multi-objective optimization

In this study, a conceptual model based on dynamic systems was developed to optimize the management of water, land, and agricultural production (tea and rice) in the irrigation zones of the Sefidroud irrigation and drainage network. To understand the behavior of the network and create a simulation model of the system, a dynamic systems modeling approach was employed, and the simulation was conducted using MATLAB/Simulink. Subsequently, the optimization model of the studied system was developed as a multi-objective model using a genetic algorithm. Various management scenarios were implemented through the weighting of the objective functions. The results showed that selecting the best response from multi-objective optimization models depends on the weighted values of the objective functions, and by changing these values, decision-makers can provide various responses to complex optimization problems. The optimization model determines the cultivated area and water allocation in such a way as to minimize water scarcity and maximize crop performance through different weighting combinations. Furthermore, the findings indicate that the canals of the irrigation network play a crucial role in meeting water needs, and equitable water allocation is essential to prevent excessive extraction and negative consequences, such as saline intrusion and land subsidence. The study demonstrates that the best solutions are contingent upon local conditions and decision-makers' policies. To achieve maximum economic benefits and address water needs, it is suggested to use a weighting combination close to (w1=1,w2=2). Ultimately, this model assists managers and decision-makers in minimizing water scarcity in the region by adjusting cropping levels and optimizing the use of available water resources.

Agriculture is the main economic pillar of the Helmand Basin; however, it faces severe water scarcity due to unsustainable consumption. Previous studies have optimized cropping patterns based on economic and water factors in arid regions. However, the unique conditions of Helmand require a multi-objective optimization approach that integrates economic, ecological, and environmental factors. This study develops a multi-objective mathematical model to determine the optimal cropping pattern for Helmand to maximize farmer profits while minimizing water consumption and environmental impacts. The model simulates cropping areas for major regional crops using multi-objective linear programming. In this regard, to obtain the optimal cultivation pattern with the desired objectives, the genetic algorithm was used as a random optimization method. The desired information was obtained from the Agricultural and Jihad Organization and Regional Water of Sistan and Baluchestan Province, and the relevant calculations were performed in MATLAB and CROPWAT software. The crop year determined in this study is 2018-2019 and the selected crops include wheat, corn, barley, black grapes, cucumber, eggplant, onion, legumes, and medicinal plants. Results indicate that the optimal cropping pattern reduces annual water consumption by 29%, nitrogen leaching by up to 14%, and increases economic yield by 11% compared to current practices. Virtual water imports of wheat and corn reduce local water consumption by 18% and improve economic yield by up to 5%. This integrated modeling approach provides data-driven scenario-based decision support for guiding policies on optimal cropping strategies. The findings demonstrate the potential of multi-objective optimization combined with virtual water imports to sustainably enhance agriculture despite water scarcity. This study can be used as a road map for policy makers and farmers to improve and sustain agriculture in the Hirmand basin.

Previous researches have often used the Firefly Algorithm (FA) as a single-purpose operation of the reservoir. For example, Garousi-Nejad and Bozorg-haddad (2014) used FA for the first time in water science and reservoir operation, using ten-year statistical data of the Aidoghmoush reservoir located in East Azerbaijan province of Iran. They used it to meet the needs of downstream irrigation. In order to show the efficiency of FA, the results of this algorithm were compared with the global optimum results obtained from the nonlinear programming (NLP) method. The results showed that FA responses differed by less than one percent from NLP. Garousi-Nejad et al. (2016) used the FA to operate the reservoir and used the superiority of this algorithm over GA using five mathematical tests, the problem of reservoir operation for agricultural water supply, and the problem of reservoir operation to generate electricity. The results showed the superiority of FA performance in terms of global optimum convergence rate compared to GA results. Therefore, further investigating the capability and application of the multi-objective of this algorithm in the multi-purpose reservoir operation is necessary.In this study, first, the performance of the MOFA algorithm is compared with the well-known and common NSGA-II algorithm from three perspectives of execution time, generation distance, and distance metric in two mathematical test functions. After ensuring they perform correctly in the test functions, an evaluation is performed for a reservoir operation problem. Then, three reservoir operation policies are selected from the policy set and reviewed.

