Decomposition and Holt-Winters Enhanced by the Whale Optimization Algorithm for Forecasting the Amount of Water Inflow into the Large Dam Reservoirs in Southern Thailand

Abstract

This study introduces hybrid forecasting models integrating the Whale Optimization Algorithm (WOA) with Holt-Winters (HW) and decomposition methods, applied in both additive and multiplicative models, for time series forecasting. Focusing on monthly water inflow into four dam reservoirs in Southern Thailand, the study compares these hybrid models against classical statistical models, Grid Search for Holt-Winters (Grid-HW) and Classical Decomposition (Classic-D). The analysis comprises two phases: the training dataset phase and the testing dataset phase. In the training phase, WOA demonstrates superior parameter optimization, enhancing both HW and decomposition methods, resulting in lower Mean Absolute Error (MAE) values compared to classical models. In the testing phase, performance metrics such as Root Mean Square Error (RMSE), MAE, and Symmetric Mean Absolute Percentage Error (sMAPE) are employed. The findings reveal that the Whale Optimization Algorithm with Holt-Winters (WOA-HW) and Decomposition (WOA-D) models surpass classical approaches in long-term forecasting accuracy for three dam reservoirs. Over 24 data points, the WOA with Multiplicative Holt-Winters (WOA-HWx) is optimal for Pran Buri dam, the WOA with Additive Decomposition (WOA-D+) for Bang Lang dam, and the WOA with Multiplicative Decomposition (WOA-Dx) for Kaeng Krachan dam. The Box-Jenkins approach, further refined through a Box-Cox transformation employing a natural logarithm, emerged as the superior forecasting model for Rajjaprabha dam. This model satisfied all critical statistical criteria, including normality of residuals (Anderson-Darling: 0.359, p-value: 0.433), homoscedasticity (Levene's test: 1.24, p-value: 0.274), independence (Ljung-Box test: 14.10, p-value: 0.169), and zero mean (t-test: -0.39, p-value: 0.702), establishing its robustness and reliability for forecast analysis.