objective function

In the present paper, crop pattern criteria have been evaluated relying on sustainable development to increase agricultural water productivity. Seven criteria were selected as the main environmental and economic criteria and were prioritized and reviewed for important and strategic products in the Tajan catchment of Mazandaran province. Criteria prioritization was done using optimization through a genetic algorithm with an objective function based on sustainable development. Then, physical and economic productivity indices were calculated to determine the productivity value. Based on the results, in the selection of the crop pattern, firstly, the category of economic criteria and finally the category of environmental criteria have been given attention to the farmers in the current situation. But in the genetic optimization algorithm, all priorities have a similar order from the environmental point of view and then from the economic point of view although each product has its order of criteria. By this prioritization, the parameters of the cultivated area, the volume of water consumed, and the amount of chemical fertilizers have decreased on average by 26%, 34%, and 21%, respectively, and the parameters of product performance and profitability have increased by 43% and 61%, respectively. In addition to providing environmental standards and increasing sustainable development, this prioritization causes an average increase in physical productivity by 84% and an increase in economic productivity by 72%.

Common genetic programming (CGP) with considering empirical data (observed) improves and evolves estimated data (calculated). However, CGP is not able to solve multi-conditional problems with satisfactory performance. In this study, capability of the CGP is improved through development and integration of mathematical functions and logical operators on it. Proposed algorithm is called logic genetic programming (LGP) that its performance improvement is investigated in comparison with CGP in field of water resources. Results show that LGP capability, is more effective and more efficient than CGP, so that LGP improves objective function by 39 percent compared to CGP, in extraction of standard operating policy (SOP) [with minimization of mean absolute error (MAE)]. Comparison of algorithms results using the evaluation criteria indicate that LGP algorithm in SOP reconstruction resulted in a 22% decrease in RMSE and a 1% increase in NSE compared to CGP.

Nowadays, water scarcity is the current issue in Iran. This issue made the more necessity of using the proper water resources management more than the past. Stochastic Dynamic programming (SDP) is one of the methods to obtain the reservoir operation rules. In this method, one of the most important factors to find the optimal solution is discretization of the storage capacity and reservoir inflow. In this research, some storage classes (3, 5, 7 and 10) are analyzed to achieve the optimum storage discretization by SDP method, considering tree types of objective function (α = 0, α = 0.5, α = 1) with the constant reservoir inflow classes.

In this study, the SDP model has been used to find the optimal storage of Jamishan reservoir by any objective functions. By using historical reservoir inflow time series, reservoir inflow and storage are discretized in 3 classes with equal length intervals method and also 3, 5, 7 and 10 classes by Moran method, respectively. This method is applied by driving objective function as a minimization of system damage for each composition of the reservoir inflow and storage classes (k, i). By achieving the steady policy at each period, the amount of reservoir Inflow, storage and release are deterministically defined.

The results showed that the optimal storage capacity, only water supply of downstream demands considered as an objective function, is k=7 and there is minimum water deficit in case of α=0. In addition, this would be 10 classes in case of α=1, which the amount of difference between reservoir storage and its desirable would be changed from constant value and the first decreasing change would be appear. Obtaining reservoir storage classes is also affected by method of discretization since this value is obtained 10 for classic and Moran method and 7 in Savarenskiy method. That is selected k = 10 based on the objective function in case of α = 0.5 considered two objectives of reservoir release storage volume simultaneously.

In case of α=0, the objective function is only reservoir release and water allocation, and of the optimal class of reservoir storage would occur at the point where water deficit is constant by increasing the number of storage classifications which k=7 is the optimal class. In the second scenario the objective function which is α=1 is selected as the best discretized class of the reservoir storage which has the closest vicinity to the target storage (Ts). So, in this case, k=10 is the optimum reservoir storage. In the third scenario, α = 0.5, there is a difference between to find the optimal solution when consider the TS or Tr as the criteria. Both objective function are well regarded in this case and also the first decreasing changes is happened in k=10.

