Traffic flow prediction becomes an essential process for intelligent transportation systems (ITS). Though traffic sensor devices are manually controllable, traffic flow data with distinct length, uneven sampling, and missing data finds challenging for effective exploitation. The traffic data has been considerably increased in recent times which cannot be handled by traditional mathematical models. The recent developments of statistic and deep learning (DL) models pave a way for the effectual design of traffic flow prediction (TFP) models. In this view, this study designs optimal attention-based deep learning with statistical analysis for TFP (OADLSA-TFP) model. The presented OADLSA-TFP model intends to effectually forecast the level of traffic in the environment. To attain this, the OADLSA-TFP model employs attention-based bidirectional long short-term memory (ABLSTM) model for predicting traffic flow. In order to enhance the performance of the ABLSTM model, the hyperparameter optimization process is performed using artificial fish swarm algorithm (AFSA). A wide-ranging experimental analysis is carried out on benchmark dataset and the obtained values reported the enhancements of the OADLSA-TFP model over the recent approaches mean square error (MSE), root mean square error (RMSE), and mean absolute percentage error (MAPE) of 120.342%, 10.970%, and 8.146% respectively.

Currently, timely and accurate traffic flow data is powerfully required for government agencies, business sectors and individual travelers, and business sectors [

With the accessibility of higher resolution traffic information from intelligent transportation systems (ITS), TFP was gradually tackled with data driven approach [

Even though there are previously numerous TFP models and schemes, many of them utilize shallow traffic systems and still are slightly unsatisfactory. This stimulates reconsideration the TFP issue depends on deep structure model with large quantity of traffic information [

Yang et al. [

Chen et al. [

This study designs optimal attention-based deep learning with statistical analysis for TFP (OADLSA-TFP) model. The presented OADLSA-TFP model intends to effectually forecast the level of traffic in the environment. To attain this, the OADLSA-TFP model employs attention-based bidirectional long short-term memory (ABLSTM) model for predicting traffic flow. In order to enhance the performance of the ABLSTM model, the hyperparameter optimization process is performed using artificial fish swarm algorithm (AFSA). A wide-ranging experimental analysis is carried out on benchmark dataset and the obtained values reported the enhancements of the OADLSA-TFP model over the recent approaches.

In this study, a novel OADLSA-TFP model has been developed to effectually forecast the level of traffic in the environment. The OADLSA-TFP model primarily employed the design of ABLSTM model for predicting traffic flow. In order to enhance the performance of the ABLSTM model, the hyperparameter optimization process is performed using AFSA and thereby boosts the predictive results.

At the initial stage, the OADLSA-TFP model primarily employed the design of ABLSTM model for predicting traffic flow. Consider

But because of the gradient exploding or vanishing problem [

In which

During this case, it can be integrated a bidirectional LSTM (BiLSTM) network with attention process. The BiLSTM network procedures input in two approaches: primary, it procedures data in the backward to forward directions, next it procedures the similar input in forward to backward. The BiLSTM technique varies in unidirectional LSTM as the network run the similar input twice, for instance, in forward to backward and backward to forward directions that preserve the further context data which is extremely useful from tourism demand predict for improving the network accuracy more. In the two input attention layers were utilized, one for feature and one for time step dimensional. The formula demonstrates the attention layer on input

Next, the hyperparameter optimization [

In which the original plant place was signified as

A novel parent distribution distance was offered as:

The off-spring plant places toward the original plant were evaluated as:

In which the selected probability was signified as

This section assesses the predictive performance of the OADLSA-TFP model under several aspects.

Methods | MSE | RMSE | MAPE (%) |
---|---|---|---|

RBF-P | 398.644 | 19.966 | 17.694 |

RBF-PCC | 310.280 | 17.615 | 17.522 |

RBF-PCA | 316.261 | 17.784 | 17.472 |

Hybrid RBF | 440.097 | 20.978 | 17.343 |

AITFP Model | 300.483 | 17.334 | 16.580 |

OADLSA-TFP | 285.120 | 16.885 | 14.259 |

With respect to MSE, the OADLSA-TFP model has provided lower MSE of 285.120 whereas the RBF-P, RBF-PCC, RBF-PCA, Hybrid RBF, and AITFP models have offered higher MSE of 398.644, 310.280, 316.261, 440.097, and 300.483 respectively. Moreover, with respect to MAPE, the OADLSA-TFP model has gained least MAPE of 14.259% whereas the RBF-P, RBF-PCC, RBF-PCA, Hybrid RBF, and AITFP models have offered higher MAPE of 17.694%, 17.522%, 17.472%, 17.343%, and 16.580% respectively.

