Water loss reduction in water distribution systems (WDSs) is a challenging task for water utilities worldwide. One of the most reliable and cost-effective ways to reduce water loss is to properly regulate operational pressure of the system through optimizing pressure reducing valve (PRV) placements. This well-known engineering problem can be casted into a mixed-integer nonlinear program (MINLP) where binary variables are introduced to represent positions of PRVs. Many works in the literature applied heuristic algorithms to address the optimization problem. In this paper, at first, we proposed a new optimization model and reformulated it as the mathematical program with complementarity constraints (MPCCs). It is due to the fact that the stationary point of the MPCCs is likely to be trapped into bad local solutions, a soft heuristic method is then proposed to determine the MINLP local solution in each iteration before a stationary point of the MPCCs is reached. This method not only enhances the quality of MINLP solution, but also decreases computation time for solving the MPCCs. The newly formulated MPCCs is applied to determine optimal localization of PRVs for two WDS benchmarks and a real-world WDS in Vietnam. The results are compared with others in the literature demonstrating that using our new optimization model, better and more reliable MINLP solution can be found for large scale WDSs.

减少配水系统 (WDS) 中的水损失对全球水务公司来说是一项具有挑战性的任务。减少水损失的最可靠和最具成本效益的方法之一是通过优化减压阀 (PRV) 的位置来正确调节系统的运行压力。这个众所周知的工程问题可以转化为混合整数非线性程序 (MINLP)，其中引入二进制变量来表示 PRV 的位置。文献中的许多工作都应用启发式算法来解决优化问题。在本文中，我们首先提出了一种新的优化模型，并将其重新表述为具有互补约束的数学程序（MPCC）。这是因为 MPCC 的静止点很可能陷入糟糕的局部解中，然后提出一种软启发式方法来确定每次迭代中的 MINLP 局部解，然后到达 MPCC 的静止点。这种方法不仅提高了 MINLP 求解的质量，而且减少了求解 MPCC 的计算时间。新制定的 MPCC 用于确定两个 WDS 基准和越南真实世界 WDS 的 PRV 的最佳定位。结果与文献中的其他结果进行了比较，表明使用我们的新优化模型，可以为大规模 WDS 找到更好、更可靠的 MINLP 解决方案。新制定的 MPCC 用于确定两个 WDS 基准和越南真实世界 WDS 的 PRV 的最佳定位。结果与文献中的其他结果进行了比较，表明使用我们的新优化模型，可以为大规模 WDS 找到更好、更可靠的 MINLP 解决方案。新制定的 MPCC 用于确定两个 WDS 基准和越南真实世界 WDS 的 PRV 的最佳定位。结果与文献中的其他结果进行了比较，表明使用我们的新优化模型，可以为大规模 WDS 找到更好、更可靠的 MINLP 解决方案。