The optimal design of WDS has been extensively researched for centuries, but most of these studies have employed deterministic optimization models, which are premised on the assumption that the parameters of the design are perfectly known. Given the inherently uncertain nature of many of the WDS design parameters, the results derived from such models may be infeasible or suboptimal when they are implemented in reality due to parameter values that differ from those assumed in the model. Consequently, it is necessary to introduce some uncertainty in the design parameters and find more robust solutions. Robust counterpart optimization is one of the methods used to deal with optimization under uncertainty. In this method, a deterministic data set is derived from an uncertain problem, and a solution is computed such that it remains viable for any data realization within the uncertainty bound. This study adopts the newly emerging robust optimization technique to account for the uncertainty associated with nodal demand in designing water distribution systems using the subsystem-based two-stage approach. Two uncertainty data models with ellipsoidal uncertainty set in consumer demand are examined. The first case, referred to as the uncorrelated problem, considers the assumption that demand uncertainty only affects the mass balance constraint, while the second case, referred to as the correlated case, assumes uncertainty in demand and also propagates to the energy balance constraint.
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