multi-objective optimization

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.

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.

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.

In this research, by considering the variable-speed pump, the effect of speed on pump performance, network hydraulics and energy consumption in a water distribution network in both single-objective and multi-objective models was investigated by using the new G-JPSO algorithm. The objective function in the single-objective problem is to minimize the amount of energy consumption throughout the day, and the decision variables are the amount of pump rounds in different hours of the day and night. In the multiobjective optimization problem, the first goal was to minimize the cost of consuming energy and the second goal was to maximize the hydraulic reliability. In order to determine optimal pump operation program, an optimization-simulation model based on G-JPSO optimization algorithm was developed. In this model, the algorithm was integrated into the MATLAB environment with the hydraulic part of the EPANET model as the reference of the commands and information. The proposed model was used in the Vanzyl distribution network and the optimal exploitation instructions were extracted and the results were compared with the JPSO algorithm and the ACO. The results of the paper showed that in the single-objective problem, the G-JPSO algorithm's results are 3.28 and 0.38 percent better than JPSO and ACO, respectively. In general, the energy consumption of variable-speed pumps was lowers the constant- speed pumps. In a multi-objective problem, in all optimization scenarios, the G-JPSO algorithm was able to achieve points in comparison with the ACO algorithm, which, in addition to cost reduction, has higher reliability.

Reservoirs operation problems have various and diverse objectives that rarely lead to a global optimized answer, and usually there are a set of optimal answers (Pareto Front). Solving these problems in the past has been possible only with the use of simpler methods, including the use of weight coefficients for various purposes and the conversion of them into a just one objective function. But in recent years, with the development of multi-objective methods, there is a good way to solve them. In this regard, the purpose of the present study was to investigate the efficiency of multi-objective optimization algorithms MOPSO, SPEA-II and NSGA-II in the reservoir operation problem using LDR, N-LDR operation models to generate the optimal Pareto front in order to sustainable development. In order to obtain the mentioned purpose, First, the NSGA-II, MOPSO, and SPEA-II optimization methods were evaluated using some benchmark problems such as standard ZDT family functions with identical conditions (equal population number and number of runs). After evaluating multi-objective optimization methods using standard ZDT family functions, NLDR, LDR and SOP operation models were coded in MATLAB programming environment and linked with multi-objective optimization methods. For each of the two optimization-simulation models (LDR and NLDR), the two objective functions were defined as follows: the first objective function was to minimize the sum of the MSI and the second objective function was the reliability maximization that the maximum of which is usually obtained under the SOP operation conditions. It turns out the two aforementioned objective functions are have a reverse relationship with each other and by increasing one of them, the other one will decrease. Reservoir operation models for a 37-year period from 1356 to 1392 were executed to find the coefficients in both linear and nonlinear models in the same conditions for each multi-objective optimization algorithm with 5000 itrations. The optimal Pareto front was obtained. By addressing obtained results, It was observed the SPEA-II optimization method in NLDR operation model, has reached to the best optimal Pareto front among others. So from its three answers were selected (by using various criteria) as sample and then sustainability indices such as reliability, resilience, vulnerability and MSI were computed for those three answers. By comparing the values of objective functions and other sustainable development criteria in SOP conditions and the NLDR-C response, it can be seen that using the multi-objective optimization model, we can by less shortages (less MSI 21, 79 compared to 32, 29), reach to approximately maximum reliability (reliability in SOP conditions). However in NLDR-A solution, the least shortage (MSI equal to 13.02) can be seen compare to other sample solutions and SOP policy. Due to research findings, it was observed the SPEA-II optimization method in all of the standard ZDT family functions has reached to a more optimal Pareto front than other optimization methods. Also this method compared to other optimization methods, has a more complete front of Pareto's solutions, which indicates the efficiency of this optimization method in multi-objective optimization problems. In the case of LDR and NLDR models with the same number of iterations, also It was observed that the NLDR model has shown better results, which can be due to the higher degree of freedom of nonlinear relationship in determining the operation policy of the reservoir releasing. In this research, a series of optimal (Pareto optimal) solutions was presented to meet the stated objectives.

