In recent years, drinking water contamination incidents have been occurring at an increasingly frequent rate, leading to significant economic losses and social issues. Establishing and improving emergency disposal mechanisms for water contamination incidents is an important issue that has become a foremost concern globally. In this study, we first perform a theoretical analysis on an optimal scheduling problem and then prove that the scheduling of the valve and hydrant is NP-complete. Subsequently, we propose a multi-objective optimization model for contaminant response and primarily investigate two conflicting objectives: first, to minimize the volume of contaminated water exposed to the public; and second, to minimize the operational costs of the hydrant and valves. Finally, a customized multi-objective non-dominated sorted genetic algorithm-II (NSGA-II) coupling with an EPANET simulation is proposed and two different sizes of water distribution networks are employed to demonstrate the validity of the proposed model and methodology. Furthermore, we investigate the impact of different parameters on the performance of our proposed algorithm.

近年来，饮用水污染事件的发生频率越来越高，导致重大的经济损失和社会问题。建立和完善水污染事故应急处理机制是一个重要问题，已成为全球最关注的问题。在这项研究中，我们首先对最佳调度问题进行理论分析，然后证明阀门和消火栓的调度是NP完全的。随后，我们提出了污染物响应的多目标优化模型，并主要研究了两个相互矛盾的目标：第一，最大程度地减少暴露于公众的污水量；第二，最小化消火栓和阀门的运营成本。最后，提出了结合EPANET仿真的定制多目标非支配排序遗传算法-II（NSGA-II），并采用两种不同规模的供水网络来证明所提出的模型和方法的有效性。此外，我们研究了不同参数对所提出算法性能的影响。