An MINLP model for the minimization of installation and operational costs in water distribution networks

Water Distribution Networks (WDN) are important systems for industrial processes and urban centers. WDN can be formed by reservoirs, pipes, nodes, loops, and pumps and its complete design can be formulated as an optimization problem. The majority of published papers in the open literature use meta-heuristics for problem solution, as well as hydraulic simulators to calculate pressures and velocities. In the present study, a Mixed Integer Non-Linear Programming (MINLP) model was developed to the synthesis of WDN considering the minimization of the WDN total cost, given by the sum of installation and operational costs, which is the novelty in the paper. All the hydraulic calculations were included in the model (mass and energy balances and velocity and pressure upper and lower bounds), avoiding the use of additional software. Reformulation techniques are applied to the model considering the use of logarithms and disjunctive programming. Two case studies extracted from real WDN were used to test the model and global optimization techniques were employed to achieve the results. The results obtained show that the operational costs play an important role in the WDN system design.