Design of a bi-level PSO based modular neural network for multi-step time series prediction

Derived from an effective strategy - direct and multiple-input multiple-output strategy, a modular neural network based on a bi-level particle swarm optimization algorithm (BLPSO-MNN) is proposed in the present study to improve the accuracy for multi-step time series prediction. While a binary particle swarm optimization algorithm is designed for the external layer to optimize the task division of prediction horizons, a multi-objective particle swarm optimization algorithm is designed for the internal layer to trade off between the prediction accuracy and structural complexity for each subnetwork in modular neural network. Besides, a set of fuzzy If-Then rules is proposed to determine the historical information to be input to subnetworks. Thus, the structure of BLPSO-MNN, including the number of modules as well as the subnetwork structure, is self-determined accordingly. Numerous experiments are conducted for 18-step-ahead time series prediction to evaluate the performance of BLPSO-MNN. Experimental results show that, although the prediction accuracy decreases when the prediction horizon is large, the overall performance of BLPSO-MNN is superior over all comparative models with greater improvement for larger horizons, indicating it is suitable for a long-term prediction. Besides, the set of fuzzy rules balances the prediction accuracy against the structural complexity caused by the subnetwork inputs.