Evaluation of Water Distribution Network Partitioning Methods Based on Graph Theory Using AHP

The dramatic decline in renewable water resources, leakage and pollution in water distribution systems has led to a significant increase in the focus on leakage management and control approaches in most parts of the world. For this purpose, water distribution networks can be subdivided into manageable subdivisions with connecting pipes of these subdivisions equipped with flow meters to control leakage and better manage the water distribution network. In the present study, based on graph theory, the concept of District Meter Area (DMA) is expressed. In order to rank the optimal design of the water distribution network, AHP has been used to minimize the balance in the subdivisions, the number of boundary pipes, the number of pipes equipped with flow meters and for maximization of both flexibility and minimum pressure indices. In this paper, by evaluating different algorithms for creating DMAs of water distribution networks, the best method is suggested. Indexes were ranked by studying the experts' opinion and forming the matrix of paired comparisons, so the first rank for maximizing the resilience index IR was 0.401 and the last one was for minimizing the number of flow meters with a score of 0.063. Based on the weight and criteria ranking, the water distribution network algorithms were scored. In terms of weighted graph, the highest score belonged to EBC algorithm and the lowest score to FGC algorithm. In terms of the unweighted graph spectral clustering algorithms rank first and FGC and MA algorithms rank last. In the unweighted graph, some algorithms have equal scores, so more indices are needed to compare them. Due to the simplification of the problem and the pairwise comparison of the criteria with each other, according to the experts, this method offers an optimal and desirable result for selecting the appropriate method for converting the water distribution network into DMAs. In this paper, the EBC algorithm with a score of 0.182 for the weighted graph, the spectral clustering algorithms with a score of 0.145 for the weighted graph were ranked first