Multi-Objective Optimization of Monitoring Point Placement in Water Supply Networks Based on Pressure-Driven Analysis and the Virtual Node Method

To improve the safe operation of urban water supply networks and support sustainable water resource management, this study proposes a multi-objective optimization framework for monitoring point placement by integrating pressure-driven analysis (PDA) and the virtual node method (VNM). A PDA-based hydraulic model combined with Wagner’s relationship is employed to overcome the limitations of traditional demand-driven analysis in simulating extreme conditions such as pipe burst events, while the VNM enables efficient representation of burst scenarios without altering network topology. Based on node pressure variations, a binary fault perception matrix is constructed by comparing pressure responses under burst conditions with background noise thresholds to quantify the detectability of pipe burst events by candidate monitoring points. A bi-objective optimization model is then formulated to maximize fault monitoring and minimize the number of monitoring points, and it is solved using the NSGA-III and NSGA-II algorithms. Case studies on the Net3 benchmark network and the real-world Drumchapel network demonstrate that NSGA-III outperforms NSGA-II in terms of convergence performance and spatial perception capability, particularly by reducing spatial redundancy and improving monitoring efficiency under limited monitoring budgets. The proposed framework provides a practical decision-support tool for optimal monitoring point deployment and contributes to the long-term sustainability of urban water supply infrastructure.