Bridging prediction and optimization: A unified MINLP, traditional machine learning and deep learning framework for water distribution networks management

This study proposes a two-phase framework for the smart management of Water Distribution Networks (WDNs). In the first phase, daily water demand in Najaf Abad, Isfahan, Iran, is predicted using Multi-Layer Perceptron (MLP), Support Vector Regression (SVR), Random Forest (RF), Gated Recurrent Unit (GRU), and Long Short-Term Memory (LSTM) models. Unlike previous studies focusing mainly on climatic factors, this research improves accuracy by integrating social and cultural features derived from the Persian calendar, including a day index and holiday continuity, to reflect demand patterns during official and religious holidays as the first novelty. The second phase optimizes pump operation through a Mixed-Integer Non-Linear Programming (MINLP) model to minimize energy, repair, and maintenance costs. The optimization incorporates predicted demand, seasonal energy tariffs, water elevation, and pump switching intervals. This framework can provide global or operator-preferred local solutions as the second novelty and can be implemented in real time using existing telemetry systems without extra costs. Finally, the obtained results highlight LSTM achieved the greatest improvement in MSE (72.1%), while RF performed best in R 2 (16%) and PCC (7.6%). Application during hot and cold periods reduced pumping energy costs by up to 9.7% (from $46.3 to $41.8) and 15.8% (from $36.6 to $30.8), and reduced pump switches by 64.9% (from 74 times to 26 times) and 75.7% (from 90 times to 22 times), respectively. Using TOPSIS, optimal pumping intervals of 12, 8, and 6 h were identified. The framework offers an efficient and practical solution for improving WDN performance.