An Integrative Evolutionary–Exact Framework for Bi-Objective Design-for-Control Optimisation of Water Distribution Networks

<p dir="ltr">Managing water distribution networks (WDNs) requires balancing infrastructure costs against operational performance. This study presents an integrative (hybrid) optimisation approach that combines evolutionary algorithms with deterministic solvers to design advanced pressure control systems. The method addresses valve placement and control settings simultaneously, minimising both water leakage and installation costs. Unlike traditional approaches using valve counts as cost proxies, we model installation expenses based on pipe diameters and site conditions. Our hybrid strategy employs NSGA-II for discrete valve placement decisions while IPOPT optimises continuous control settings. By testing the method on two benchmark networks (pescara, Net25) and an operational UK system (BWFL), we demonstrate superior convergence speed and solution quality compared to conventional methods. The approach identifies cost-effective designs achieving 64-87% of maximum pressure reduction at 30-51% of full implementation cost. Results reveal that looped networks enable efficient pressure management through flow redistribution, requiring fewer valves than branched systems. The method consistently produces well-defined Pareto fronts with clear trade-off points, facilitating practical decision-making. This work advances water infrastructure optimisation by providing scalable tools for the design of advanced multi-feed pressure management schemes.</p><p dir="ltr">This paper was presented at the 21st Computing and Control in the Water Industry Conference (CCWI 2025) at the University of Sheffield (1st - 3rd September 2025).</p>