## Ai Ruibo , Cheng Li and Na Li## |

Optimization model | Parameter | Initial value |
---|---|---|

PSO | Weight c1, c2 Elasticity coefficient | 1.0 1.7, 2.0 1.0 |

GA | Pc Pm | 0.85 0.02 |

ABC | Quantity of food source Employed bee, onlooker bee limit Maximum number of iterations | 20 10, 10 100 120 |

Table 2.

Parameter | PSO-SVR | GA-SVR | ABC-SVR |
---|---|---|---|

[TeX:] $$C$$ | 14.31 | 20.19 | 48.22 |

[TeX:] $$\mathcal{\varepsilon}$$ | 0.10 | 0.16 | 0.23 |

[TeX:] $$\sigma$$ | 0.64 | 0.68 | 0.56 |

The wavelet neural network time series (WNN-TS) model time series delay is set to 4. There are 6 hidden layer nodes, and the learning rate is lr1=0.09 and lr2=0.03. Meanwhile, the maximum iteration number is set to 120.

The comparison curves between the true values and the predicted values of the WNN-TS model in 3 days are illustrated in Figs. 8–10. The comparison curves between the true values and the predicted values of the ABC-SVR model in 3 days are illustrated in Figs. 2(b), 3(b), and 4(b).

The horizontal comparison results between the true values and the predicted values of the SVR model and ABC-SVR model are illustrated in Figs. 2–4. The curve trend shows that the predicted value curve of the ABC-SVR model fits well with the true value curve, which illustrates these predicted results of the ABC-SVR are preciser than those of SVR. From the evaluation index mean square error (MSE) in Table 3, it can be proved that the MSE of the ABC-SVR is lower, indicating these predicted results of the ABC-SVR are preciser than those of the SVR.

Table 3.

Date | MSE | |
---|---|---|

SVR | ABC-SVR | |

September 7, 2017 | 36.48 | 24.59 |

September 8, 2017 | 25.67 | 12.67 |

September 9, 2017 | 78.67 | 24.11 |

Through the analysis of the MSE results, it has been demonstrated that the prediction based on ABC optimization SVR in our research is more feasible as well as the higher accuracy has been achieved.

By analyzing Figs. 5–7, it can be observed that the curve fitting between the true values and the predicted values of the ABC-SVR, PSO-SVR, and GA-SVR are all fairly well. And it proves the accuracy of prediction for all three algorithms is preciser than that of SVR. From the evaluation indexes of prediction results of each optimization algorithm, it has been demonstrated that ABC-SVR presents much higher prediction accuracy, and the MSE of each model prediction result is shown in Table 4.

Table 1.

Date | MSE | ||
---|---|---|---|

PSO-SVR | GA-SVR | ABC-SVR | |

September 7, 2017 | 29.07 | 28.70 | 24.59 |

September 8, 2017 | 12.96 | 15.56 | 12.67 |

September 9, 2017 | 51.19 | 29.33 | 24.11 |

Through the further analysis, the experimental results confirm that the ABC-SVR of the paper has more favorable prediction accuracy as well as higher prediction property, which verifies that the ABC algorithm has the optimal optimization effect on SVR parameters. F test is carried out by adopting SPSS for the three groups of the predicted results, and [TeX:] $$p<0.05$$, indicating that the difference among the three groups has statistical significance. In the meantime, from Table 2, it is observed that the parameter range of the SVR obtained by the ABC optimization algorithm is larger, which demonstrates that the global search ability of ABC algorithm is stronger than those of the PSO algorithm and GA algorithm, and ABC algorithm is more suitable aiming at large randomness.

By horizontal comparison experiments among the predicted values of WNN-TS, the predicted values of ABC-SVR and the true values, it is verified the predicted results for the ABC-SVR model have higher accuracy, from MSE of the evaluation index of results of each optimization model (Table 5).

Through the analysis of MSE, it has been observed that the short-term traffic flow prediction algorithm based on ABC optimization SVR of the paper has the optimal prediction capability and prediction accuracy.

According to the characteristics of the strong global search ability of the ABC algorithm and the suitability for small samples of the SVR algorithm, the short-term traffic flow prediction algorithm by SVR is proposed based on ABC optimization algorithm, and the satisfactory results have been attained. The intelligent combination prediction algorithm is one of research focuses at home and abroad, and the ABC-SVR proposed in the paper can also be applied to other fields. The optimal algorithm will show its more important and more practical value in the future. Meanwhile, the adaptability in different fields of prediction algorithm, the public data set construction of traffic flow, the computational complexity of prediction process as well as the own optimization of optimization algorithms need further investigations and explorations in the future research.

He received his M.S. degree in science and technology of computer from Qiqihar University in 2013. Now, he is currently pursuing the Ph.D. degree in science and technology of computer in Harbin Engineering University. He is a professor at College of Computer and Control Engineering, Qiqihar University. His research interests include artificial intelligence, optimization algorithm, network security, etc.

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