Extensive traffic flow data are received from the loop detector networks every second, which requires us to develop an effective and efficient algorithm to predict future traffic flow. However, dynamic traffic conditions on a road are not just influenced by sequential patterns in the temporal dimension, but also by other roadways in the spatial dimension. Although many successful models have been developed in previous studies to forecast future traffic flows, most of them have shortcomings in modeling spatial and temporal dependencies. In this article, we focus on spatial-temporal factors and propose a new adaptive spatial-temporal transformer graph network (ASTTGN) to improve the accuracy of traffic forecasting by jointly modeling the spatial-temporal information of road networks. Specifically, we propose an adaptive spatial-temporal transformer module, which contains two developed adaptive transformer modules for capturing dynamic spatial dependence and temporal dependence across multiple time steps, respectively. Finally, feature fusion is performed through a gated feature aggregation layer to simulate the effect of complex spatial-temporal factors on traffic conditions. In particular, the multihead attention mechanism employed by the transformer can effectively explore the potential spatial-temporal dependence patterns in different subspaces. Experimental results on two real-world traffic data sets demonstrate the superiority of the proposed model compared to existing techniques.

Accurate and timely short-term traffic flow forecasting is an essential component for intelligent traffic management systems. However, developing an effective and robust forecasting model is challenging due to the inherent randomness and nonlinear characteristic of the traffic flow. In this paper, a gravitational search algorithm optimized extreme learning machine, termed GSA-ELM, is proposed to unlock the potential performance for short-term traffic flow forecasting. The extreme learning machine avoids the tedious backpropagation by analytically determining the optimal solution. The gravitational search algorithm globally searches the optimal parameters for the extreme learning machine. The forecasting performance of the GSA-ELM is evaluated on four benchmark datasets by comparing several state-of-the-art models. The four benchmark datasets are real-world traffic flow data from highways A1, A2, A4, A8 near the ring road of Amsterdam. The MAPEs of the GSA-ELM model are $11.69\%$, $10.25\%$, $11.72\%$ and $12.05\%$ on four benchmark datasets, respectively, whereas the RMSEs of the GSA-ELM model are 287.89, 203.04, 221.39 and $163.24$, respectively. The experimental results demonstrate the superior performance of the proposed model.

Credible and accurate traffic flow forecasting is critical for deploying intelligent traffic management systems. Nevertheless, it remains challenging to develop a robust and efficient forecasting model due to the nonlinear characteristics and inherent stochastic traffic flow. Aiming at the nonlinear relationship in the traffic flow for different scenarios, we proposed a two-stage hybrid extreme learning model for short-term traffic flow forecasting. In the first stage, the particle swarm optimization algorithm is employed for determining the initial population distribution of the gravitational search algorithm to improve the efficiency of the global optimal value search. In the second stage, the results of the previous stage, rather than the network structure parameters randomly generated by the extreme learning machine, are used to train the hybrid forecasting model in a data-driven fashion. We evaluated the trained model on four real-world benchmark datasets from highways A1, A2, A4, and A8 connecting the Amsterdam ring road. The RMSEs of the proposed model are 288.03, 204.09, 220.52, and 163.92, respectively, and the MAPEs of the proposed model are $11.53\%$, $10.16\%$, $11.67\%$, and $12.02\%$, respectively. Experimental results demonstrate the superior performance of our proposed model.

The traffic flow forecasting proposed for a series of problems, such as urban road congestion and unreasonable road planning, aims to build a new smart city, improve urban infrastructure, and alleviate road congestion. The problems encountered in traffic flow forecasting are also relatively difficult; the reason is that traffic flow forecasting is uncertain, dynamic, and nonlinear. It is challenging to build a reliable and safe model. Aiming at this complex and nonlinear traffic flow forecasting problem, this paper proposes a solution of an ABC-ELM model optimized by an artificial bee colony algorithm to solve the above problem. It uses the characteristics of the artificial bee colony algorithm to optimize the model so that the model can better and faster find the optimal solution in space. Moreover, it also uses the characteristics of the limit learning machine to quickly deal with this nonlinear specific problem. Experimental results on the Amsterdam road traffic flow dataset show that the traffic flow prediction model proposed in this paper has higher prediction accuracy and is more sensitive to data changes.