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This paper presents a Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) for the optimal operation of a complex multipurpose and multi-reservoir system. Firstly, MOEA/D decomposes a multi-objective optimization problem into a number of scalar optimization sub-problems and optimizes them simultaneously. It uses information of its several neighboring sub-problems for optimizing each sub-problem. This simple procedure makes MOEA/D have lower computational complexity compared with non-dominated sorting genetic algorithm II (NSGA-II). The algorithm (MOEA/D) is compared with the Genetic Algorithm (NSGA-II) using a set of common test problems and the real-world Zohre reservoir system in southern Iran. The objectives of the case study include water supply of minimum flow and agriculture demands over a long-term simulation period. Experimental results have demonstrated that MOEA/D can improve system performance to reduce the effect of drought compared with NSGA-II superiority. Therefore, MOEA/D is highly competitive and recommended to solve multi-objective optimization problems for water resources planning and management.

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To deal with severe drought when water supply is insufficient hedging rule, based on hedging rule curve, is proposed. In general, in discrete hedging rules, the rationing factors have changed from a zone to another zone at once. Accordingly, this paper is an attempt to improve the conventional hedging rule to control the changes of rationing factors. In this regard, the simulation model has employed a fuzzy approach, and this causes rationing factor changing during a long term simulation gradually. To optimize different parameters of the purposed hedging a Multi-objective Particle Swarm Optimization (MOPSO) algorithm has been considered. The minimum of two objectives Modified Shortage Index (MSI) involving water supply of minimum flow and agriculture demands can be taken as the optimization objectives. The results of the proposed hedging rule indicate long term and annual MSI values have considerably improved compared to the conventional hedging rule. This determines that the proposed method is promising and efficient to mitigate the water shortage problem.

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Planning for supply water demands (drinkable and irrigation water demands) is a necessary problem. For this purpose, three subjects must be considered (optimization of water supply systems such as volume of reservoir dams, optimization of released water from reservoir and prediction of next droughts). For optimization of volume of reservoir dams, yield model is applied. Reliability of yield model is more than perfect model and cost of solution of this model is less than other methods. For optimization of released water from reservoir dams, different methods can be applied. In this research, dynamic programming method (a discrete method for optimization) and genetic algorithm (a searcher method for optimization) are considered for optimization of released water from the Karaj reservoir dam. The Karaj dam locates in west of Tehran. This research shows that reliability and resiliency of GA method is more than DP method and vulnerability of GA method is less than DP method. For improving of results of GA method, mutation rate of GA method is considered from 0.005 to 0.3 for different generations. For prediction extreme droughts in future, the Markov chain method is used. Based on generated data by Markov chain method, optimum volume of reservoir dam is determined by yield model. Then optimum released water from reservoir dam is determined by DP and GA methods for different scenarios that produced by Markov chain method. The Markov chain and yield model show that volume of reservoir Karaj dam should increase 123 MCM for overcoming to next droughts.

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In this study, optimum combinations of available rainfall gauging stations are selected by a model which is consist of geo statistics model as an estimator  and an optimized model. At the  first,  watershed  is  approximated  to  several  regular  geometric  shapes.  Then  kriging calculates  the  variance  of  the  estimation  error  of  different  combinations  from  available rainfall gauging stations using inside and outside stations of watershed. In each combination, n is number of considered stations and N is number of available stations (N>n). At the end, the best combination is selected by genetic algorithm (the  error variance of this combination is minimum). For optimal set with one sample point (station) estimator model and optimize model select station that locates near to center of watershed. While for two stations case, these models select two stations that l ocate in boundaries face to face. Also for combination n  stations  of  N  stations,  selected  stations  have good  and  proportional  distribution  in watershed. These results show correctness of research methodology.
In this study, effects of variations of paramet ers of theoretical variogram and number of blocks  in  block  estimation  of  kriging  method  are  evaluated  too.  The  variance  of  the estimation error from block estimation with 8*8 blocks has showed the acceptable results.
This research shows a linear relation between variations of error variance and scale of variogram. Optimum combination does not vary with variations of scale of variogram but it varies with variations of range of variogram. Increasing of nugget effect of variogram would raise the variance but does not vary optimum combinations.

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Digging of geotechnical boreholes and soil resistance tests are time-consuming and expensive activities. Therefore selection of optimum number and suitable location of boreholes can reduce cost of their drilling and soil resistance tests. In this research, a model which is consisting of geo statistics model as an estimator and an optimized model is selected. The kriging calculates the variance of the estimation error of different combinations from available geotechnical boreholes. In each combination, n is number of considered boreholes and N is number of available boreholes (N>n). At the end, the best combination is selected by genetic algorithm (the error variance of this combination is minimum). Also the Kean Shahr of Ahvaz city (in Khuzestan province, Iran) is selected as case study in this research. Location of selected boreholes is in points that soil resistance of these points represents mean soil resistance of total region. Optimum number of boreholes is 15. Also results show that location of selected boreholes depends to soil resistance and diameter and length of applied piles are not important for this purpose.