### Multiobjective Design of Water Distribution Systems Under Uncertainty

Abstract

The water distribution system (WDS) design problem is defined here as a multiobjective optimization problem under uncertainty. The two objectives are (1) minimize the total WDS design cost and (2) maximize WDS robustness. The WDS robustness is defined as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in the network. Decision variables are the alternative design options for each pipe in the network. The sources of uncertainty are future water consumption and pipe roughness coefficients. Uncertain variables are modeled using probability density functions (PDFs) assigned in the problem formulation phase. The corresponding PDFs of the analyzed nodal heads are calculated using the Latin hypercube sampling technique. The optimal design problem is solved using the newly developed RNSGAII method based on the nondominated sorting genetic algorithm II (NSGAII). In RNSGAII a small number of samples are used for each fitness evaluation, leading to significant computational savings when compared to the full sampling approach. Chromosome fitness is defined here in the same way as in the NSGAII optimization methodology. The new methodology is tested on several cases, all based on the New York tunnels reinforcement problem. The results obtained demonstrate that the new methodology is capable of identifying robust Pareto optimal solutions despite significantly reduced computational effort.