Aidoghmoush dam is one of the dams built in East Azerbaijan Province, located at 19 km from Mianeh city. Aydoghmoush dam is located in the Sefidrood catchment area and Aidoghmoush sub-basin on the Aidoghmoush river. The structure of the dam is a clay-core rockfill. In this study, the Aidoghmoush reservoir's operation is examined from 1990 to 1996. The FA algorithm was developed by Yang (2008). This algorithm is based on the idealization of the behavior and flashing patterns of fireflies.The test functions used in the present study are (1) Schaffer test function (SCH) and (2) Fonesca test function (FON) (Coello et al. 2007). The MOFA algorithm was used to solve two multi-objective test functions, and its performance was compared with NSGA-II. The Generational Distance (GD) metric, introduced by Van Veldhuizen and Lamont (1998), was used to measure the proximity of the non-dominated solutions obtained to the true Pareto front (PFtrue) (Coello et al. 2007). The spacing (SP) metric introduced by Schott (1995) was also used to measure the distribution of the obtained non-dominated solutions.

In both test functions, the MOFA with good solution quality has a significant time difference in execution time compared to the NSGA-II algorithm; the MOFA is 30% faster in the SCH test function and 15% more quickly in the FON test function than the NSGA-II. Therefore, the MOFA can be a good algorithm for optimizing complex and time-consuming problems such as reservoir operation. The MOFA algorithm in two groups of parameters compared with the NSGA-II algorithm was evaluated in the problem of reservoir operation to maximize reservoir storage and minimize deficit. Extracted solutions from the MOFA algorithm improved by 11% compared to the NSGA-II algorithm by considering better parameter values in terms of proximity to the PFtrue. Also, the execution time of the MOFA algorithm was improved by 13% compared to the NSGA-II algorithm's execution time.

Nature-inspired meta-heuristic algorithms have been considered in recent decades due to their suitable ability to derive optimal reservoir operation policies compared to classical methods. In this research, the Multi-Objective Firefly Algorithm (MOFA) is compared with the widely-used Non-Dominated Genetic Algorithm (NSGA-II) in two test functions [Schaffer (SCH) and Fonseca (FON)]. These algorithms are then used to solve the optimizing the reservoir operation problem. Aidoghmoush reservoir, located in East Azerbaijan province, is used as a case study. Two conflicting objective functions are considered, including the first objective function of maximizing reservoir storage and the second objective function of minimizing deficiency. The algorithm runtime, generation distance, and Spacing matric are used to evaluate and compare the studied algorithms. The results showed that the execution time of the MOFA algorithm in the two test problems examined was, on average, 22% less than the execution time of the NSGA-II algorithm, and the quality of the answers could be better or worse than NSGA-II. The results obtained in the multi-objective operation of the reservoir showed that the set of solutions obtained from the MOFA algorithm became closer to the PFtrue averagely of 13% by considering the parameters α, β, and γ equal to 10, 1, and 0.1, instead of considering the parameters α, β, and γ equivalent to 0.25, 1 and 1, and the average execution time of the algorithm was improved by 3%. This improvement of the solution's quality and runtime was 13 and 11, respectively, compared to the NSGA-II algorithm.Since the MOFA algorithm is fast, the quality of the resulting set of answers can be improved by adjusting parameters, modifying, or integrating with other methods, such as different optimization algorithms or machine learning algorithms, and using it to Optimize real-time problems that are important in terms of computational time and burden. It is further suggested that the MOFA algorithm be developed for more complex models such as multi-purpose reservoir operation with more than two objectives of multi-reservoir systems, and its performance in reservoir operation management problems be compared with other meta-heuristic algorithms.