In this study, the values of moisture and soil temperature were estimated at different depths and times under unsteady conditions by solving the Richards’ equation in an explicit finite difference method provided in Visual Studio C#. For the estimation of soil hydraulic parameters, including av and nv (coefficients of van Genuchten’s equation) and Ks (saturated hydraulic conductivity), soil moisture and temperature at different depths were measured by TDR probes and the stability apparatus, respectively. The objective function [equal to Root Mean Square Error (RMSE)] was minimized by the optimization of a parameter separately, using the Newton-Raphson method, while, the other parameters were considered as the constant values. Then, by replacing the optimized value of this parameter, the same was done for other parameters. The procedure of optimization was iterated until reaching minor changes to the objective function. The results showed that soil hydraulic parameters (coefficients of van Genuchten’s equation) could be optimized by using the SWCT (Soil Water Content and Temperature) model with measuring the soil water content at different depths and meteorological parameters including the minimum and maximum temperature,, air vapor pressure, rainfall and solar radiation. Finally, the measured values of soil moisture and temperature were compared to the depth of 70cm in spring, summer, and autumn of 2015. The values of the normalized RMSE of soil water content were 0.090, 0.096 and 0.056 at the soil depths of 5, 35 and 70 cm, respectively, while the values of the normalized RSME of soil temperatures were 2.000, 1.175 and 1.5 oC at these depths, respectively. In this research, the values of soil hydraulic parameters were compared with other previous models in a wider range of soil moisture varying from saturation to air dry condition, as more preferred in soil researches.

The reservoir operation is a multi-objective optimization problem with large-scale which consider reliability and the needs of hydrology, energy, agriculture and the environment. There were not the any algorithms with this ability which consider all the above-mentioned demands until now. Almost the existing algorithms usually solve a simple form of the problem for their limitations. In the recent decay the application of meta-heuristic algorithms were introduced into the water resources problem to overcome on some complexity, such as non-linear, non-convex and description of these problems which limited the mathematical optimization methods. In this paper presented a Simple Modified Particle Swarm Optimization Algorithm (SMPSO) with applying a new factor in Particle Swarm Optimization (PSO) algorithm. Then a new suggested hybrid method which called HGAPSO developed based on combining with Genetic algorithm (GA). In the end, the performance of GA, MPSO and HGAPSO algorithms on the reservoir operation problem is investigated with considering water supplying as objective function in a period of 60 months according to inflow data.
The GA is one of the newer programming methods which use of the theory of evolution and survival in biology and genetics principles. GA has been developed as an effective method in optimization problems which doesn’t have the limitation of classical methods. The SMPSO algorithm is the member of swarm intelligence methods that a solution is a population of birds which know as a particle. In this collection, the birds have the individual artificial intelligence and develop the social behavior and their coordinate movement toward a specific destination. The goal of this process is the communication between individual intelligence with social interaction. The new modify factor in SMPSO makes to improve the speed of convergence in optimal answer. The HGAPSO is a suggested combination of GA and SMPSO to remove the limitation of GA and SMPSO. In this paper the initial population which caused randomly in all metha-heuristic algorithms consider fixing for the three mentioned algorithms because the elimination of random effect in initial population may make increase or decrease the convergence speed. The objective function is the minimum sum of the difference between the downstream demand reservoir and system release in the period time. Also the constrains problem is continuity equation, minimum and maximum of reservoir storage and system release.
The performance of GA, SMPSO and HGAPSO evaluated based on the objective function for Dez reservoir in the south east of Iran. In this study the programming of GA, SMPSO and HGAPSO was written in Matlab software and then was run for the time period with a maximum of 400 iterations. The minimum of the objective function for GA, SMPSO and HGAPSO was obtained 1.19, 1.05 and 0.9 respectively, and the maximum of objective function was calculated 1.66, 1.26 and 1.10 respectively. The results showed that the minimum of the objective function by HGAPSO was estimated 32 and 16 percent lower than the counts which calculated by GA and SMPSO. The standard deviation of SMPSO and HGAPSO were near to each other and less than GA which shows the diversity between solutions for SMPSO and HGAPSO are much less than GA. Also the HGAPSO had the better performance rather than previous method in terms of minimum, maximum, average and standard deviation. The convergence speed of HGAPSO for finding the optimal solution is much faster of GA and SMPSO. The difference graphs between system release and monthly demand in HGAPSO is much less than GA and SMPSO. Also the storage calculated in HGAPSO and SMPSO is highly close to each other but in GA method the storage calculated more in the first and second years.
The convergence speed in finding the optimal solution in SMPSO in more than GA but in other hand the probability of caughting in local optima for SMPSO is great whereas GA can make the diverse optimal solutions. For this reason, in this paper was trying to improve the performance of the GA and SMPSO and remove their disadvantage based on combining them and presenting a new hybrid method. The results showed the HGAPSO method which presented in this paper to use without any complexity and additional operator to GA and SMPSO has the ability to use for reservoir operation with large-scale. In addition it is suggested which the HGAPSO apply to other water resources engineering problems.

