Infeasibility Maps: Application to the Optimization of the Design of Pumping Stations in Water Distribution Networks

Abstract

The design of pumping stations in a water distribution network determines the investment costs and affects a large part of the operating costs of the network. In recent years, it was shown that it is possible to use flow distribution to optimize both costs concurrently; however, the methodologies proposed in the literature are not applicable to real-sized networks. In these cases, the space of solutions is huge, a small number of feasible solutions exists, and each evaluation of the objective function implies significant computational effort. To avoid this gap, a new method was proposed to reduce the search space in the problem of pumping station design. This method was based on network preprocessing to determine in advance the maximum and minimum flow that each pump station could provide. According to this purpose, the area of infeasibility is limited by ranges of the decision variable where it is impossible to meet the hydraulic constraints of the model. This area of infeasibility is removed from the search space with which the algorithm works. To demonstrate the benefits of using the new technique, a new real-sized case study was presented, and a pseudo-genetic algorithm (PGA) was implemented to resolve the optimization model. Finally, the results show great improvement in PGA performance, both in terms of the speed of convergence and quality of the solution.