Surface border irrigation design and variables determination using multi-objective optimizationM. Saleki , M.R. Nouri , H.R. Salemi , R. Fatahi AbstractDesign of surface border irrigation systems is usually performed based on empirical relations presented in the literature or through simulation results in various models. These methods do not allow investigating the impact of all design variables on different irrigation indices.Designing based on minimizing the volume of water input along with maximizing indices such as application efficiency, distribution uniformity, and irrigation adequacy is a new approach that can provide the best results through multi-objective optimization. The best choice for design variables, including length, width, slope, inflow rate, and cut-off time in a field, can be obtained using this method to achieve optimal indices.In this research, by measuring the water advance in sample plots in a field in Isfahan and simulating water movement in the border strips, the soil infiltration coefficients were obtained. Based on this, for a net irrigation depth of 75 mm and a roughness coefficient of 0.15, 56700 closed-end border irrigation events were simulated using WinSRFR 5.1 software. Among the obtained results, using the constrained objective function multi-objective optimization method, with the aim of minimizing the volume of water input and application efficiency higher than 90%, distribution uniformity and irrigation adequacy more than 0.8, 515 optimal options for designing the irrigation border strips were determined, and among them, some options were presented for the optimal design of the irrigation border strips in this field and similar fields.The results show that the volume of water input in the optimized options is between 712.8 and 757.3 cubic meters per hectare, which is significantly different from the measured values in the field. The method presented in this research can be used as a new approach for designing surface border irrigation systems and increasing water productivity in agriculture.

The Dez-River's surface water resources system between the Dez regulatory dam and Bandar-e-Ghir is the focus of the current study to create a qualitative-quantitative-model that can be used to determine the best operating strategies. for replicate the existing operational state, a dynamic link between quantitative and qualitative models is built under the "reference-scenario" such that hydraulic linkages are generated between all of the system's components in the coupled system. The monthly environmental demands of the river are one of the choice factors in the optimization-scenario. The goals are to maximize the percentage of needs met and minimize quality standard violations. The implementation of the optimization scenario increased the reliability of providing all the needs of the plain with any priority. This problem illustrates how the reservoir should operate in an ideal state. In many places along the river, particularly the agricultural water withdrawal sites, the minimum violation of water quality standards has happened, according to a comparison of the pollution and quality parameters in the optimization scenario and the reference scenario. The amount of pollution and quality parameters has also improved. The findings show that it is possible to plan more effectively for the appropriate use of currently available water resources by taking into account all stakeholders and utilizing the qualitative-quantitative dynamic connection method of water resources to develop a coupled model using the MOPSO-algorithm. This will ensure that, in addition to meeting needs, the quality and pollution of the river remain close to the standard limits during the operation period.

Stepped spillways have received special attention today for their simultaneous operation in energy transfer and dissipation. In designing these spillways, the best way is to achieve a design with the highest amount of energy dissipation in the downstream and the lowest design cost. In this study, a multi-objective optimization model based on weed algorithms (IWO) and water cycle (WCA) is used to design stepped spillways with the aim of minimizing implementation costs and maximizing energy dissipation. The efficiency of the developed model was tested on the spillway of the down Siah Bisheh Dam. The results showed that the IWO algorithm has better accuracy and convergence speed than the WCA algorithm in solving the problem of multi-objective stepped spillway optimization. It was also found that using a multi-objective optimization approach can provide a set of answers to designers who can choose a suitable design for implementation in any situation depending on the amount of cost and energy consumption. Comparison between the responses with the lowest concreting volume provided by the IWO compared to the Spillway plan implemented, reduced the concreting volume by 20% and increased the energy dissipation by 12%. For the WCA, it also reduced the volume of concreting by 10 percent and increased energy dissipation by 4.89 percent.

