Strategies to develop warm solutions for real-time pump scheduling for water distribution systems

An optimal pump operation schedule that maintains satisfactory hydraulics conditions can generally reduce energy consumptions compared to the traditional trial and error based pump operation schedule. Linking an evolutionary based optimization algorithm with a hydraulic simulation model has gained attention for obtaining the optimal schedule. However, this technique requires significant computation time and thus has difficulty in real-time implementation. This paper presents several tactics to generate warm solutions that can be used in the initial population of the evolutionary algorithms to reduce the computation times. Strategies to generate warm solutions include the use of linear programming, surrogate model known as machine learning or meta-model, and historical pump schedule for similar demand pattern. Providing warm solutions from approximate methods or previous day’s results to stochastic search methods can improve solution convergence and offers significant computation time benefits. Results obtained from different strategies are compared.