Meta-evolved multi-task transformers for integrated water utility forecasting: a comparative study of population-based hyperparameter optimization

Abstract Background Effective management of urban water utilities necessitates highly accurate forecasting models capable of disentangling complex temporal dependencies across interrelated managerial objectives. While Transformer-based architectures excel in sequential modeling, their real-world efficacy is critically constrained by an inherent sensitivity to architectural hyperparameters and a predominant reliance on single-task paradigms. Objective To address these bottlenecks, this study introduces a novel Meta-Evolved Multi-Task Transformer (MET) framework designed to jointly predict interconnected utility indicators, including aggregate water consumption, financial liabilities, and tariff revenues, by circumventing the suboptimal nature of manual hyperparameter tuning. Methods The Transformer’s hyperparameter space is systematically explored and optimized utilizing four prominent population-based metaheuristics: Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Bees Algorithm (BA), and Differential Evolution (DE). The framework is empirically validated through a rigorous multi-stage experimental protocol using a real-world, localized dataset from Ardabil Province, Iran. Initially, a robust single-task baseline is established by benchmarking ten classical machine learning and deep learning models via $$K$$ -fold cross-validation. Subsequently, the metaheuristic-driven multi-task configurations are fine-tuned and evaluated against standard predictive metrics. Results Empirical evaluations reveal a compelling operational trade-off: while the Random Forest (RF) algorithm achieves superior predictive accuracy in single-task consumption forecasting, the DE-optimized Multi-Task Transformer consistently dominates in the joint-learning environment. The DE-MET architecture achieved an optimal multi-objective balance, yielding $$R^{2} = 0.41$$ for consumption forecasting and $$R^{2} = 0.39$$ for tariff revenue prediction. Conclusion These findings underscore the critical role of evolutionary hyperparameter optimization in mitigating structural vulnerabilities within Transformers. The proposed framework delivers a scalable, robust, and AI-driven decision-support mechanism for integrated real-world water resource management. Graphical Abstract