The process of optimal operation of multipurpose reservoirs is accompanied by large dimensions of decision variables and the uncertainty of hydrological parameters and water demands. Therefore, in determining the optimal operation policies (OOPs), the decision making for water allocation is faced with problems and complexities. One of the effective approaches for sustainable management and optimal allocation from water resources is the multi-objective structural development based on the uncertainty of input parameters. The purpose of this study is to provide OOPs from Karaj AmirKabir multi-purpose reservoir with applying uncertainty in the inflow to reservoir and downstream water demand. The proposed approach has been investigated in two certain and uncertain models, and three objective functions of the system including maximizing hydropower generation, water supply demands, and flood control have been considered to formulate OOPs. Non-dominated sorting genetic algorithm-II (NSGA-II) was performed to optimize the three proposed objective functions and by applying multi-criteria decision making (MCDM) methods, the best operation scenario was selected. In the uncertainty model, using the interval method and repeated implementation of the deterministic model for completely random scenarios that generated based on the variation interval of the uncertain parameters, the non-deterministic optimal allocation values were produced. Based on these optimal allocation values and the fitting of the standard probability distribution on it, the probability of occurrence of the deterministic allocation values was determined. Production of optimal probabilistic allocation policies can be very useful and efficient in providing real vision to managers to select appropriate policies in different conditions and rare hydrological events. The results obtained from the certain model shows that as a result of optimal allocation to demands, the fuzzy reliability, resiliency, and system stability indexes were improved to 67.81, 21.99, and 24.98 percentage, respectively. Also, in an uncertain model, applying changes of 48% and 22%, respectively for the inflow and downstream demand has led to changes of 23%, 55%, and 18%, respectively, in the first, second, and third objective functions. The highest impact from uncertain conditions, has been related to the water supply demands with 55% of the range of variations So, the water supply demands, has a higher sensitivity and priority than other reservoir objective functions under uncertain conditions. Another important result extracted from this study is to determine the monthly probability of optimal allocations achievement. Accordingly, in the warm seasons and years in which the reservoir is facing drought, the occurrence probability of the optimal allocations decreases. Given the comprehensiveness of the proposed methodology, this approach is a very suitable tool for determining the optimal water allocations as probabilistic based on the scenarios desired by managers and reservoir operators.

The process of optimal operation of multipurpose reservoirs is accompanied by large dimensions of decision variables and the uncertainty of hydrological parameters and water demands.Therefore, in determining the optimal operation policies (OOPs), the decision making for water allocation is faced with problems and complexities. One of the effective approaches for sustainable management and optimal allocation from water resources is the multi-objective structural development based on the uncertainty of input parameters. The purpose of this study is to provide OOPs from Karaj AmirKabir multi-purpose reservoir with applying uncertainty in the inflow to reservoir and downstream water demand. The proposed approach has been investigated in two certain and uncertain models, and three objective functions of the system including maximizing hydropower generation, water supply demands, and flood control have been considered to formulate OOPs. Non-dominated sorting genetic algorithm-II (NSGA-II) was performed to optimize the three proposed objective functions and by applying multi-criteria decision making (MCDM) methods, the best operation scenario was selected. In the uncertainty model, using the interval method and repeated implementation of the deterministic model for completely random scenarios that generated based on the variation interval of the uncertain parameters, the nondeterministic optimal allocation values were produced. Based on these optimal allocation values and the fitting of the standard probability distribution on it, the probability of occurrence of the deterministic allocation values was determined. Production of optimal probabilistic allocation policies can be very useful and efficient in providing real vision to managers to select appropriate policies in different conditions and rare hydrological events. The results obtained from the certain model shows that as a result of optimal allocation to demands, the fuzzy reliability, resiliency, and system stability indexes were improved to 67.81, 21.99, and 24.98 percentage, respectively. Also, in an uncertain model, applying changes of 48% and 22%, respectively for the inflow and downstream demand has led to changes of 23%, 55%, and 18%, respectively, in the first, second, and third objective functions. The highest impact from uncertain conditions, has been related to the water supply demands with 55% of the range of variations So, the water supply demands, has a higher sensitivity and priority than other reservoir objective functions under uncertain conditions.Another important result extracted from this study is to determine the monthly probability of optimal allocations achievement. Accordingly, in the warm seasons and years in which the reservoir is facing drought, the occurrence probability of the optimal allocations decreases. Given the comprehensiveness of the proposed methodology, this approach is a very suitable tool for determining the optimal water allocations as probabilistic based on the scenarios desired by managers and reservoir operators.