Bayesian Optimization of Booster Disinfection Scheduling in Water Distribution Networks

Chlorine remains the most widely used disinfectant in drinking water treatment and distribution systems worldwide. To maintain a minimum residual throughout the distribution network, chlorine dosage needs to be regulated by optimizing the locations of chlorine boosters and their scheduling (i.e., chlorine injection rates). Such optimization can be computationally expensive since it requires numerous evaluations of water quality (WQ) simulation models. In recent years, Bayesian optimization (BO) has garnered considerable attention due to its efficiency in optimizing black-box functions in a wide range of applications. This study presents the first attempt to implement BO for the optimization of WQ in water distribution networks. The developed python-based framework couples BO with EPANET-MSX to optimize the scheduling of chlorine sources, while ensuring the delivery of water that satisfies water quality standards. Using Gaussian process regression to build the BO surrogate model, a comprehensive analysis was conducted to evaluate the performance of different BO methods. To that end, systematic testing of different acquisition functions, including the probability of improvement, expected improvement, upper confidence bound, and entropy search, in conjunction with different covariance kernels, including Matérn, squared-exponential, gamma-exponential, and rational quadratic, was conducted. Additionally, a thorough sensitivity analysis was performed to understand the influence of different BO parameters, including the number of initial points, covariance kernel length scale, and the level of exploration vs exploitation. The results revealed substantial variability in the performance of different BO methods and showed that the choice of the acquisition function has a more profound influence on the performance of BO than the covariance kernel.