Beyond Evolutionary Algorithms: A Scalable River-Network Approach to Water Distribution Network Design

The optimal design of Water Distribution Networks (WDNs) is an NP-hard problem governed by nonlinear hydraulics and exponentially increasing discrete design choices. Conventional optimisation methods frequently struggle with computational burden, scalability limits, and premature convergence. Recent graph theory (GT) and complex network analysis (CNA) approaches offer rapid diameter assignment but rely on surrogate friction weights and lack topographic and hydraulic integration. To address these limitations, we introduce a scalable probabilistic growth algorithm inspired by the energy-minimising evolution of natural river networks. The method evaluates candidate connections using a composite metric of flow, distance, and elevation, while incorporating full hydraulic feedback by running EPANET at every iteration. The algorithm was tested on benchmark networks of increasing size, including the GoYung network, a large network with 3,558 nodes, and the 150,630-pipe VertRome network, which is beyond the computational reach of traditional evolutionary algorithms. The proposed approach achieved optimal solutions for GoYung and high-quality designs for the larger networks with significantly reduced computation times. Overall, this probabilistic framework provides an efficient, hydraulically informed, and highly scalable methodology for large-scale WDN optimisation.