Optimal design of district metered areas based on graph theory and multi-objective optimization

Partitioning a water distribution system (WDS) into district metered areas (DMAs) is a challenging task due to the complexity of WDSs structures and simultaneously consideration of technical constraints/objectives. Further, multiple metrics can be applied to define DMA goals and expressing and quantifying those objectives in an efficient algorithm is also be challenging. Given this multi-faceted set of objectives, this paper presents a novel multi-step DMA design method that simultaneously determines optimal DMA boundaries and flow meter and closed (isolation) valve positions. The algorithm begins by applying a pipe importance index to generate the branched transmission network considering the sensitivity matrix of pipe flow to node demands combined with a minimum spanning tree algorithm. The main flow meters locations in this branched network and other flow meters and isolation valves that define the DMA boundaries are determined in a multi-objective optimization to minimize the number of flow meters and pressure nonuniformity while maximizing the network modularity. The effectiveness of the overall scheme is demonstrated through two water distribution systems. The results indicate that the method can identify DMAs effectively.