Combined recursive clustering and partitioning to define optimal DMAs of water distribution networks

As known, the water network partitioning in district meter areas (DMAs) is one of the most effective way to improve water loss detection, pressure management and user protection from accidental and intentional contamination. Nevertheless, the definition of permanent DMAs is very complex because can drastically change the hydraulic performance of a network, since the insertion of gate valves in several pipes can reduce its energy and topological redundancy. In the last years, some optimization procedures, based on graph theory, network analysis and heuristic optimization methods, allowed to overcame the empirical approaches traditionally adopted to define the permanent district meter areas (DMAs) of a water distribution system. These approaches are essentially arranged in two phases: the clustering, in which the optimal shape and dimension of each DMA is found minimizing the number of boundary pipes and balancing the number of nodes between each districts, and the partitioning, in which the optimal positioning of flow meters and gate valves is found minimizing the energy decreasing of the network due to the closure of some pipes with valves. However, these procedures apply the clustering and partitioning phases only on the original network layout not considering that, for each pipe closure, the network topology changes and it is possible to face the optimization problem recursively adding an optimal closure at time. This paper proposes a novel combined recursive optimization for clustering and partitioning phases that, for each step, before found the optimal positioning of a single gate valve and then, on the changed network topology obtained closing the pipe, found the next positioning of gate valves. The case study confirms, using some energy and topological performance indices that the recursive procedure, even on a small Italian network, is able to find a better water network partitioning than previous solutions.