Human-inspired hyperparameter optimization for long-horizon forecasting of freshwater and desalination per-capita dynamics

Growing imbalance between freshwater availability and demand, driven by population growth, infrastructure constraints, and climate variability, has increased the need for reliable long-horizon forecasting of freshwater withdrawal and desalination dynamics on a per-capita basis. Although transformer-based models can capture complex temporal dependencies, their performance is highly sensitive to hyperparameter configuration, especially for multivariate and nonstationary environmental data. This study proposes a data-driven framework that integrates the Frequency Enhanced Decomposed Transformer (FEDformer) with the Improved Horse Herd Optimization algorithm (iHOW) for systematic hyperparameter optimization. The framework constructs policy-relevant per-capita indicators from country-level time-series data and evaluates the optimized model through controlled comparison with multiple metaheuristic optimizers under identical computational budgets. The iHOW-optimized FEDformer achieves the best overall performance, with a mean squared error of \(2.10\times 10^{-5}\) , root mean squared error of \(4.58\times 10^{-3}\) , Pearson correlation coefficient of 0.986, and Nash–Sutcliffe efficiency of 0.985. Convergence analysis further shows that iHOW reaches lower best-fitness values more rapidly and more stably than the competing optimizers. Repeated-run uncertainty summaries, omnibus statistical comparison, a lightweight hyperparameter-optimization budget sensitivity study, and a quantitative feature-importance analysis further strengthen the empirical characterization of model performance and stability under the evaluated design. Additional robustness experiments indicate that the framework preserves useful predictive structure across longer forecasting horizons, input-perturbation scenarios, temporal aggregation levels, and alternative missing-data treatments. Architecture ablation further shows that the gains depend materially on FEDformer’s frequency-aware, decomposition-based, and multivariate design. Overall, the proposed framework provides a robust, transparent, and computationally reasonable tool for long-term water-resource assessment and policy-oriented analysis of freshwater stress and desalination reliance under the evaluated data, assumptions, and computational budget.