The design of district metered areas (DMA) in potable water supply systems is of paramount importance for water utilities to properly manage their systems. Concomitant to their main objective, namely, to deliver quality water to consumers, the benefits include leakage reduction and prompt reaction in cases of natural or malicious contamination events. Given the structure of a water distribution network (WDN), graph theory is the basis for DMA design, and clustering algorithms can be applied to perform the partitioning. However, such sectorization entails a number of network modifications (installing cut-off valves and metering and control devices) involving costs and operation changes, which have to be carefully studied and optimized. Given the complexity of WDNs, optimization is usually performed using metaheuristic algorithms. In turn, optimization may be single or multiple-objective. In this last case, a large number of solutions, frequently integrating the Pareto front, may be produced. The decision maker has eventually to choose one among them, what may be tough task. Multicriteria decision methods may be applied to support this last step of the decision-making process. In this paper, DMA design is addressed by (i) proposing a modified k-means algorithm for partitioning, (ii) using a multiobjective particle swarm optimization to suitably place partitioning devices, (iii) using fuzzy analytic hierarchy process (FAHP) to weight the four objective functions considered, and (iv) using technique for order of preference by similarity to ideal solution (TOPSIS) to rank the Pareto solutions to support the decision. This joint approach is applied in a case of a well-known WDN of the literature, and the results are discussed.

中文翻译：

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通过多准则和多目标优化的区域计量区域设计

饮用水供应系统中的区域计量区域 (DMA) 的设计对于自来水公司正确管理其系统至关重要。伴随着他们的主要目标，即为消费者提供优质水，好处包括减少泄漏和在自然或恶意污染事件的情况下迅速反应。给定配水网络 (WDN) 的结构，图论是 DMA 设计的基础，并且可以应用聚类算法来执行分区。然而，这种部门化需要进行大量的网络改造（安装截止阀以及计量和控制装置），涉及成本和运营变化，必须仔细研究和优化。鉴于 WDN 的复杂性，通常使用元启发式算法进行优化。反过来，优化可以是单目标或多目标。在最后一种情况下，可能会产生大量的解决方案，经常整合帕累托前沿。决策者最终必须在其中选择一个，这可能是一项艰巨的任务。可以应用多标准决策方法来支持决策过程的最后一步。在本文中，DMA 设计通过以下方式解决：(i) 提出改进的 k-means 分区算法，(ii) 使用多目标粒子群优化来适当放置分区设备，(iii) 使用模糊层次分析法 (FAHP) 来加权考虑的四个目标函数，以及（iv）使用与理想解决方案相似度的优先顺序技术（TOPSIS）对帕累托解决方案进行排名以支持决策。