Multi objective simulation–optimization operation of dam reservoir in low water regions based on hedging principles

The high level of reliability of water resources is always an advantage for consumers, but in arid and semi-arid regions where the inflow to the reservoir is faced with severe fluctuations, it makes sense to decrease the percentage of reliability of the system and allocate less water to consumption zones to prevent critical conditions such as emptying of the reservoir. In this research, the employed operation model is based on the simulation–optimization combination by considering the objectives of minimizing the violation of the allowed capacity of the reservoir and maximizing the percentage of supplying the demands. The optimal hedging variables are specified by linking the WEAP (Water Evaluation and Planning System) to the MOPSO multi-objective optimization algorithm. According to the available data, the duration of the simulation and optimization period in the model is 360 months. After 1000 iterations, the optimal reservoir volume values are obtained at the hedging level and hedging coefficient in different months. Finally, the model results are compared with the results obtained from the standard operation policy (SOP). The results show that the proposed model is able to manage the allocation to needs in the dry months and prevent the reservoir from emptying. Also, by storing a part of the flow in the reservoir in watery months and consuming it in low water months, it increases the supply of needs by 20 to 35% and reduces the failure rate in dry months.


Introduction
The issue of the operation of dam reservoirs, especially in arid and semi-arid geographical regions, has complexities in terms of decision diversity and their target functions. In such climates, the implementation of hedging policies to decrease severe stress during droughts via storage in the months prior to stress has been considered by researchers. Despite the capability of this approach to decrease the reliability of the system to supply demands and increase the number of failures in drought periods, it noticeably reduces the vulnerability (severity of deficiency during the failure period) of the system.
In this approach, serious damages to the whole system in dry periods are mitigated by decreasing the percentage of supplying of demands. Although this solution can lead to decrease the system reliability in supplying demands and increase the number of failures in the dry periods, noticeably decreases the system vulnerability (shortage severity during the failure period).
Applying the standard operation policy (SOP) is one of the most common methods when the goal is to minimize the total deficiencies during the operation period (Loucks and Van Beek 2017;Li et al. 2015). However, the utilization of the SOP in dry conditions leads to severe shortages and the occurrence of maximum vulnerability in the dry period. Therefore, the use of hedging rules is effective in drought conditions (Neelakantan and Sasireka 2015).
With the development of the structure of optimization techniques and the widespread use of meta-heuristic algorithms and the particle swarm optimization (PSO) method in particular, the optimal planning and operation of dam reservoirs have started a new stage as one of the crisis management solutions in low water areas.
Many studies have been conducted on the application of the PSO algorithm in different fields of water resources , Nagesh Kumar and Janga Reddy (2007), Izquierdo et al. (2008), Daraeikhahet al. (2009)). The PSO algorithm has been used in multi-dam systems and hybrid simulation-optimization structures as a single objective (Zhang et al. (2011), Vasan (2013) and Rafiee Anzab et al. (2016)).
The single-objective version of the PSO algorithm solves complex nonlinear, multimodal, and multi-objective problems as a sum of the objectives. Therefore, due to not considering the exchange and conflict between different goals, in the last iteration of the algorithm, it provides only one optimal solution. But the multi-objective particle swarm optimization (MOPSO) method causes conflicting goals to be evaluated separately. In the last iteration, instead of one answer, several answers are displayed on the Pareto curve. The implementation of each of these solutions has results commensurate with the expected goals of each user and tries to satisfy all involved parties to some extent. Therefore, this algorithm has been widely used in various fields of water resources.
The MOPSO algorithm uses the crowding distance function to select the best answers in each iteration. This function was first developed by Deb et al. (2002) in the NSGA-II algorithm structure.
Due to the fast performance of this algorithm in selecting superior responses in each iteration on the basis of the simultaneous evaluation of conflicting goal functions on the Pareto graph, this algorithm has received more attention from researchers than the usual PSO (Sen et al. 2017). In many recent studies, the MOPSO algorithm has replaced the PSO to solve complex problems of water resources with multiple objective functions (Rezaei et al. 2017;Mousavi et al. 2017;Xilin et al. 2019;Moghaddam et al. 2020;Rezaei and Safavi 2020). In this research, the MOPSO algorithm is used to optimize the system.
In the SOP method, the amount of water released from the reservoir is considered based on the amount of downstream needs and equal to it. In dry periods, when the reservoir is not able to fully meet the needs, it will inevitably meet some of these needs. The implementation of this policy reduces the overall shortage by increasing the total reliability, but the severity of shortages is high, especially during the low water months. This method is not efficient in dry periods and needs major modifications. One of the useful management strategies to improve the structure of reservoir operation in arid and semi-arid areas is to use the rules of reservoir hedging. Therefore, although in rainy months it is possible to release the flow to meet all the downstream needs, only part of the flow is released to meet part of the needs and another part is stored in the reservoir to meet the needs in drier periods. This method prevents the occurrence of possible severe shortages in future periods and reduces the vulnerability of the system, which is very important in terms of reducing social and economic consequences in arid and semi-arid areas (Draper and Lund 2004).
By implementing the hedging rules, the amount of water shortage is moderated over a longer period and the reservoir performance is improved, especially in dry and critical periods (Neelakantan and Pundarikanthan 1999;Shih and ReVelle 1994).
Extensive applied research in the field of water hedging and modification of reservoir operation structure has been done to improve the system performance and determine the optimal level and volume of hedging in the reservoir (Felfelani et al. (2013), Taghian et al. (2014), Azari et al. (2018), Bayesteh and Azari (2021), Jalilian et al. 2022).
The present study focuses on the reservoir zoning based on the hedging rules with the objective of the optimal operation of the reservoir utilization using the simulatoroptimizer coupled models(WEAP-MOPSO). The use of this method during the operation of the system reduces the failure intensity, especially in low water and dry seasons. The main objective of this study is to develop a hybrid method based on the zoning of the operation level of the reservoir in WEAP and use of multi-objective functions in the structure of the MOPSO algorithm in MATLAB. To apply the reservoir hedging rules in the body of the optimization algorithm, two parameters of the useful volume of the reservoir at the hedging level and the reservoir buffer coefficient (hedging percent) are defined as decision parameters in different months. This modern structure was developed to proper operation of reservoirs in low water zones and is evaluated in this paper. In this method, unlike the common planning structure in most low water areas (flow release based on the SOP), after identifying dry or low water periods in the MOPSO-WEAP coupled model, the optimal hedging rules are implemented in the model and the reservoir role curve is optimized. By utilizing this method in real-time reservoir operation, it is possible to calculate the hedging level, start time and volume of hedging in different months. Therefore, based on hydrological conditions of the basin and inflows to the reservoir and characteristics of the reservoir, by limiting the allocation of water in the wet months, some flow can be stored in the reservoir for downstream needs in drier months.

