Research on predictive control model of RBF neural network based on group intelligence optimization

Lei XIAO, Li-lu GUO， Xiao-jie WANG, Jie QIU

(1College of Computer Science and Technology， Yulin Normal University， Yulin 537000, China)(2College of Computer Science and Technology， Xidian University, Xi’an 710000, China )(3School of Information Science and Engineering, Xinjiang University, Urumqi 830011, China)

Abstract: In order to improve the accuracy of the predictive control model, the RBF neural network is used to complete the network traffic prediction, and the model parameters are optimized by using the hybrid leapfrog algorithm in the swarm intelligence algorithm. First, the hybrid leapfrog algorithm is introduced in the modeling process. Then, the weights and thresholds of the RBF neural network are used as individual frogs, and multiple randomly combined individuals with weights and thresholds constitute a frog group. Group the frog groups, and obtain global optimal individuals through continuous regrouping and iteration within the group to obtain the optimal weights and thresholds in order to determine the optimal predictive control model. Experiments prove that the predictive control model based on RBF neural network optimized by swarm intelligence has higher accuracy.

Key words: RBF neural network, Swarm intelligence, Hybrid leapfrog algorithm, Network traffic forecast, Fitness function

With the development of the mobile Internet, the types of equipment connected to the Internet have become more diversified, and the types of data accessed have become significantly different, and users have higher requirements for data upload and download rates. This all places higher requirements on the development of the Internet, especially support for network traffic, which is particularly important for the user experience. The Internet must provide a guarantee that a large number of users can smoothly upload and download data, and at the same time ensure the full use of network equipment resources. Therefore, it is very important to make a good network prediction and make a reasonable network flow control strategy based on the actual network traffic.

In the case of limited network resources, using historical data to predict current and future network traffic based on network traffic in order to continuously balance and allocate network resources can effectively improve the utilization of network equipment and resources. However, in the face of the increasing amount of data and the heterogeneity of user equipment, how to meet the different traffic refinement requirements of different types of equipment needs further research. Ref. [1] provided a more comprehensive discussion on the direction of wireless network traffic prediction, explained the characteristics of wireless network user increment and its demand for traffic, and provided a basis for further targeting the direction and focus of wireless network traffic. Ref. [2] adopts a support vector machine method combining artificial bee colony and artificial fish swarm to complete the traffic prediction, which integrates multiple swarm intelligence algorithms. Ref. [3] uses a swarm intelligence algorithm to implement wireless sensor network traffic prediction, which expands the range of traffic prediction to wireless sensor networks. Therefore, this paper combines swarm intelligence algorithm with RBF neural network to realize network traffic prediction and improve its adaptability to traffic prediction.

1 RBF neural network

Let the input sample beXk=(x1,x2,…,xn),k=1,2,…,m, where m and n respectively represent the total number of samples and the total number of features in one sample. Generally speaking, the number of neurons in the input layer is equal to the total number of features. The number of layer neurons is generally less than the total number of features. The output of the K-th sample after the model isYk=(y1,y2,…,yn), and n is the number of neurons in the output layer.

First, the value of the input sample after reaching the first layer of the hidden layer after weighting isS1j[4].

(1)

After the value ofS1jis passed through the feature conversion function,b1jcan be obtained.

(2)

The feature conversion function selected by RBF neural network is Gaussian function[5]. Whereσis a real number greater than 0, andcjis the center value of the j-th hidden layer. Taking the first hidden layer as input, the value that reaches the second hidden layer after weighting isS2j.

(3)

Then solve the transformation function to getb2j.

(4)

The output through all hidden layers is weighted byVjtand the result isLt.

(5)

The above formula is solved by the Gaussian function to obtain the output of the entire model:

(6)

The error result of the k-th sample isEk.

(7)

The error of all samples isE.

(8)

Formula (8) is derived from formula (9) by first-order derivation.

ΔVjt=-?Ek/?Vjt

(9)

Solve the weights from the hidden layer to the output layer. Continue to solve the weights ΔWjtof the input and hidden layers.

(10)

2 Swarm intelligence optimized RBF neural network

The swarm intelligence algorithm has a wide content and contains more algorithms[6]. This paper selects a hybrid frog-leaping algorithm in the swarm intelligence algorithm to optimize the parameters of the RBF neural network and improve the accuracy of the network traffic prediction of the RBF neural network.

2.1 Hybrid frog leaping algorithm

(11)

(12)

2.2 Hybrid frog jump optimized RBF neural network

The hybrid frog leaping algorithm of Section 2.1 is used to realize the weight and threshold determination of RBF neural network. The main process is that: during the (t+1)-th calculation iteration, using the results after the t-th iteration, the frogXb(t) with a larger RMSE is continuously approached to the frogXw(t) with a smaller RMSE. In order to ensure that the frogs in the group can move closer to the frog with a smaller RMSE, a hungry moving method is proposed as shown in formula (13)[9].

Δw(t)=rand()(Xb(t)-x(t))

(13)

Xw(t+1)=Xw(t)Δw(t)

Rmin≤Δw(t)≤Rmax

(14)

If the value ofXw(t+1) at time (t+1) is larger thanXw(t), that is, it has better fitness, then replaceXw(t) withXw(t+1). Otherwise, continue to execute formulas (13) and (14). With regard to the frog moving step size, a step size factorCcan be introduced[10]. Then the calculation of thei-th moving distance of thek-th frog is shown in formula (15).

