Multi-objective optimization of LSTM models for forecasting urban water consumption using demographic and meteorological drivers

Abstract

This study introduces a forecasting framework based on Long Short-Term Memory (LSTM) neural networks, whose performance is enhanced through optimization by both multi-objective and single-objective metaheuristic algorithms. These include the Non-dominated Sorting Genetic Algorithm II (NSGA-II), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Grey Wolf Optimizer (GWO). The NSGA-II algorithm was specifically employed to jointly minimize forecasting error and model complexity, thereby addressing the trade-off between prediction accuracy and model simplicity. Validation using long-term monthly water consumption data revealed that the NSGA-II-optimized model achieved the lowest Root Mean Square Error (RMSE), highest Nash–Sutcliffe Efficiency (NSE), and the smallest residual variance, surpassing the results of the other optimization techniques. Seasonal performance analysis further demonstrated the robustness of the NSGA-II model, particularly during peak summer demand periods, where single-objective optimization methods exhibited instability. Benchmarking against contemporary hybrid and probabilistic forecasting models highlighted the methodological innovation of the proposed framework. The study concludes that this multi-objective LSTM model significantly enhances the reliability of peak-load predictions, offering valuable support for urban infrastructure planning, reservoir operations, and optimized water distribution.