An integrated hydraulic–economic evaluation of pressure-based leak localization under multi-leak conditions using evolutionary optimization

Graphical abstract showing two-stage sensor configuration evaluation: economic screening followed by leak localization using DE, GA, and NSGA-II across multiple leak scenarios. Leakage remains a major challenge for water utilities. However, pressure-based leak localization studies are often limited to single-leak assumptions and economic assessments that are disconnected from actual detection performance. This paper presents an integrated hydraulic–economic framework that links pressure-based leak localization outcomes with life-cycle economic evaluation under realistic multi-leak conditions. The framework adopts a two-stage approach: (1) predefined sensor configurations are screened using a volume-based Net Present Value model driven by detection and false-negative rates, (2) the most economically competitive configurations are subjected to detailed hydraulic leak localization analysis. Leak localization is performed using Genetic Algorithm, Differential Evolution, and NSGA-II. These algorithms are evaluated across single-leak, clustered multi-leak, and multi-leak scenarios including dominant and minor leaks. A pre-selection strategy is used to identify candidate leak nodes using distance-weighted pressure residual formulation and a Jacobian sensitivity matrix to enhance spatial discrimination and computational efficiency. Results reveal a hydraulic observability limitation, where certain leaks remain undetectable regardless of sensor configuration or algorithm. While higher sensor density maximizes total economic benefit, marginal returns diminish significantly. NSGA-II proves to be more robust against false negatives, while moderate densities are near-optimal for economic benefits. The findings support decision-oriented sensor deployment in water distribution networks.