experiment, the data is measured every fifteen minutes in one day, 96 groups of data are measured every day, and 5376 groups of experimental data are combined. The invention takes 4704 load data of the first 7 weeks as a training set sample and 672 load data of the 8 th week as a test set sample. All data are stored in 7 data subsets according to the types from monday to sunday respectively, in other words, load data of each monday in twelve weeks are stored in one subset, and the other data are similarly stored, so that 7 data subsets with different week types are obtained in total. A predictive model was created for each subset of data separately, trained using the data from the first 7 weeks, and then the load data from week 8 was predicted, in such a way as to verify the accuracy and reliability of the proposed model. The trend of the raw data is shown in fig. 3, and it is obvious that the data distribution has a certain rule, and the period is seven days. The block diagram of the seven data subsets is shown in fig. 4, and it can be seen that the power consumption of monday weekly is the most, the power consumption of Saturday and sunday is the least, the power consumption of monday to friday is relatively balanced, the power consumption data of monday and sunday is relatively scattered, and the power consumption data of sunday is relatively concentrated.
In order to verify the reliability of the model proposed by the present invention, in this embodiment, a Root Mean Square Error (RMSE), a mean absolute percentage pair error (MAPE), a mean square error (MAE), and a Mean Absolute Error (MAE) are mainly selected as evaluation criteria for model accuracy. The definition is shown in the following table.
TABLE 2 model Performance evaluation criteria
In order to test the reliability of the model provided by the invention, the standard WOA-LSSVM and the FA-CAWOA-LSSVM model provided by the invention are selected for comparison, and the result shows that the support vector machine prediction model based on the improved whale optimization algorithm has better stability and prediction precision compared with the support vector machine prediction model based on the standard whale optimization algorithm, and the improved whale optimization algorithm is proved to greatly improve the optimizing capability of the whale optimization algorithm.
Table 3 error comparison plot of predicted and actual values for two models
The table again shows that the algorithm provided by the invention has better optimizing performance, and the prediction accuracy of the FA-CAWOA-LSSVM is remarkably improved compared with that of the WOA-LSSVM.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the invention in any way, and any person skilled in the art may make modifications or alterations to the disclosed technical content to the equivalent embodiments. However, any simple modification, equivalent variation and variation of the above embodiments according to the technical substance of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims (9)

1. An improved whale optimization method is characterized in that: the method comprises the following steps:
s1, collecting sample data and normalizing the sample data, and dividing the data into a training set and a testing set;
s2, optimizing the nuclear parameters and the penalty factors of the support vector machine by using an improved whale optimization algorithm, and establishing a support vector machine prediction model based on the improved whale optimization algorithm;
s3, training the support vector machine prediction model by using a training set sample to obtain an optimal kernel parameter and a penalty factor support vector machine prediction model;
s4, importing the sample characteristics of the test set into a support vector machine prediction model based on the optimal nuclear parameters and penalty factors to obtain a predicted value of the data;
s5, evaluating model prediction effects by using RMSE, MAE and MAPE;
a method for optimizing the kernel parameters and penalty factors of a support vector machine using an improved whale optimization algorithm, comprising the steps of:
s3.1, initializing parameters;
s3.2, generating an initial position of an individual by using a chaotic mapping strategy;
s3.3, calculating the fitness of each individual, and finding out the individual with the optimal fitness;
s3.4, updating the position of the whale optimization algorithm;
s3.5 firefly disturbance strategy: calculating fitness, namely updating a current optimal position by utilizing a sine and cosine disturbance strategy, calculating the updated optimal individual fitness of the position, comparing the calculated optimal individual fitness with a current optimal fitness value of a prey, and taking the individual position with the better fitness value as a new optimal position if the updated individual fitness value is better than the prey;
s3.6, judging whether the maximum iteration times are reached, if so, going to the step S3.7, otherwise, going to the step S3.3;
and S3.7, deriving the optimal whale position to obtain the optimal kernel parameters and penalty factors of the support vector machine.
2. The improved whale-based optimization method according to claim 1, wherein: the normalization processing method comprises the following steps:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,for normalized values, ++>For the original data +.>And->Representing the maximum and minimum values of the sample data.
3. The improved whale-based optimization method according to claim 1, wherein: the method further comprises the following steps of:
；
where k is the current iteration number, in order to have randomness in the population initialization,。
4. the improved whale-based optimization method according to claim 1, wherein: the method further comprises the step of calculating accuracy ACC of the extreme learning machine by an internal K-fold cross validation method:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,representing the accuracy of the calculated results on each fold data.
5. The improved whale-based optimization method according to claim 1, wherein: the method further comprises the steps of:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,representing the position of the whale individual in D-dimensional space.
6. The improved whale-based optimization method of claim 5, wherein: the method further comprises swimming towards the optimal position whale, the position update formula being as follows:
；
；
；
；
wherein, the liquid crystal display device comprises a liquid crystal display device,position of the ith individual after the t+1st iteration, +.>Position of i-th individual for current iteration number, < ->For the current optimal whale position, A and C are both coefficients, < >>、/>Is->Random number of->The self-adaptive weight is adopted, T is the current iteration number, and T is the maximum iteration number;
the nonlinear convergence factor is:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,and->The two parameters are selected as +.>，/>；
The position update of swimming the whale towards the position of a random whale is as follows:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,for the position of randomly selected whales in the current population, when +.>When whale chooses to swim towards the optimal individual, when +.>When whale chooses to swim towards random individuals.
7. The improved whale-based optimization method of claim 5, wherein: the method further comprises, using the bubble network, updating the position of whales as follows:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,is constant (I)>Is uniformly distributed in->A random number within; />；
Prior to each action, each whale will determine whether to choose to surround the prey or to use a net of bubbles to repel the prey using an adaptive thresholdThe method comprises the following steps:
。
8. the improved whale-based optimization method according to claim 1, wherein: the relative fluorescence intensity of fireflies is:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,is the maximum fluorescence brightness of firefly, +.>Is the light intensity absorption coefficient>Is the Euclidean distance between firefly i and j;
the attractive force of fireflies is expressed as:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,is the maximum attraction.
9. The improved whale-based optimization method of claim 8, wherein: firefly position updates are:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,∈/>is a step factor; />Is->Random numbers obeying normal distribution.
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