An improved cross-entropy method for the water pump scheduling optimization problem

The growing demand for urban freshwater supply often corresponds to rising electrical and labor costs for pump stations. Optimizing the operation of water pumps, ensuring they run at their most efficient working points, and improving their scheduling systems offer effective ways to mitigate costs and conserve water resources. These water pump stations and their associated systems can be mathematically modeled, enabling the use of optimization algorithms to assess optimal operating conditions. Conventional optimization methods often fall short when dealing with such complex models, underscoring the significance of investigating recent algorithms. In this study, we expand the research on the cross-entropy method and introduce an improved version to address water pump scheduling optimization. Notable enhancements include an improved update step for the multivariate normal distribution used in sampling, resulting in faster and more accurate outcomes, as well as reduced susceptibility to local minima. Moreover, our adaptive objective function takes into account various cost factors and penalty functions associated with complex constraints, with the primary aim of further minimizing power consumption costs. To validate our approach, we conducted a series of experiments within a simulated environment and on a real-life-inspired scenario modeled after a water pump station located in Shanghai. The results of these experiments demonstrate the adaptability of our optimization method to complex models and constraints and highlight its satisfactory performance outcomes.