| Summary: | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>11.53</mn><mo>%</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>10.16</mn><mo>%</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>11.67</mn><mo>%</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>12.02</mn><mo>%</mo></mrow></semantics></math></inline-formula>, respectively. Experimental results demonstrate the superior performance of our proposed model.
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