This study aims to develop and solve a multi-objective water distribution systems optimization problem incorporating pumps’ optimal scheduling and leakage minimization. An iterative optimization model was presented for calibrating and computing leakages in water distribution systems to recognize the critical impact of leakage control on system operation. The multi-dimensional and nonlinear optimization model, incorporating pump control, consumer demands, storage, and other water distribution systems’ components, was constructed and was minimized using a multi-objective genetic algorithm coupled with hydraulic simulations. The model was demonstrated on two example applications with increasing complexity through base runs and sensitivity analyses. Results showed that leakage minimization competes against pumping, mainly when significant differences occur between demands during low and high energy tariffs. Pumping during the periods with high electricity tariffs (when the demands are high) generated pressure distribution that decreased the overall leakage related to pump scheduling that replicated the natural inclination to pump as much as possible at low tariffs (when the demands are low). The optimal fronts were found to be very sensitive to the leakage exponent value, and changing its value indeed contradicted the balance between minimizing the leakage and the energy cost significantly. Altogether, the idea presented in this paper was found capable of facilitating the decision-makers to conveniently select between the energy-efficient pump scheduling and pump scheduling reflecting minimum leakage based on the system operator’s preferences. The research also paves the way to rebuild the optimization model by incorporating water distribution reliability and water quality that, in some cases, may also contradict the choice between energy cost and leakage minimization.
A new mathematical program with complementarity constraints for optimal localization of pressure reducing valves in water distribution systems
