Monthly Runoff Forecasting Using Particle Swarm Optimization Coupled with Flower Pollination Algorithm-Based Deep Belief Networks: A Case Study in the Yalong River Basin

Accuracy in monthly runoff forecasting is of great significance in the full utilization of flood and drought control and of water resources. Data-driven models have been proposed to improve monthly runoff forecasting in recent years. To effectively promote the prediction effect of monthly runoff, a novel hybrid data-driven model using particle swarm optimization coupled with flower pollination algorithm-based deep belief networks (PSO-FPA-DBNs) was proposed, which selected the optimal network depth via PSO and searched for the optimum hyper parameters (the number of neurons in the hidden layer and the learning rate of the RBMs) in the DBN using FPA. The methodology was divided into three steps: (i) the Comprehensive Basin Response (COM) was constructed and calculated to characterize the hydrological state of the basin, (ii) the information entropy algorithm was adopted to select the key factors, and (iii) the novel model was proposed for monthly runoff forecasting. We systematically compared the PSO-FPA-DBN model with the traditional prediction models (i.e., the backpropagation neural network (BPNN), support vector machines (SVM), deep belief networks (DBN)), and other improved models (DBN-PLSR, PSO-GA-DBN, and PSO-ACO-DBN) for monthly runoff forecasting by using an original dataset. Experimental results demonstrated that our PSO-FPA-DBN model outperformed the peer models, with a mean absolute percentage error (MAPE) of 18.23%, root mean squared error (RMSE) of 230.45 m3/s, coefficient of determination (DC) of 0.9389, and qualified rate (QR) of 64.2% for the data from the Yalong River Basin. Also, the stability of our PSO-FPA-DBN model was evaluated. The proposed model might adapt effectively to the nonlinear characteristics of monthly runoff forecasting; therefore, it could obtain accurate and reliable runoff forecasting results.