This paper investigates control and design-for-control strategies to improve the resilience of sectorized water distribution networks (WDN), while minimizing pressure induced pipe stress and leakage. Both evolutionary algorithms (EA) and gradient-based mathematical optimization approaches are investigated for the solution of the resulting large-scale non-linear (NLP) and bi-objective mixed-integer non-linear programs (BOMINLP). While EAs have been successfully applied to solve discrete network design problems for large-scale WDNs, gradient-based mathematical optimization methods are more computationally efficient when dealing with large search spaces associated with continuous variables in optimal network control problems. Considering the advantages of each method, we propose a sequential hybrid method for the optimal design-for-control of large-scale WDNs, where a refinement stage relying on gradient-based mathematical optimization is used to solve continuous optimal control problems corresponding to design solutions returned by an initial EA search. The proposed method is applied to compute the Pareto front of a bi-objective design-for-control problem for the operational network BWPnet, where we consider reopening closed connections between isolated supply areas. The results show that the considered design-for-control strategy increases the resilience of BWPnet while minimizing pressure induced leakage. Moreover, the refinement stage of the proposed hybrid method efficiently improves the coarse approximation computed by the initial EA search, returning a continuous and even Pareto front approximation.

本文研究了控制和设计控制策略，以提高分区配水网络 (WDN) 的弹性，同时最大限度地减少压力引起的管道应力和泄漏。研究了进化算法 (EA) 和基于梯度的数学优化方法，以解决由此产生的大规模非线性 (NLP) 和双目标混合整数非线性规划 (BOMINLP)。虽然 EA 已成功应用于解决大规模 WDN 的离散网络设计问题，但在处理与最优网络控制问题中的连续变量相关的大型搜索空间时，基于梯度的数学优化方法的计算效率更高。考虑到每种方法的优点，我们提出了一种用于大规模 WDN 的最优控制设计的顺序混合方法，其中依赖于基于梯度的数学优化的细化阶段用于解决与初始 EA 搜索返回的设计解决方案相对应的连续最优控制问题。将所提出的方法应用于计算运营网络的双目标控制设计问题的帕累托前沿BWPnet，我们考虑重新开放隔离供应区之间的封闭连接。结果表明，所考虑的控制设计策略提高了BWPnet的弹性，同时最大限度地减少了压力引起的泄漏。此外，所提出的混合方法的细化阶段有效地改进了由初始 EA 搜索计算的粗略近似，返回一个连续且均匀的 Pareto 前近似。