Effective management in metropolitan planning of urban green space water resources is very important due to the rapid growth of urbanization and the limitation of water resources. The purpose of this research is multi-objective optimization and management of treated wastewater allocation using dynamic system models for urban green space irrigation in Shiraz metropolis.

The factors affecting the supply of water resources and irrigation of the green spaces of Shiraz city have been simulated and according to that, the consumption forecast and the number of available resources and the allocation optimization have been presented. Also, in the current research, effective factors in the current and future conditions that can affect the proposed model have been taken into consideration, and two scenarios have been applied, including increasing the efficiency of green space irrigation and the use of treated wastewater.

The results showed that increasing the efficiency of irrigation through management of transfer, storage and distribution of water and also irrigation at the right times has a much greater effect compared to the use of purified wastewater in order to reduce the extraction of limited resources. In such a way, by increasing the irrigation efficiency by 40% and 50%, respectively, 14% and 39% of water shortages will be solved.

The simulation results showed that in order to achieve the stability of the system, a combination of scenarios of reducing per capita water consumption in green spaces, increasing irrigation efficiency, using purified wastewater and dry landscaped spaces should be considered in the development of urban spaces.

The development of mechanization and machine technology can have positive and negative effects on the economic, social, and environmental conditions of a region. Conflicts in these areas complicate the selection and optimization of sustainable mechanization systems. One of the basic questions in the selection of a sustainable agricultural mechanization system is how and with what methodology would it be possible to propose the closest mechanization model that will overcome the simultaneous contradictions between the three pillars of sustainability; taking into account the natural and technical limitations in agricultural production. What is the appropriate approach considering the economic, environmental, and social aspects? The current research aims to provide a framework for an optimal mechanization model to achieve the goals of agricultural sustainability so that it can be implemented and applied practically. It is possible to provide a model that addresses the conflicting economic, social, and environmental aspects by quantitatively optimizing the level of mechanization.

In this study, a framework is applied whereby contradictory goals of agricultural sustainability can be achieved simultaneously. After selecting the indices and data collection, by combining Shannon entropy and TOPSIS, the similarity index was obtained for each objective. The similarity indices and values of the Benefit-Cost Ratio calculated for each system were considered as coefficients of three objective (economic, social, and environmental) functions in multi-objective optimization. The multi-objective optimization model was applied to achieve sustainable mechanization patterns and was solved using the NSGA-II algorithm. For framework validation, paddy production mechanization systems in the Ramhormoz region located in southwestern Iran were analyzed with constraints: land, water, and machinery. The five mechanization systems of paddy production included puddled transplanted, un-puddled transplanted, water seeded, dry seeded, and, no-till.

Pareto-optimal solutions of different scenarios with water and machine constraints showed that this framework cannot only meet the sustainable goals, but also the optimal allocation of mechanization systems is identified and the effect of different scenarios under different constraints can be examined. The sustainability goals between the no-tillage and planting with puddling systems are highly contradictory. The no-tillage system has the highest score in the environmental aspect and the lowest score in the social and economic aspects. This modern system was developed in Ramhormoz three years ago and has faced technical, economic, and social challenges ever since. The cultivated area using this system was 43 hectares in 2019. Despite the speed and ease of planting with this system, and its direct environmental benefits, the possibility of fungal outbreaks is raised due to the presence of wheat residues from previous cultivation and the warm and humid environment of cultivation. Additionally, weed outbreaks caused by periodic irrigation have greatly affected the satisfaction and profitability of this system, leading to the highest amount of pesticides consumed among the studied systems. The results of multi-objective optimization of sustainable rice mechanization systems in Ramhormoz city showed that the total surface area of optimal point systems is in the range of 2700 to 3200 hectares, which is close to the area under rice cultivation in Ramhormoz (3310 hectares) and it indicates that the output of the model is according to the applied restrictions and close to reality. The limitation of machinery and water has made the two planting systems of un-puddled transplanting and dry-seeding better than other systems. Removing only the machinery restriction can lead to an increase in the area under rice cultivation by about 700 hectares. This means that the requirement for the development of sustainable rice cultivation in Ramhormoz is to strengthen and support modern mechanized systems of no-tillage, dry-seeding, and planting with puddling, with a focus on systems with less water consumption which are the systems with higher levels of mechanization. Without water limitation, if the model is subject to the current machinery limitations, the optimal mechanization systems are the more traditional ones such as transplanting without puddling and wet-seeding.

