Approaches for Optimizing the Performance of Adaptive Neuro-Fuzzy Inference System and Least-Squares Support Vector Machine in Precipitation Modeling

This study employs two heuristic algorithms, including the genetic algorithm (GA) and ant colony optimization for continuous domains (${\mathrm{ACO}}_{\mathrm{R}}$), for optimizing the parameters of two soft computing models, namely adaptive neuro-fuzzy inference system (ANFIS) and least-squares support vector machine (LSSVM), which were used for modeling monthly precipitation for all 12 months of the year. Data from 40 meteorological stations situated in different parts of Iran were used. The effectiveness of input data was determined by internal correlation-coefficient and nonlinear sensitivity analysis. Selected input data were further evaluated by another sensitivity analysis method, cosine amplitude (CA). Considering different evaluation months, LSSVM was more accurate and reliable than ANFIS. It was also found that both algorithms improved the performance of models for most months of the year. ${\mathrm{ACO}}_{\mathrm{R}}$ was better and more reliable than was GA in optimizing the models. ${\mathrm{ACO}}_{\mathrm{R}}$ produced the best results in autumn that led to the improvement of performance of ANFIS in terms of correlation coefficient ($R$) and root-mean square error (RMSE) by 35% and 0.40 mm for October; 42% and 0.99 mm for November; and 31% and 0.74 mm for December. The performance of LSSVM was enhanced by 6% and 0.28 mm for October; 22% and 0.20 mm for November; and 4% and 0.10 mm for December, respectively. For July and August, the suggested algorithms could not improve the performance of ANFIS. The algorithms did optimize LSSVM in all months, so the RMSE and mean absolute error were improved by 0.15 and 0.28 mm for July and 0.28 and 0.56 mm for August, respectively.