CN116468181A - Improved whale-based optimization method - Google Patents

Abstract

An optimization method based on improved whales belongs to the field of big data technology. S1 collects sample data and normalizes it, and divides the data into training set and test set; S2 uses the improved whale optimization algorithm to optimize the kernel parameters and penalty factors of the support vector machine, and establishes the support vector machine prediction model based on the improved whale optimization algorithm; S3 uses the training set samples to train the support vector machine prediction model, and obtains the support vector machine prediction model with optimal kernel parameters and penalty factors; MAE and MAPE evaluate the prediction effect of the model. The invention improves the optimization speed and optimization accuracy of the algorithm; adds the firefly disturbance strategy to the whale algorithm, further improves the ability of the algorithm to jump out of the local optimum, and greatly improves the optimization accuracy of the algorithm.

Description

An Optimization Method Based on Improved Whale

technical field

An optimization method based on improved whales belongs to the field of big data technology.

Background technique

With the development of swarm intelligence optimization algorithms, scholars have used some optimization algorithms to optimize the parameters of some prediction models such as neural networks, support vector machines, and extreme learning machines. Common swarm intelligence optimization algorithms include particle swarm optimization algorithm, ant colony optimization algorithm, fruit fly optimization algorithm, whale optimization algorithm, and some new optimization algorithms with good performance, such as sparrow search algorithm. The whale algorithm is a heuristic optimization algorithm proposed by Mirjalili et al. in 2016 to simulate the predation behavior of whale groups. The predation behavior is called the bubble net predation method, which is divided into three stages: searching for prey, surrounding prey, and bubble net attack. The algorithm is concise and easy to implement, and has loose requirements on the objective function conditions and less parameter control.

Like other swarm intelligence algorithms, the whale algorithm also has some shortcomings in solving complex combinatorial optimization problems, such as low solution accuracy and easy to fall into local optimum.

Contents of the invention

The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art, provide a highly nonlinear and random complex load sequence that is difficult to predict in data forecasting by a single forecasting model, and improve the accuracy of load forecasting based on an improved whale optimization method.

The technical scheme that the present invention solves its technical problem adopts is: this optimization method based on improved whale, it is characterized in that: comprise the steps:

S1 collects sample data and normalizes it, and divides the data into training set and test set;

S2 uses the improved whale optimization algorithm to optimize the kernel parameters and penalty factors of the support vector machine, and establishes a support vector machine prediction model based on the improved whale optimization algorithm;

S3 uses the training set samples to train the support vector machine prediction model, and obtains the support vector machine prediction model with optimal kernel parameters and penalty factors;

S4 imports the sample features of the test set into the support vector machine prediction model based on the optimal kernel parameters and penalty factors to obtain the predicted value of the data;

S5 uses RMSE, MAE and MAPE to evaluate the prediction effect of the model.

Preferably, the normalization processing method is as follows:

;

in, is the normalized value, /> for raw data, /> and /> Indicates the maximum and minimum values of the sample data.

Preferably, the method for optimizing the kernel parameters and the penalty factor of the support vector machine using the improved whale optimization algorithm comprises the following steps:

S3.1 parameter initialization;

S3.2 Use the chaotic mapping strategy to generate the initial position of the individual;

S3.3 Calculate the fitness of each individual and find out the individual with the best fitness;

S3.4 Position update of whale optimization algorithm;

S3.5 Firefly disturbance strategy: calculate the fitness, use the sine-cosine disturbance strategy to update the current optimal position, calculate the optimal individual fitness after the position update, and compare it with the current optimal fitness value of the prey, if the updated individual fitness value is better than the prey, then use the individual position with a better fitness value as the new optimal position;

S3.6 Judging whether the maximum number of iterations has been reached, if it has been reached, go to step S3.7, otherwise go to step S3.3;

S3.7 Deriving the optimal whale position, that is, obtaining the optimal kernel parameters and penalty factors of the support vector machine.

Preferably, the method also includes that the Tent chaotic map is:

;

Among them, k is the current number of iterations, in order to make the population initialization random, .

Preferably, the method also includes calculating the accuracy ACC of the extreme learning machine with the internal K-fold cross-validation method:

;

in, Indicates the accuracy calculated on each fold of data.

Preferably, the method also includes, the position of each whale in the D-dimensional space is:

.

Preferably, the method further includes, swimming towards the optimal position of the whale, and the position update formula is as follows:

;

;

The nonlinear convergence factor is:

;

;

in, is the current optimal whale position, /> , /> for /> The random number of , t represents the current number of iterations, and T represents the maximum number of iterations;

Swim towards the position of a random whale The position of the whale is updated as follows:

;

in, is the position of the randomly selected whale in the current group, when |A<1|, the whale chooses to swim towards the optimal individual, and when |(A≥1)|, the whale chooses to swim towards the random individual.

Preferably, the method also includes, when using the bubble net, the whale's position is updated as follows:

;

in, is a constant, /> for uniform distribution over /> random number inside; /> ;

Before each action, each whale will use the adaptive threshold to judge whether to choose to surround the prey or use the bubble net to drive the prey, and its position is updated as follows:

.