One of the most fundamental challenges in the development of mechanization is identifying systems that can best balance the economic, social, and environmental aspects of sustainability and minimize environmental damage whilst maximizing economic and social benefits. Using the framework for sustainable mechanization will not only accomplish sustainable goals in identifying the optimum agricultural mechanization level, but it will also allow researchers and implementers in the agricultural sector to examine the outcome of various scenarios under different constraints. This framework can be used to find the optimal model for mechanization of all stages of tillage, planting, harvesting, and post-harvest in diverse geographical areas.

Step spillways are an example of these massive hydraulic structures that, in addition to passing the excess water of the dams, also cause the consumption of flow energy downstream of the dams. Considering the complex hydraulics of the flow on these spillways and the presence of nonlinear limitations, their optimal design is a very difficult problem. In this study, a new framework based on Metaheuristic algorithms, including Harris's hawk Optimization (HHO), gray wolf Optimizer (GWO), invasive weeds Optimization (IWO) and water cycle Algorithm (WCA), considering the minimization of the amount of concrete used in spillway and the maximization of energy dissipation in Spillway toe were developed as objective functions to design these spillways. Algorithms' performance was first checked and validated on basic functions. Then, to achieve the objectives of the study, the spillway of the Siah Bisheh dam was selected as the study dam and the efficiency of the developed models based on the four mentioned algorithms was evaluated on it. The results showed that, in addition to improving the current spillway design in terms of construction costs and dissipation energy, the HHO-based model has good accuracy and convergence compared to other Metaheuristic algorithms. As the comparison of the design obtained from HHO with the current spillway design showed, in addition to a 35% reduction in the volume of concrete consumed, the amount of energy dissipation increased by 15%, which indicates the success of the design model developed in a multi-objective manner using HHO.

Excessive exploitation of groundwater in Damghan plain has caused many problems such as land subsidence in the study area, along with the reduction of the groundwater level and the loss of a part of the aquifer and the reduction of the specific yield of aquifer. Therefore, in order to control the withdrawal from the aquifer and as a result to reduce the drop in the groundwater level in that plain, it was investigated. For this purpose, in this research, the mathematical modeling of Damghan Plain was done for the optimal management of exploitation and providing the optimal cultivation pattern in order to save water consumption with the focus on controlling the groundwater level and limiting land subsidence.

In this research, Damghan plain aquifer was first simulated using MODFLOW mathematical model. Then, taking into account different scenarios of aquifer exploitation, using the NSGAII genetic algorithm, optimization of multi-objective exploitation of water resources and optimal management of water supply and demand in the agricultural sector was done. The results of the model were evaluated based on statistical error parameters to predict the ground water level.

The results of this research showed that the MODFLOW numerical model was able to simulate the groundwater level of the studied plain well in steady and unsteady conditions in the calibration and validation stages. Also, the results of the simulation-optimization algorithm showed that by changing the cultivation pattern and also by changing the type of irrigation system from traditional to modern irrigation and as a result of increasing the irrigation efficiency (90 percent), the average drop of the groundwater level of the plain can be reduced. It reduced the groundwater level of the study area from 0.49 m in existing conditions to 0.07 m in optimal conditions. This will compensate the deficit of the aquifer from 31.90 to 5.1 million cubic meters per year.

Using management strategies such as changing the cultivation pattern, increasing irrigation efficiency, and also by controlling surface water and injecting it into groundwater, the process of reducing the groundwater level in the studied plain can be completely controlled and provided 100% of the water needs of the plain.