Next, a comprehensive comparative study of the OADLSA-TFP model with recent models is made in

Methods | MSE | RMSE | MAPE (%) |
---|---|---|---|

LSTM model | 131.251 | 11.456 | 11.988 |

GRU model | 135.889 | 11.657 | 11.360 |

Cascaded LSTM | 137.157 | 11.711 | 11.313 |

Cascaded GRU | 165.866 | 12.879 | 10.799 |

Stacked encoder (SAE) | 137.908 | 11.743 | 10.758 |

F-ANN | 134.976 | 11.618 | 10.142 |

SAERBF | 153.582 | 12.393 | 10.021 |

AITFP-WC | 127.762 | 11.303 | 9.724 |

OADLSA-TFP | 120.342 | 10.970 | 8.146 |

MSE | ||||||
---|---|---|---|---|---|---|

Methods | 5_min | 10_min | 15_min | 20_min | 25_min | 30_min |

LSTM model | 131.251 | 137.450 | 143.065 | 151.874 | 160.306 | 166.802 |

GRU model | 135.889 | 142.470 | 150.675 | 159.396 | 166.602 | 174.984 |

Cascaded LSTM | 137.157 | 145.746 | 154.724 | 163.000 | 168.240 | 174.337 |

Cascaded GRU | 165.866 | 174.764 | 180.355 | 186.564 | 193.565 | 200.791 |

Stacked encoder | 137.908 | 145.644 | 152.696 | 158.800 | 164.474 | 171.405 |

F-ANN | 134.976 | 143.374 | 148.539 | 154.399 | 163.232 | 170.203 |

SAERBF | 153.582 | 161.160 | 167.924 | 176.718 | 184.119 | 190.654 |

AITFP-WC | 127.762 | 136.690 | 145.658 | 152.476 | 157.933 | 163.148 |

OADLSA-TFP | 120.342 | 126.654 | 131.751 | 137.446 | 143.296 | 151.175 |

Similarly, with 10_min, the OADLSA-TFP model has provided least MSE of 126.654. Likewise, with 15_min, the OADLSA-TFP model has gained decreased MSE of 131.751. Moreover, with 20_min, the OADLSA-TFP model has depicted minimum MSE of 137.446. Furthermore, with 30_min, the OADLSA-TFP model has accomplished least MSE of 151.175.

RMSE | ||||||
---|---|---|---|---|---|---|

Methods | 5_min | 10_min | 15_min | 20_min | 25_min | 30_min |

LSTM model | 11.46 | 11.72 | 11.96 | 12.32 | 12.66 | 12.92 |

GRU model | 11.66 | 11.94 | 12.27 | 12.63 | 12.91 | 13.23 |

Cascaded LSTM | 11.71 | 12.07 | 12.44 | 12.77 | 12.97 | 13.20 |

Cascaded GRU | 12.88 | 13.22 | 13.43 | 13.66 | 13.91 | 14.17 |

Stacked encoder | 11.74 | 12.07 | 12.36 | 12.60 | 12.82 | 13.09 |

F-ANN | 11.62 | 11.97 | 12.19 | 12.43 | 12.78 | 13.05 |

SAERBF | 12.39 | 12.69 | 12.96 | 13.29 | 13.57 | 13.81 |

AITFP-WC | 11.30 | 11.69 | 12.07 | 12.35 | 12.57 | 12.77 |

OADLSA-TFP | 10.97 | 11.25 | 11.48 | 11.72 | 11.97 | 12.30 |

For instance, with 5_min, the OADLSA-TFP model has presented reduced RMSE of 10.97. In the same way, with 10_min, the OADLSA-TFP model has provided least RMSE of 11.25. Equally, with 15_min, the OADLSA-TFP model has gained decreased RMSE of 11.48. Also, with 20_min, the OADLSA-TFP model has depicted minimum RMSE of 11.72. Additionally, with 30_min, the OADLSA-TFP model has accomplished least RMSE of 12.30.

MAPE (%) | ||||||
---|---|---|---|---|---|---|

Methods | 5_min | 10_min | 15_min | 20_min | 25_min | 30_min |

LSTM model | 11.988 | 14.340 | 17.462 | 19.580 | 21.852 | 25.169 |

GRU model | 11.360 | 13.498 | 15.975 | 18.424 | 21.074 | 23.176 |

Cascaded LSTM | 11.313 | 14.763 | 18.659 | 20.711 | 22.965 | 26.097 |

Cascaded GRU | 10.799 | 14.021 | 17.266 | 20.476 | 23.809 | 25.890 |

Stacked encoder | 10.758 | 13.563 | 17.495 | 21.170 | 23.506 | 26.961 |

F-ANN | 10.142 | 12.453 | 15.872 | 19.451 | 21.683 | 23.800 |

SAERBF | 10.021 | 13.540 | 16.770 | 18.873 | 21.985 | 24.986 |

AITFP-WC | 9.724 | 11.997 | 15.748 | 18.767 | 22.730 | 25.619 |

OADLSA-TFP | 8.146 | 11.195 | 14.359 | 17.563 | 19.710 | 23.150 |

By observing the above mentioned tables and figures, it is apparent that the OADLSA-TFP model has resulted in maximum TFP performance over the other methods.

In this study, a novel OADLSA-TFP model has been developed to effectually forecast the level of traffic in the environment. The OADLSA-TFP model primarily employed the design of ABLSTM model for predicting traffic flow. In order to enhance the performance of the ABLSTM model, the hyperparameter optimization process is performed using AFSA and thereby boosts the predictive results. A wide-ranging experimental analysis is carried out on benchmark dataset and the obtained values reported the enhancements of the OADLSA-TFP model over the recent approaches. Thus, the OADLSA-TFP model can be used for effective TFP in real time platform. In future, hybrid metaheuristic algorithms can be designed for improved hyperparameter tuning processes.

This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University (KAU), Jeddah, Saudi Arabia, under grant no. (G: 665-980-1441). The authors, therefore acknowledge with thanks DSR for technical and financial support.