A fuzzy multi-objective optimization approach for treated wastewater allocation

In face of the new climate and socio-environmental conditions, conventional sources of water are no longer reliable to supply all water demands. Different alternatives are proposed to augment the conventional sources, including treated wastewater. Optimal and objective allocation of treated wastewater to different stakeholders through an optimization process that takes into account multiple objectives of the system, unlike the conventional ground and surface water resources, has been widely unexplored. This paper proposes a methodology to allocate treated wastewater, while observing the physical constraints of the system. A multi-objective optimization model (MOM) is utilized herein to identify the optimal solutions on the pareto front curve satisfying different objective functions. Fuzzy transformation method (FTM) is utilized to develop different fuzzy scenarios that account for potential uncertainties of the system. Non-dominated sorting genetic algorithm II (NSGA-II) is then expanded to include the confidence level of fuzzy parameters, and thereby several trade-off curves between objective functions are generated. Subsequently, the best solution on each trade-off curve is specified with preference ranking organization method for enrichment evaluation (PROMETHEE). Sensitivity analysis of criteria's weights in the PROMETHEE method indicates that the results are highly dependent on the weighting scenario, and hence weights should be carefully selected. We apply this framework to allocate projected treated wastewater in the planning horizon of 2031, which is expected to be produced by wastewater treatment plants in the eastern regions of Tehran province, Iran. Results revealed the efficiency of this methodology to obtain the most confident allocation strategy in the presence of uncertainties.