The restoration and remodeling of the urban water supply system are traditional challenges for water companies due to either aged existing water supply networks or lodging expansion. These challenges involve the uncertainties induced by their lengthy-planned prospects and the impossible exact prediction of forthcoming events. In this regard, correlations exacerbate unpredictable data and parameters and probably undermine taking effective decisions in this context. Therefore, the remodel and restoration decision of water supply systems must be made using approaches that can effectively deal with correlation uncertainties. The present study develops a bi-objective stochastic optimization model that can handle interrelated uncertain parameters in the water supply system remodeling and restoration issue. The proposed mathematical model is validated using the data of the Mashhad Plain water supply system as a real case study, followed by performing and comparing different levels of conservatism and reliability. As a complex optimization problem, an efficient algorithm is needed to solve the problem. To this end, a hybrid meta-heuristic algorithm,which is a combination of the Red Deer Algorithm (as a newly introduced nature-inspired heuristic) and Simulated Annealing (as a traditional local search algorithm), is proposed. Considering the advantages of these algorithms, it is possible to alleviate the disadvantages of current methods when solving large-scale networks. Finally, an extensive comparison and discussion are made and then the main findings with practical solutions are presented to significantly evaluate the proposed model and algorithm.

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