Expansion of urbanization, increasing in the population of planet, excessive exploitation of water resources and wastewater release in nature have negative and irreversible impacts on the environment. The present research has been carried out in order to optimize the redesign model of the green water and wastewater network.

In this research, a bi-objective optimization model for the green redesign of the water and wastewater network is proposed. The model includes locating the optimal place of storage ponds and also optimally allocating the treated wastewater to agricultural areas and industrial settlements in order to mitigate the devastating effects of discharging industrial wastewater into the municipal wastewater treatment plants and eventually mitigating the entry of such pollutants into the environment. The proposed model, has been solved using the - constraint method.

Accordingly, the total system cost is minimized, the demand is met and simultaneously the environmental issues are met and the environmental pollution load of the network is minimized, because of network redesign. Also, a sensitivity analysis is performed on some important parameters.

The results showed that the proposed model can help the designers in this field to design the distribution network, because despite the increase in costs the environmental pollution is reduced by installing COD meters and performing environmental disinfection. In addition, in this model, it has been tried to compensate part of the increased costs by selling activated sludge.

The cost of implementing spillways includes a large part of the dam construction budget. Optimizing these structures can significantly reduce the cost of building dams. So far, many studies have been done on optimizing the dimensions of spillways in order to reduce the amount of materials used. Among the used optimization methods, the methods based on meta-heuristic algorithms have had stunning results. The review of the studies conducted in the field of stepped and labyrinth spillways shows that the goals of all studies in stepped spillways have been to provide an acceptable plan for energy dissipation and in labyrinth spillways to reach a the largest amount of water passing. The purpose of this study is to combine stepped spillways with labyrinth spillways and optimization in order to increase the water passage coefficient and energy consumption at the same time. For this purpose, the multi-objective optimization approach has been used.

In the present study, the redesign of the spillway of the Sarouk rockfill dam located in West Azarbaijan province has been studied. In the case of labyrinth-stepped spillway, the decision variables, constraints and objective functions of the two spillways are combined and analyzed as a multi-objective optimization problem. In this study, a dynamic coefficient is used to improve the performance of the dragonfly algorithm in the search and exploitation stage. After determining the optimal values of the regulatory parameters of the MODA, NSGA-II, MOPSO and MOIDA algorithms, four benchmark examples were solved with each of them 20 times with an initial population of 50 and a maximum number of iterations equal to 100.

After validating the improved dragonfly algorithm on benchmark functions and evaluating its performance in solving multi-objective problems, this algorithm was used to design a combined spillway on the introduced dam. In multi-objective problems, there is a set of optimal solutions rather than a single optimal solution, which appear as a Pareto front. The implementation of the improved dragonfly algorithm with 200 initial population and 500 repetitions has resulted in providing 200 optimal answers on the Pareto chart. After performing the calculations related to the fuzzy decision-making method, a design with the values of the objective functions of concreting volume: 59795.54 cubic meters, dissipated energy: 75.18%, flow rate: 1255.19 cubic meters per second was selected as the optimal answer. In addition, the design with the highest and lowest cost of concrete consumption was selected as two other answers. The flow rate passing over the spillway has increased by 120% in plans A and B, and by 25% in plan C compared to the initial design flow rate. The amount of energy dissipation of plans A and B is about 76 and 75%, respectively. In plan C, where the flow rate has not increased significantly (25%), energy dissipation has reached about 81%, which is more than the other two cases.

Among the available answers, according to the priority of the cost, the plans with the lowest (C) and the highest (A) implementation cost based on the volume of concrete were selected. Also, by using the fuzzy decision-making approach, an optimal plan (B) that has a suitable balance between the three objectives was selected. Based on the results, it was found that each of the plans A, B and C can be used based on the needs of the employer. From the economic point of view, according to the project conditions and the needs of the employer, all the proposed plans are suitable options for replacing the actual spillway and reduce the implementation costs. Also, the comparison of plan C with the stepped spillway plan presented by previous researchers showed that with almost the same volume of concrete, using a multi-objective approach in comparison with a single-objective optimization approach, in addition to increasing flow energy consumption, also led to an increase in flow through the spillway.