Preferably, the relative fluorescence brightness of fireflies is:

;

in, is the maximum fluorescence brightness of fireflies, /> is the light intensity absorption coefficient, /> is the Euclidean distance between fireflies i and j;

The formula expression for the attraction of fireflies is:

;

in, is the maximum attractiveness.

Preferably, the position of the firefly is updated as:

;

in, ∈/> is the step factor; /> for /> random numbers that follow a normal distribution.

Compared with prior art, the beneficial effect that the present invention has is:

Based on the improved whale optimization method, the nonlinear convergence factor, adaptive threshold and adaptive weight are added in the optimization process of the whale optimization algorithm, which balances the global search and local search of the algorithm, and improves the optimization speed and optimization accuracy of the algorithm; the firefly disturbance strategy is added to the whale algorithm to further improve the algorithm's ability to jump out of the local optimum, and greatly improve the algorithm's optimization accuracy.

Description of drawings

Fig. 1 is the flowchart of the method for optimizing data prediction by improving the whale optimization algorithm;

Fig. 2 is a schematic diagram of a support vector machine prediction model based on the improved whale optimization algorithm;

Fig. 3 is the trend diagram of the original experimental data used for prediction by the algorithm;

Figure 4 is a block diagram of the seven data subsets of the original experimental data that the algorithm used for prediction.

Detailed ways

The present invention will be further described below in conjunction with specific embodiments, but those who are familiar with the art should understand that the detailed description given here in conjunction with accompanying drawings is for better explanation, and the structure of the present invention must exceed these limited embodiments, and for some equivalent replacement schemes or common means, this paper does not describe in detail again, but still belongs to the protection scope of the present application.

Fig. 1～4 is preferred embodiment of the present invention, below in conjunction with accompanying drawing 1～4 the present invention is described further.

As shown in Figures 1 and 2: an optimization method based on improved whales, including the following steps:

S1 collects sample data and normalizes it, and divides the data into training set and test set.

The specific process is to obtain the relevant historical data of the problem to be solved, divide the data into training set and test set, and perform normalization processing, and use the formula (1) to perform standard normalization processing;

; (1)

in, is the normalized value, /> for raw data, /> and /> Indicates the maximum and minimum values of the sample data.

S2 uses the improved whale optimization algorithm to optimize the kernel parameters and penalty factors of the support vector machine, and establishes the support vector machine prediction model based on the improved whale optimization algorithm.

S3 uses the training set samples to train the support vector machine prediction model, and obtains the support vector machine prediction model with optimal kernel parameters and penalty factors.

Specifically include the following steps:

S3.1 Parameter initialization. The initialization parameters are: the maximum number of iterations, the current number of iterations, the number of populations, and the upper and lower boundaries of the search space.

S3.2 Initialize the population. The initial position of the individual is generated using a chaotic mapping strategy.

Use the chaotic mapping strategy to generate the initial position of the individual, and the Tent chaotic mapping is as formula (2).

; (2)

Among them, k is the current number of iterations, in order to make the population initialization random, .

S3.3 Calculate the initial fitness. Calculate the fitness of each individual and find the individual with the best fitness.

Among them, the fitness of each individual is based on the input layer weight and threshold of the current position, and the accuracy ACC of the extreme learning machine is calculated by the internal K-fold cross-validation method according to the formula;

; (3)

in, Indicates the accuracy calculated on each fold of data.

S3.4 Position updates for the whale optimization algorithm.

The position of each whale in the D-dimensional space is:

. (4)

Surround the prey: the whale swims towards the optimal position, the position update formula is as follows:

; (5)

;(6)

The nonlinear convergence factor is:

;(7)

; (8)

in, is the current optimal whale position, /> , /> for /> The random number of , t represents the current number of iterations, and T represents the maximum number of iterations.

Swim towards the position of a random whale The position of the whale is updated as follows:

; (9)

in, is the position of the randomly selected whale in the current group, when |A<1|, the whale chooses to swim towards the optimal individual, and when |(A≥1)|, the whale chooses to swim towards the random individual.

Bubble net: When hunting, whales will eject steam drums to form a bubble net to drive away prey. In order to use the bubble net to drive away the prey, the whale will constantly update its position. When using the bubble net, the position update formula of the whale is as follows:

;(10)

in, is a constant, /> for uniform distribution over /> random number in

;(11)

Before each move, each whale uses an adaptive threshold to decide whether to encircle the prey or use the bubble net to drive the prey away. The formula is as follows:

. (12)

S3.5 Firefly disturbance strategy: Calculate the fitness, use the sine-cosine disturbance strategy to update the current optimal position, calculate the optimal individual fitness after the position update, and compare it with the current optimal fitness value of the prey. If the updated individual fitness value is better than the prey, the individual position with a better fitness value will be used as the new optimal position.

The relative fluorescence brightness of fireflies is:

;(13)

in, is the maximum fluorescence brightness of fireflies, the better the objective function value is, the higher the brightness will be;/> is the light intensity absorption coefficient; /> is the Euclidean distance between fireflies i and j;

The formula expression for the attraction of fireflies is:

;(14)

in, is the maximum attractiveness.

