This manuscript investigates the design-for-control (DfC) problem of minimizing pressure induced leakage and maximizing resilience in existing water distribution networks. The problem consists in simultaneously selecting locations for the installation of new valves and/or pipes, and optimizing valve control settings. This results in a challenging optimization problem belonging to the class of non-convex bi-objective mixed-integer non-linear programs (BOMINLP). In this manuscript, we propose and investigate a method to approximate the non-dominated set of the DfC problem with guarantees of global non-dominance. The BOMINLP is first scalarized using the method of \(\epsilon \)-constraints. Feasible solutions with global optimality bounds are then computed for the resulting sequence of single-objective mixed-integer non-linear programs, using a tailored spatial branch-and-bound (sBB) method. In particular, we propose an equivalent reformulation of the non-linear resilience objective function to enable the computation of global optimality bounds. We show that our approach returns a set of potentially non-dominated solutions along with guarantees of their non-dominance in the form of a superset of the true non-dominated set of the BOMINLP. Finally, we evaluate the method on two case study networks and show that the tailored sBB method outperforms state-of-the-art global optimization solvers.

该手稿研究了控制设计（DfC）问题，该问题使压力造成的泄漏最小化，并在现有的供水网络中最大化了弹性。问题在于同时选择安装新阀门和/或管道的位置，以及优化阀门控制设置。这导致属于非凸双目标混合整数非线性程序（BOMINLP）类的具有挑战性的优化问题。在本手稿中，我们提出并研究了一种在保证全局非支配性的情况下，对DfC问题的非支配集进行近似的方法。首先使用\（\ epsilon \）方法对BOMINLP进行标量-约束。然后，使用定制的空间分支定界（sBB）方法，为所得的单目标混合整数非线性程序序列计算具有全局最优范围的可行解。特别是，我们提出了非线性弹性目标函数的等效重新表述，以实现全局最优性边界的计算。我们证明了我们的方法以BOMINLP的真实非支配集的超集的形式返回了一组潜在的非支配解以及其非支配性的保证。最后，我们在两个案例研究网络上对该方法进行了评估，结果表明，定制的sBB方法优于最新的全局优化求解器。