Due to the rapid rate of population growth, water resource topics wasmainly affected by the economic and social components, however, the importance of environmental issues in such projects has gained more attention. As pollution loads are increasing, it has become more essential to incorporate water quality in water resource management issues. Under this condition, optimal water allocation by considering multiple objectives of water quality and quantity issues can lead to sustainable and optimal benefit of stakeholders. This study was done in order to balance environmental and economic concerns in water resource allocation.
Based on game theory concepts and fuzzy programming procedure, two new methodologies were developed for sustainable water resource allocation in river systems. The proposed methods which include a multi-objective bargaining and fuzzy programming approaches were utilized to analysis strategies of interaction between environmental protection and economical income. Two groups of players, consists of player 1 for environmental and player 2 for economic issues were considered in order to apply the developed models. As players will not be satisfied with the outcome of each other, they will begin the bargaining process. Throughout the bargaining rounds, players will reduce their expectations. After several negotiations, the interval between the reset goal values and outcomes will be decreased. The bargaining process will be finished if final solutions reach to the determined goals. In the study, the Total Dissolved Solids (TDS) were considered as water quality indicators of environmental objective function, since salinity is the important problem of the study area. Using crop production function in economic income objective function makes it possible to incorporate deficit irrigation in different crop growth stages. Since allocation problems include many decision variables, conventional (non-linear) crop production function will have high computational costs and linear form of it can reduce the complexity of the optimization model. Therefore,additive (linear) form of crop production function was taken into consideration instead of multiplicative form. Total pollution load discharged into the river (ton per year) and economical income of the system (thousand dollars per year) wasconsidered as environmental and economic values, respectively. During the fuzzy programming procedure, the purpose is to achieve a compromise solution. In this approach, the individual maximum and minimum values of objectives is used to define the membership function. This procedure will maximize the satisfaction degree of the constructed membership functions of the objectives. The presented methodology was illustrated in a part of Karoon-Dez river system between Gotvand dam, Dez dam and Ahvaz city, as a case study. The area of Karoon-Dez river basin is about 67000 square kilometers and it is located in the southwestern part of Iran. The selected area includes 8 agro-industrial and 3 traditional agricultural sub-sectors.
Using a linear form of crop production function for calculating the total benefit of the system leads to significant reduction in run-time of the optimization model and make irrigation programming possible by regarding crop growth stages and the available water amount. The results of this study showed that Nash equilibrium, which provides a base for decision makers to choose a strategy, was reached at the fourth round of bargaining process. Moreover, balance between economic and environmental objectives is available by reducing economical expectation and environmental concerns from 553636 to 496216 thousand dollars per year and from 68264 to 87251 tons per year, respectively. In these cases, the annual allocated water to environmental and economical player will be 6123 MCM (5318 to agro-industrial sub-sectors and 805 to agricultural sub-sectors) and 6453 MCM (5730 to agro-industrial sub-sectors and 723 to agricultural sub-sectors) respectively. The results of the fuzzy programming approach demonstrated that at optimal condition, environmental and economic objective function was 85999 tons per year 500422 thousand dollars per year, respectively and allocated water to water users are 6354 MCM per year (agricultural and agro-industrial sub-sectors of the system will be (763 and 5591 MCM per year). Agro-Industrial sub-sector 3 will take the maximum allocated annual water (1789 MCM per year) and Agro-Industrial sub-sector 5 will receive the minimum annual allocated water (151 MCM per year). Comparison of two investigated approaches showed that their results are in agreement with each other.
Results of applying the developed methodology to the Karoon-Dez river system demonstrated that it is effective and applicable to determine sustainable water allocation policies. Finding of this study reveals that the proposed framework can facilitate decision-making process and optimize allocated water to different water users under conflicting objectives. Therefore, the developed procedure can be used as a managerial tool for optimal water allocation strategies, which is in accordance with sustainable development approach. It is easy to apply the presented methodology to other river systems with high pollution loads of agricultural return flows.

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.