The firefly position is updated to:

;(15)

in, ∈/> is the step factor; /> for /> random numbers that follow a normal distribution.

S3.6 Judging whether the maximum number of iterations has been reached, if it has been reached, go to step S3.7, otherwise go to step S3.3;

S3.7 Deriving the optimal whale position, that is, obtaining the optimal kernel parameters and penalty factors of the support vector machine.

S4 imports the sample features of the test set into the support vector machine prediction model based on the optimal kernel parameters and penalty factors to obtain the predicted value of the data.

S5 uses RMSE, MAE and MAPE to evaluate the prediction effect of the model.

The details of the support vector machine are: the least squares support vector machine (LSSVM) is a model that can realize classification and regression, and it can turn the problem into a problem of solving convex quadratic programming. Compared with other classification or regression models, least squares support vector machines provide a clearer and more powerful way to learn complex nonlinear equations. The basic idea of SVM is to infer the corresponding output value y through any input sample x. For a given set of training data samples, it is , where i=1, 2, 3, ..., l. The regression theory of SVM is to make a nonlinear mapping on the sample data x, complete the conversion from low-dimensional space to high-dimensional space, and solve the regression problem in high-dimensional space. Its prediction model expression is:

;(16)

in, is the weight; b is the bias item, which is a constant; /> Is the kernel function, which represents the nonlinear mapping from low-dimensional space to high-dimensional space.

The expression and constraints of the optimization objective are:

;(17)

;(18)

;(19)

;(20)

Its dual form is:

; (twenty one)

where C is the penalty factor; and /> is the relaxation factor; /> is the loss function.

When predicting nonlinear samples, the kernel function is generally used to convert the data from low-dimensional to high-dimensional, and the selection of the kernel function is very important. The commonly used kernel functions are shown in Table 1.

Table 1 Kernel function of support vector machine

After confirming that the kernel function is determined, then the penalty factor C and the kernel parameter g are determined, and the present invention mainly uses an improved whale optimization algorithm to optimize these two parameters.

The present invention discloses a support vector machine based on an improved whale optimization algorithm used for prediction models. The effectiveness and superiority of the present invention will be described below in conjunction with specific embodiments. This embodiment takes power load forecasting as an example. Since power load has a certain change law and is also affected by factors such as temperature and time, the key to obtaining accurate forecast results is to take into account the properties of the load itself and the influence of other important factors when performing load forecasting.

In order to test the reliability and stability of the prediction model proposed by the present invention, the actual power load data of an area for 8 weeks from 0:00 on July 6, 2009 to 24:00 on August 30, 2009 was selected as the data of the simulation experiment, and the data was measured every fifteen minutes in a day. A total of 96 sets of data were measured every day, and there were 5376 sets of experimental data in total. In the present invention, a total of 4,704 load data in the first 7 weeks are used as a training set sample, and a total of 672 load data in the 8th week are used as a test set sample. Store all the data in 7 data subsets according to the type of Monday to Sunday. In other words, the load data of each Monday in twelve weeks is stored in a subset, and so on, and a total of 7 data subsets of different week types are obtained. Create a prediction model for each data subset, use the data of the first 7 weeks to train the model, and then predict the load data of the 8th week, using this method to verify the accuracy and reliability of the model proposed by the present invention. The trend of the original data is shown in Figure 3. It can be clearly seen that the data distribution has certain rules, and every seven days is a cycle. The frame diagram of the seven data subsets is shown in Figure 4. It can be seen that the power consumption is the most on Monday, and the power consumption on Saturday and Sunday is the least.

In order to verify the reliability of the proposed model of the present invention, root mean square error (RMSE), mean absolute percentage pair error (MAPE), mean square error (MAE), mean absolute error (MAE) are mainly selected as the evaluation criteria of model accuracy in the present embodiment. Definitions are shown in the table below.

Table 2 Model performance evaluation criteria

In order to test the reliability of the model proposed by the present invention, the standard WOA-LSSVM and the FA-CAWOA-LSSVM model proposed by the present invention were selected for comparison. The results show that the support vector machine prediction model based on the improved whale optimization algorithm has better stability and prediction accuracy than the support vector machine prediction model based on the standard whale optimization algorithm, indicating that the improved whale optimization algorithm has greatly improved the optimization ability of the whale optimization algorithm.

Table 3 Comparison chart of the error between the predicted value and the real value of the two models

The above table shows again that the algorithm proposed by the present invention has better optimization performance, and the prediction accuracy of FA-CAWOA-LSSVM is significantly improved compared with WOA-LSSVM.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention in other forms. Any person skilled in the art may use the technical contents disclosed above to change or modify them into equivalent embodiments with equivalent changes. However, any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still belong to 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,,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,,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,,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,,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,,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,,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,,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,,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,,is the maximum attraction.

9. The improved whale-based optimization method of claim 8, wherein: firefly position updates are:

；

wherein,,∈/>is a step factor; />Is->Random numbers obeying normal distribution.