Deterministic versus Stochastic Design of Water Distribution Networks

The paper describes a procedure for the robust design of water distribution networks which incorporates the uncertainty of nodal water demands and pipe roughness in a multiobjective optimization scheme aimed at minimizing costs and maximizing hydraulic reliability. The methodology begins with a deterministic system design in order to generate a set of optimal networks that serves as the initial population for subsequent multiobjective stochastic design. This approach does not depend on the choice of multiobjective optimizer (for example, a multiobjective genetic algorithm is used here) and can drastically reduce the number of "stochastic" runs needed for searching robust solutions. A collection of probability density functions based on the beta function is introduced and applied to modeling variable uncertainty according to different physical requirements. The approach is tested in a case study involving a real network, illustrating its computational advantages.