Pressure management and reduction of high pressures are necessary to reduce leakage and extend the life of water distribution network equipment. There is a need for a benchmark and indicator to compare the distribution network pressure management. Investigation of the presented indicators shows that the reliability index is a suitable criterion for evaluating pressure management. In this research, using optimization methods, pressure reducing valves and changing the diameter of the pipe, the possibility of increasing the reliability of Javanrood water distribution network was investigated. In this study, using single-objective and two-objective optimization algorithms, the position and settings of pressure relief valves were determined for this network. In the single-objective Harmony Search algorithm, network reliability was considered, and in the two-objective algorithm, pressure and velocity reliability were considered as the objective functions. The results showed that the single-objective algorithm has increased the reliability of the network by 17% and the two-objective algorithm by 14% compared to the current situation. Examining the changes of network reliability in 24 hours of the day shows that the network reliability values obtained from the two-objective algorithm had very little fluctuations compared to the single-objective algorithm. In other words, the reliability of the network has been almost constant throughout the day.

As for the severe limitation of water resources, costly construction and operation of water supply systems and rapid population growth, the optimal design of these networks is essential. The problem of cost minimization is done by minimizing the diameter of the network pipes, which reduces the pressure in the network. Since providing adequate pressure in the nodes is one of the important design principles, so in this study, the problem of optimization in several sample networks was defined with the objectives of minimizing the cost and lack of pressure in the whole network. EPANET software was used for hydraulic analysis of sample networks and the multi-objective optimization process through coding of PESA-II and SPEA-II algorithms in MATLAB software and their connection to EPANET face Took. The cost function was initially defined only by considering the relationship between cost, diameter, and pipe length. Then, in the next definition, the cost of exceeding the allowable pressure range, where the minimum and maximum allowable pressures are 30 and 60 meters, respectively, was added to this function, and the program again with the number of repetitions that ended in the best answer Was implemented. The results showed that these algorithms have a high ability to find optimal solutions. In these algorithms, considering the cost of exceeding the allowable pressure limits results in the best answer that other researchers have ever obtained for sample networks, which for the two-loop and lansey network, The cost was 419000 and 1069393 $ respectively, and the pressure shortage was zero and with a low number of iterations, in the two-loop network for both algorithms with 20 iterations and in the lansey network for PESA-II and SPEA-II algorithms  with 200 and 140 iterations respectively, to achieve a higher number of optimal answers and the time to achieve convergence is significantly reduced, so that in the two-loop network, the execution time of PESA-II and SPEA-II algorithms are 0.55 and 0.59 minutes respectively, and in the lansey network It was 1/8 and 7.4 minutes respectively.

Increasing the water productivity by cropping pattern optimization is one of the best ways for development in agriculture. In this study, in order to maximize farmers' income and minimize blue water footprint of wheat, barley, alfalfa, and maize, the NSGA-II multi-objective optimization algorithm and United Nations commission on sustainable development’s indicator has been used in four cropping pattern scenarios in the 56 cities of the eastern provinces of Iran. The results showed that in some scenarios it was not possible to fully achieve these goals in the multi-objective model. The results also showed that the production of 50, 75 and 100% of the current values causes a low, moderate and severe water stress in the study region, that on average, save 55, 40 and 30 % of the region's water resources, respectively. Implementation of this model in the study area would increase revenue, reduce water consumption and, consequently make more environmental sustainability.

