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Sectorization of a water distribution network (WDN) into district meter areas (DMAs) is considered a key strategy for an efficient management of WDNs. Typically, it involves a two-stage procedure: a clustering stage, in which the division of the WDN into clusters is performed, and a dividing stage, which involves the placement of valves and flow meters on the cluster's boundary pipes to define the DMAs. While recently published methods attempt to enhance both the clustering and dividing stages, they fail to provide decision-making flexibility. They also neglect to consider the presence of existing valves in the WDN, which can significantly affect the evaluated implementation cost, often considered the primary decision-driving factor. This paper presents improvements to the previously introduced DeNSE method for sectorization of WDNs, aiming to address these deficiencies. The methodology consists of a clustering stage, based on the network uniformity index, and a dividing stage, in which the originally used heuristic procedure is replaced with Genetic Algorithm (GA) optimization, minimizing implementation cost. Consideration of existing valves in WDN and criteria for water supply security are also included in the dividing stage to offer a better estimate of implementation costs and post-sectorized operational efficiency of the WDN. Finally, GIS visualization is implemented, and a hydraulic model of the sectorized WDN (EPANET file) is generated, providing practitioners with valuable insights and decision-making flexibility. The methodology is tested on a part of the Amsterdam WDN in the Netherlands, serving as a pilot for methodology evaluation. A range of feasible sectorization solutions is generated and compared based on implementation cost and three performance indicators (PIs). The paper provides an in-depth discussion on the selection of preferable sectorization solution. The reported results demonstrate the method's efficiency in optimizing sectorization solutions with minimum implementation cost whilst preserving the WDN operational efficiency and meeting the local design criteria. [ABSTRACT FROM AUTHOR]

Sectorization is concerned with dividing a large territory into smaller areas, also known as sectors. This process usually simplifies a complex problem, leading to easier solution approaches to solving the resulting subproblems. Sectors are built with several criteria in mind, such as equilibrium, compactness, contiguity, and desirability, which vary with the applications. Sectorization appears in different contexts: sales territory design, political districting, healthcare logistics, and vehicle routing problems (agrifood distribution, winter road maintenance, parcel delivery). Environmental problems can also be tackled with a sectorization approach; for example, in municipal waste collection, water distribution networks, and even in finding more sustainable transportation routes. This work focuses on sectorization concerning the location of the area's centers and allocating basic units to each sector. Integer programming models address the location-allocation problems, and various formulations implementing different criteria are compared. Methods to deal with multiobjective optimization problems, such as the ϵ -constraint, the lexicographic, and the weighted sum methods, are applied and compared. Computational results obtained for a set of benchmarking instances of sectorization problems are also presented. [ABSTRACT FROM AUTHOR]

The aim of the current paper is to revisit the performance of spectral clustering algorithms for water distribution networks. In the literature, there have been attempts to introduce improved algorithms based on graph theory. We focus on a class of these algorithms that applies the concepts of the spectral clustering approach. We assess the performance of spectral clustering algorithms on a wider range of water network types (i.e. large, medium, and small sized networks) using a wider range of clustering methods (both partitioning and hierarchical) and performance indicators. Our findings suggest that partitioning methods, such as k-means are not consistently efficient in all types of networks. Nonetheless, the Partitioning Around Medoids (PAM) algorithm shows a relatively good performance according to modularity, while the internal indices of k-means and hierarchical clustering algorithms are more efficient. Stability indices show that PAM and CLARA algorithms are more efficient. [ABSTRACT FROM AUTHOR]

Water distribution network (WDN) leakage management has received increased attention in recent years. One of the most successful leakage-control strategies is to divide the network into District Metered Areas (DMAs). As a multi-staged technique, the generation of DMAs is a difficult task in design and implementation (i.e., clustering, sectorization, and performance evaluation). Previous studies on DMAs implementation did not consider the potential use of existing valves in achieving the objective. In this work, a methodology is proposed for detecting clusters and reducing the cost of additional valves and DMA sectorization by considering existing valves as much as possible. The procedure of DMAs identification has been divided into three stages, i.e., a) clusters identification; b) sectorization or boundaries optimization and c) performance evaluation of the partitioned network. The proposed methodology is evaluated on a simple network and a real-world water network with the findings provided and compared to the DMAs, established for a raw water network with no existing valves. It is found that there is an adequate difference in cost of strategy implementation in both the cases for the network under consideration and the existing valve system achieved better network performance in terms of resilience index. [ABSTRACT FROM AUTHOR]

