Spectral Clustering and Genetic Algorithm for Design of District Metered Areas in Water Distribution Systems

District metered areas (DMAs) is an innovative layout and control technology to improve efficiency for water distribution systems (WDSs), there are many factors to be considered in DMAs design to reduce the adverse impact due to closure of valves. A new methodology for DMAs design is proposed based on complex network spectral clustering algorithm and graph theory. Water distribution network is regarded as undirected graph, which is mapped by weighted topology matrix. And normalized Laplacian matrix can be deduced to calculate the nontrivial eigenvectors. The k-means and genetic algorithm are used to determine clusters to minimize the sum of squared distance error between nodes in clusters and their centroids in Euclidean space. Eigenvector centrality is adopted for importance analysis of nodes in order to ascertain the location of meter of each DMA, which should be in the shortest path among the source and the central node in each DMA, and the other pipes between different DMAs will be installed with valves, at last the design of DMAs is achieved. And a real water distribution system is tested to ascertain the feasibility of the proposed method.