Optimization of reservoir treatment levels considering uncertainty in mixing at cross junctions in water distribution systems using Info-gap decision theory

Abstract

Water distribution systems are affected by several uncertainties in multiple stages. This uncertainty makes solving the optimal design and management of WDS a multifaceted problem. Past research has focused only on solving design and management problems of system hydraulics. There have been very few studies that involve considering uncertainties that affect the water quality aspect of WDS. One of the major assumptions in solving the design and management problems of WDS is considering uniform and instantaneous mixing at the cross junctions. However, in reality, this is not true. This assumption is made due to the lack of computational power to accurately estimate the level of mixing at every junction in a water distribution network. This study focuses on considering this level of mixing as uncertain/unknown and provides the optimal treatment levels required at the reservoirs to ensure the system is immune to the level of mixing occurring at the junctions to satisfy the water quality requirements at the customer level. Info-gap decision theory-based optimization approach combined with the cuckoo search metaheuristic is proposed in this study to handle the uncertainty. The proposed methodology is applied to a 4x4 grid hypothetical network example. The study's objective is to provide the best designs that can handle the maximum variation of the level of mixing at junctions within the given budget by the designer. The maximum variation of the level of mixing is reported for different budget levels. The designs are compared with the deterministic case using Monte-Carlo simulations.