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Most water supply utilities in the world need to deal with daily operations of their systems while at the same time they are required to increase their efficiency. One way to increase the efficiency of the system is to divide the water distribution network into smaller subsystems called sectors. This article presents a new sectorization approach, which has been developed as part of the European FP7 research project ICeWater, focused on increasing energy efficiency. The approach is based on the combination of graph theory and multi-objective optimization applied to the system of Milan (Italy). Most existing approaches for sectorization deal with gravity sources. The methodology presented here has been applied to a system with 26 pump stations, which is an innovation and a step forward for other utilities facing similar challenges. The application of sectorization to the network of Milan has the advantage of allowing to fix the number of sectors and enabling the exploration of multiple scenarios of system operation. [ABSTRACT FROM AUTHOR]

Abstract: The introduction of cyanide with a backflow attack into a water system was studied. The recent development of techniques for water network sectorization, aimed to improve the management of water systems, represents also an efficient way to protect networks from intentional contamination. The possibility of closing gate valves by a remote control system to create an i-DMA (isolated District Meter Area) can reduce the risk of contamination and thus the extent of damage of a terroristic attack. The study proposes a novel technique for designing i-DMAs compatible with hydraulic performance and optimized for water network protection. [Copyright &y& Elsevier]

Regionalization is of great practical importance, being applied in fields ranging from air space to water distribution. Canada has one of the highest waste generation rates in the world, disposing an average of 694.4 kg/cap in 2018. Waste management costed Canadians about CAD $3.3 billion in 2016, with collection and transportation making up 41.3% of this expenditure. Regionalized waste management systems are becoming popular in Canada and around the world; and design and optimization of regions is vital. Different spatial statistics are used to optimize 3 sub-regions in Saskatchewan (Regina, Leinan, and Beatty). Centroidal Voronoi Tessellation is generally the most efficient method. When the ratio of populated places to road length is low (0.010), 'median center' better optimized populated places in each sub-region. Computational demand was highest in Beatty (19.0 iterations), followed by Regina (9.67 iterations) and Leinan (5.33 iterations) indicating a trade-off between the number of sub-regions, computational efficiency, and optimized percent standard deviation. A strong linear relationship is observed in some cases between percent SD of optimized parameters and standard deviation of area, indicating the importance of relative size in optimization. In Regina, Median center (rank = 2) was ranked higher than mean center (rank = 3), while the opposite was true in Beatty. Feature distribution within regions and different spatial statistics in the algorithm should be explored. This work is of practical importance in waste management and other fields where region development is important. [ABSTRACT FROM AUTHOR]

Sectorization of a water distribution network (WDN) into district metered areas (DMAs) is a proven solution for proactive leakage control. Traditionally, WDN sectorization is conducted by local experts using a trial-and-error approach, often resulting in the identification of arbitrary solutions. Some recently published methods try to improve WDN sectorization by automating the process, especially by using optimization. Various sectorization criteria, constraints, and limitations are introduced, which often fail to consider the issues faced by poorly managed WDNs such as limited funds and shortage of water balance data. These methods also have poor computational efficiency imposed by optimization methods used. This paper presents a new distribution network sectorization method (DeNSE), that overcomes these deficiencies. This method is based on a heuristic procedure in which WDN sectorization is driven by efficient tracking of water balance data and determining the lowest cost investment needed to maintain the same level of operational performance. The above-mentioned set of criteria is particularly well suited for initial sectorization of WDNs when major uncertainties in water balance data often lead to poor management decisions. The DeNSE method is validated and benchmarked against other sectorization methodologies in a case study of a large, real-world WDN. The results show that DeNSE can identify sound, realistic sectorization solutions that are in some respects better than corresponding solutions reported in the literature. DeNSE also enables high computational efficiency, ensuring its applicability to real-world WDNs. [ABSTRACT FROM AUTHOR]

This paper considers the sectorization of a large water distribution network into district metered areas (DMAs) and simultaneously optimizes rehabilitation of the network with new pipes, control valves, and storage tanks. Because available water resources are much lower in the dry season, both the design and operational settings are optimized to satisfy water-demand, water-quality, and pressure constraints, as well as efficiency indices under stringent conditions. Because of the heterogeneity of the multiple decision variables and the complicated way they interact through the multiple objectives (some complimentary and some conflicting), it is not possible to fully automate the simultaneous sectorization, rehabilitation, and operational optimization. Therefore, a multistage approach is used where engineering judgment and network graph simplification and visualization tools are used to find a good feasible solution that serves as a first guess for further optimization of sectors and operational settings, to achieve feasible solutions with better cost of implementation, demand similarity among DMAs, and better pressure uniformity in operations. A multiobjective agent swarm optimization framework is used to iteratively change the sectors at the boundaries. For the final configuration, sequential linear programming is used to find optimal valve and pump settings. [ABSTRACT FROM AUTHOR]