Deterministic design as starting point for Stochastic multi-objective design of water distribution networks

Roughness and demand are two basic areas of uncertainty in water distribution network design and are usually treated deterministically, obfuscating their important stochastic nature. The paper describes a procedure for the robust design of water distribution networks which incorporates demand and roughness uncertainty in a multi-objective optimization scheme aimed at minimizing costs and maximizing hydraulic reliability. The procedure starts with a multi-objective deterministic design (i.e. constrained least-cost design procedure) using minimization of pipe costs and nodal pressure deficit as objective functions. Solutions generated by this phase serve as an initial population for the second phase, the stochastic design, which is solved as a multi-objective optimization problem by minimizing pipe costs and maximizing network robustness. The approach is tested in a case study involving a real network, yielding encouraging results and illustrating its computational time advantages.