Macro-grammatical evolution for nonlinear time series modeling—a case study of reservoir inflow forecasting

Abstract

Streamflow forecasting is significantly important for planning and operating water resource systems. However, streamflow formation is a highly nonlinear, time varying, spatially distributed process and difficult to forecast. This paper proposes a nonlinear model which incorporates improved real-coded grammatical evolution (GE) with a genetic algorithm (GA) to predict the ten-day inflow of the De-Chi Reservoir in central Taiwan. The GE is a recently developed evolutionary-programming algorithm used to express complex relationships among long-term nonlinear time series. The algorithm discovers significant input variables and combines them to form mathematical equations automatically. Utilizing GA with GE optimizes an appropriate type of function and its associated coefficients. To enhance searching efficiency and genetic diversity during GA optimization, the macro-evolutionary algorithm (MA) is processed as a selection operator. The results using an example of theoretical nonlinear time series problems indicate that the proposed GEMA yields an efficient optimal solution. GEMA has the advantages of its ability to learn relationships hidden in data and express them automatically in a mathematical manner. When applied to a real world case study, the fittest equation generated through GEMA used only a single input variable in a reasonable nonlinear form. The predicting accuracies of GEMA were better than those of the traditional linear regression (LR) model and as good as those of the back-propagation neural network (BPNN). In addition, the predicting of ten-day reservoir inflows reveals the effectives of GEMA, and standardization is beneficial to model for seasonal time series.