Multiphase DMA Design Methodology Based on Graph Theory and Many-Objective Optimization

Partitioning a water distribution system (WDS) into district metered areas (DMAs) is a difficult task due to the complex WDS structure and simultaneous consideration of multiple constraints. Further, alternative metrics can define DMA goals, and expressing and quantifying those objectives in an efficient algorithm is also challenging. To address the multifaceted set of objectives, a multiphase DMA design method is developed. DMA feed pipes are identified as the primary flow paths in a branched network. In the methodology presented here, the feed pipe network is first laid out by determining node clusters and boundary pipes that maximize the dissimilarity of pressures and modularities between clusters and minimize the number of cuts between clusters while defining the number of DMAs closest to the desired number. In the methodology's second phase, secondary DMA feed pipes are identified by minimizing the number of secondary feed pipes and maximizing the nodal excess energy while maintaining desired pressure. Finally, a postoptimization analysis compares the performance of the Pareto solutions based on their availability, water quality, and daily leakage. System availability is calculated based on the minimum cut-set method combined with a new pressure-driven analysis method. To accelerate the optimization algorithm, two strategies are applied: step-by-step optimization and reducing the decision variable searching space by considering desirable DMA characteristics. The effectiveness of the methods is examined by applying it to the C-Town and real B-Town water distribution networks. Results demonstrate that the search space reduction method effectively decomposes the full network into DMAs in the face of multiple hydraulic and water quality metrics.