(15)

C=Cmin+inow/Gglobal×(Cmax-Cmin)

(16)

WhereCminandCmaxare the minimum and maximum moving step sizes of the frogs in the current group, which can be set according to the actual situation.Gglobalis the sum of fitness values of all frogs in the group, andinowis the number of times the frog moves at the current moment.

When the fitness value of all frogs in the group is closer toXb(t), and the error is within the set threshold, then the algorithm stops iteratively and outputs the frog distribution map at the current moment, which is the optimal solution.

2.3 Network flow forecasting process based on hybrid frog leap optimization RBF neural network

The process of frog leap hybrid optimization to obtain the optimal individual is actually the process of solving the RBF neural network weight and threshold optimal solution. With the optimal solution of weights and thresholds, the network traffic prediction model of RBF neural network can be determined. In the process of the hybrid frog jumping algorithm, it is necessary to continuously group the entire frog group, and continuously update the position of the individual with a larger RMSE in the group to improve the fitness value of all individuals in the group. The parameter adjustment method of this neural network model is highly efficient, and each iteration increases the fitness value.

The network flow prediction process of the RBF neural network optimized by the hybrid frog leap is shown in Fig.1.

Fig.1 Flow chart of network traffic prediction of leapfrog hybrid optimization RBF neural network

3 Experimental design and results analysis

In order to verify the performance of hybrid frog leap-optimized RBF neural network for network traffic prediction, a case simulation was performed. The simulation data comes from a large power grid platform[11-13], and the data flow for one month is selected as the simulation object.

3.1 Simulation of prediction accuracy

The RBF neural network and the RBF neural network through the hybrid frog jumping algorithm were used to simulate the network traffic for one month on a weekly basis[14]. The root mean square error (RMSE) was selected as the accurate criterion for network prediction[15]. In the simulation process, in order to fully verify the impact of the hybrid frog jump optimization on the prediction accuracy rate, the RBF neural network structure is differentiated. The simulation results are shown in Table 1.

Table 1 prediction accuracy of the two algorithms

It can be seen from Table 1 that under the same neural network scale, the RBF neural network traffic prediction based on the hybrid frog leap optimization has a lower RMSE, which indicates that the prediction accuracy is higher. Especially when the number of hidden layers is 10, the predictions for 4 weeks all show lower RMSE, and more ideal prediction results can be obtained. Therefore, in actual operation, the appropriate neural network scale can be selected according to Table 1 to complete the network traffic prediction.

In addition, in order to further verify the advancedness of the proposed method, a comparison experiment is performed with a network prediction method using a wavelet neural network. The test data set is one month of network traffic. The comparison result is shown in Fig.2. Among them, the number of hidden layers of the RBF neural network optimized by the hybrid leapfrog is ten. As can be seen from Fig.2, compared to the wavelet neural network, the hybrid frog leap-optimized RBF neural network shows a lower RMSE.

Fig.2 Comparison results of RMSE

3.2 Optimization of leapfrog mixed parameters

In order to further analyze the optimal performance of RBF neural network optimized by frog leap hybrid, the main parameters of the hybrid frog leap algorithm were differentiated and simulated. The main purpose is to simulate the number of frog groups, the step size of frog movement, and the number of iterations within the group after grouping frog groups to verify the impact of different parameters on the accuracy of prediction. The number of hidden layer neurons in the RBF neural network is set to 10. Select the number of packets 10, 20, 30, 40, and 50, with steps of 1, 3, and 5, to predict the network traffic for one month. After 10 predictions, the predicted maximum, average, and minimum RMSE values are solved, as shown in Table 2.

Table 2 RMSE of different groups and steps

As can be seen from Table 2, when the number of packets belongs to [10, 20, 30, 40, 50] and the step size is [1, 3, 5], RMSE does not exceed 0.7. Moreover, the maximum and minimum deviations from the mean are not large, and the algorithm is relatively stable. By comparison, when the number of groups is 30 and the step size is 3, the average value of RMSE is the smallest, only 0.049 9. In actual application, the parameters of the hybrid frog jumping algorithm can be fine-tuned by repeatedly changing the main parameter simulation method to achieve better prediction results.

Table 3 RMSE of iterations in different groups

The number of groups and step size were fixed to 30 and 3, and the number of different iterations was adjusted to verify its impact on prediction accuracy.

It can be concluded from Table 3 that as the number of iterations in the group increases, the maximum, minimum, and average values of RMSE decrease slowly. However, when the number of iterations is 40 and 50, the minimum and average RMSE of the two do not change. In addition, the maximum value is almost unchanged and stable, and it does not always decrease as the number of iterations increases. Therefore, the setting of the number of iterations should be reasonable, and if the number of iterations is increased blindly, the prediction time will definitely increase. The reasonable number of iterations in the group should be set according to the actual situation.

4 Conclusion

The hybrid frog leap is used to optimize the network traffic prediction of the RBF neural network, which improves the network traffic prediction accuracy. The following conclusions are obtained through experimental simulations: 1) The specific operation process of traffic prediction should reasonably set the size of the neural network; 2) By fine-tuning the main parameters of the hybrid frog jumping algorithm, better network traffic prediction results can be obtained.