On the use of entropy for designing safe water distribution systems in the case of multiple sources

<p dir="ltr">Resilient water distribution systems are key elements of modern city infrastructure. However, defining resilience and finding a single measure that reflects this property objectively and can be used as an objective function for optimisation is challenging. In this study, we apply the entropy definition of Tanyimboh and Templeman in the case of water distribution systems of arbitrary size and complexity and adopt it for water quality computations, notably, for chlorine concentration. We use EPANET for hydraulic and water quality computations and MATLAB’s standard genetic algorithm for optimisation. Unlike in the original paper, where flow rates were the decision variables, we optimise flows indirectly by using pipe diameters as decision variables. As an initial case study for illustration, we optimise a simple, two-pipe, two-reservoir system, then move to Alperovits’s two-loop network. We provide optimal diameter layouts for (1) minimum cost, (b) maximum resilience (entropy), (c) maximum chlorine distribution and (d) maximum chlorine safety (entropy). As a third example, we run the same computations on the Anytown network. We highlight the key topological differences of networks optimised for investment cost and resilience.</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><p dir="ltr"><br></p>