Deterministic vs. Stochastic Design of Water Distribution Networks

The paper describes a procedure for the robust design of water distribution networks which incorporates the un-certainty of nodal water demands and pipes roughness in a multi-objective optimization scheme aimed at mini-mizing 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 multi-objective stochastic design. This approach does not depend on the choice of multi-objective optimizer (for example, a multi-objective 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 ap-proach is tested in a case study involving a real network, illustrating its computational advantages.