Groundwater resource management depended on data obtained from the aquifer. Groundwater monitoring network can provide groundwater levels, but sometimes this information so much and not useful. This study develops a new multi-objective simulation-optimization model involving two objectives minimization of the total sampling cost for monitoring and maximization the spatially monitoring accuracy. Optimal design of groundwater network was considered in the Silakhor plain, regions of Lorestan, Iran. As the first step, a database includes of groundwater elevation in potential wells with use empirical Bayesian kriging (EBK) method in ArcGIS was produced. Inverse distance weighting (IDW) method used as simulation model and objective functions written in MATLAB software. Optimal groundwater monitoring network determines with preset conventions and finds by the non-dominated sorting genetic algorithm (NSGA-II). At final, a network with twelve observation stations that shown root mean square error (RMSE) value 0.605 meter. The optimal monitoring network, in comparison with the existing observation network, has been able to reduce the number of monitoring stations by 60%, improve the spatial distribution of stations, and predict appropriate zoning for unpredictable points.

Nowadays, with increasing energy consumption costs, the optimization of energy efficient processes is being more considered than before. The essential part of the operational cost of water conveyance systems is energy consumption and maintenance costs of pumping stations. Therefore, it is necessary to develop an efficient method for optimal operation of these stations in order to reduce energy consumption and pumps maintenance costs. In this study, the optimal operation of pumping stations is considered as a multi-purpose optimization problem with the objective functions: 1- energy costs 2- maintenance costs. In order to resolve this problem, an optimization— simulation model based on Non-Dominated Sorting Genetic Algorithm (NSGA-II) is coupled to the EPANET hydraulic simulation model. The proposed model is applied to find the optimal pump scheduling program of Shiraz water conveyance system from Doroudzan Dam. Results revealed that by considering all different limitations of the problem, the energy costs were 30% and 5% less than the current state of operation and previous studies respectively. Also, the proposed model can decrease the cost of pumps maintenance by controlling the number of pump switches.

Risk-based optimization in flood diversion system is a framework that allows the designer to involve uncertainties in the decision-making process and determine the reliability of the hydraulic structure. This study was conducted to incorporate hydrological and hydraulic uncertainties in the probabilistic design of Karun-4 diversion system in Khuzestan province, southwestern Iran. The risk-based multivariate probabilistic model was developed for determining the effect of uncertainty sources on the characteristics of the flow diversion system. For this purpose, the time series of annual maximum peak flow and maximum flood volume data for a period of 37 years were prepared and evaluated. Archimedean copula function and non-dominated sorting genetic algorithm were adopted to minimize the overtapping risk and construction cost as objective functions. Diameter, slope, wall covering and tunnel entrance height, cofferdam height at upstream and downstream were searched as decision variables in the possible space of the problem. The results show that optimal values of upstream cofferdam height, downstream cofferdam height and the diameter of the first and second tunnels were estimated as 44.5, 12.5, 10.5 and 9.9 m, respectively, all corresponding to 25-year return period. Moreover, the results suggest that the proposed framework could be valuable for decision makers when economic, hydraulic and hydrological uncertainties are expected.

A multi-objective linear optimization model has been formulated, which is used for water and crop area allocation in two irrigation and drainage networks of Dorudzan and Karbal, including five farming regions. The developed model is based on four bankruptcy rules of proportional cutback (PC), constrained equal awards (CEL), constrained equal losses (CEL), and adjusted proportional (APR) in terms of the certainty and uncertainty in the water availability. The developed model has four objective functions to reflect the various agricultural and environmental consumptions and is solved for two dry and non-dry conditions using a fuzzy compromise approach. The outputs of the model showed that the regions with higher shares of water receives the most allocated water through the bankruptcy rules of the PC and CEL in dry and non-dry condition, respectively. On the other hand, the most allocated water for the regions with lower shares of water occurs through the bankruptcy rule of the CEA in both hydro climatic conditions. The outcome of the stability evaluation using the bankruptcy stability index (BASI) indicated that this criterion could not be used to evaluate stability under all bankruptcy situations; thus, one should take the necessary precaution for making a decision according to its output