The biggest consumer of water in the world is agricultural sector. So¡ optimization of agricultural water usage is considered of a great importance. In this research¡ optimization of irrigation scheduling in ShahidChamran irrigation and drainage network has been investigated at the scale of farm channels using a combined model including AquaCrop simulation model¡ a multi-objective classic optimization algorithm (weighted sum)¡ and genetic algorithm. Two types of irrigation scheduling methods of constant depth-interval and variable depth- interval proportionate with soil type in maize farm units (cropping pattern plant with high demand) were proposed. Objective functions were developed to optimize soil type 1 (coarse-textured) water productivity¡ leaching fraction¡ yield and the number of irrigation events while for soil type 2 (fine-textured) the objective functions were water productivity¡ soil saturated extract salinity¡ crop yield and the number of irrigation events. Each objective function component contains concepts of water resources sustainable development¡ control on drainage volume and environment¡ lands stability and utilization issues. For soil type 1¡ optimization results showed a reduction about 50% in water consumption¡ an increase up to 94 % in water productivity¡ a reduction of 62% in leaching fraction¡ three times reduction in irrigation events in constant depthinterval schedule. The results also showed a reduction of 50% in water consumption¡ 111% increase in water quantities efficiency¡ a reduction of 66% in leaching fraction¡ and three times reduction in irrigation events in variable depth-interval method in soil type 1. Furthermore¡ the results for soil type 2¡ were a reduction of 35% in water consumption¡ an increase of 63% in water productivity¡ 52% reduction in leaching fraction¡ reducing an irrigation event in constant depth-interval schedule. For variable depth-interval method¡ the results indicate a reduction of 35% in water concumption¡ an increase of 70% of water usage efficiency¡ 11% increase in crop yield and a reduction of an irrigation event¡ compared with the proposed irrigation scheduling.

Hydraulic analysis of water networks contains determination of the distribution ratein each pipe and head of network nodes. Nowadays using meta -heuristic algorithm Simulated Annealing is increasing in solving complex engin eering problems according to capabilities. Purpose of this study hydraulic analysis of water distribution network based on simulated annealing and comparing the results according to statistical indices: AE and RMSE with numerical Hardy Cross, Newton-Raphson, Linear theory, Gradient and Epanet software. To determine the ability of a variety of methods to simultaneously continuity equation and energy loss network, the Objective Function is used. At the end amount of Objective Function Simulated Annealing for two loop snetwork is 0.00016 and assessing index results indicates its accuracy in reaching problem solutions. These results prove efficiency of this method towards the other conventional methods. According the assessment can recommend Simulated Annealing as a new method and reliable in designing and analysing pressurized water networks.

Modeling of flow and transport processes in variably saturated porous media requires detailed knowledge of the soil hydraulic properties. The hydraulic properties to be determined by the inverse problem solution are the unsaturated hydraulic conductivity K(h) and the water retention curve θ(h). The inverse modeling approach assumes that both θ(h) and K(h) as well as transport parameters can be determined simultaneously from transient flow data by numerical inversion of the governing flow and transport equations. In order to find answers to the questions of uniqueness, identifiability and stability of different experimental setups, a new numerical experiment of redistribution was carried out. To study the shape of the objective function near its minimum, response surfaces for the estimated parameters were generated. The sensitivity of model outputs with respect to changes in input parameters was also computed and analyzed. Results of the redistribution experiment suggest that the non-uniqueness increases when the model output variables are not sensitive enough to the optimized parameters. As expected, the estimated values of parameters were sensitive to the magnitude of error in the measured data. In this experiment, the parameter estimation based on the pressure head observations provides unique solution. Due to preferential flow in the sample, tensiometric observations may provide poor results for inverse problem solution. Taking into account information about saturated hydraulic conductivity, Ks improved the likelihood of uniqueness and reduced the errors in parameter estimation of the shape parameters (α, n). It was found that the sensitivity analysis could be a useful tool to design the optimal time and location distribution of experimental observations.