Ensemble of Differential Equations using Pareto Optimal for Traffic Forecasting

The formal and empirical proof is that the ensemble of the learning models performs better than the single one. In order to construct the ensemble of the system of ordinary differential equations (ODEs), the two problems (diversity and accuracy of ODEs) are considered. In the paper, we estimate experimentally the model ensemble using multi-objective optimization. This paper presents a pareto optimal approach for identifying a family of the additive tree models which are used to reconstruct and identify the system of ordinary differential equations to predict the small-time scale traffic measurements data. We employ the tree-structure based evolution algorithm and particle swarm optimization (PSO) to evolve the architecture and the parameters of the additive tree model. The small-scale traffic measurements data is used to test ODE ensemble, and experimental results reveal that the proposed method is feasible and efficient for forecasting the time series.