Study area
Ilam Dam is located in an arid and semi-arid region in Western Iran. The watershed of this dam is formed from three sub-basins including Golgol, Chaviz, and Ema. The main river entering the dam is the Konjan Cham dam, which includes the Chaviz and Golgol tributaries (Fig. 1). Ilam Dam is used for supplying the drinking water of the city of Ilam and the agricultural needs of Amir Abad and Konjan Cham farms. In the WEAP model, information and maps of the rivers, location of the hydrometric stations, location of the dams, and various uses are defined (Fig. 1).
The discharge values recorded upstream of Ilam Dam and close to the dam site for 30 years (360 months) are considered as the inflow to the system (from Oct 1991 to Sep 2021). To assess the efficiency of the reservoir during the 30-year period, two scenarios including reference (based on the continuation of the current operation) and optimal are considered. Time series of discharge data, values of agricultural, drinking and environmental uses, reservoir operation parameters, water withdrawal points, and other required information are imported into the model (Table 1).
The inflow values to the reservoir of Ilam Dam are calculated using the discharge values of the rivers located upstream of the dam at the Chaviz, Golgol, and Ema hydrometric stations and are defined in the model. The average discharge at these locations during the entire system simulation time-frame is illustrated in Fig. 2.
Water demands of lands downstream of Ilam dam (Amirabad and Konjan Cham plains) and part of drinking water required by Ilam city and downstream environmental needs are specified in the model. The monthly amounts of these consumptions are shown in Fig. 3.
To calculate the environmental demand of the river located downstream of Ilam dam, the Tenant method is utilized (Tennant (1976)). In this method, based on the fairly distribution of environmental water, 30 and 10% of the average annual flow, Monthly amounts of net evaporation from the dam reservoir surface are defined as one of the components of the reservoir water budget in the model (Table 2).

Model configuration and simulation
The WEAP model is used to simulate system performance. This model is used in many studies to simulate surface and groundwater systems (Zeinali et al. 2020a(Zeinali et al. , 2020bGoorani and Shabanlou 2021). In general, in the WEAP model, the first series of data required for the model includes general parameters such as the base year, the month of simulation start, and length of the planning period. The simulation period is considered to be about 30 years (from Oct 1991 to Sep 2021). The second series of parameters in the WEAP model includes time series parameters of hydrologically recorded data and information on monthly demands (agricultural, drinking and environmental demands), and information on reservoirs and places of withdrawal, coefficients, and required parameters, etc., which are mostly in the form of text files (CSV file) and according to the instructions for setting the input files are prepared and introduced to the model using the auto-call feature in the model functions section. The third series of parameters are the decision variables in the optimization process (hedging level and hedging coefficient) which are generated by the optimization algorithm.

Preparation of proposed simulation-optimization model
In this paper, in order to optimize the system, the MOPSO algorithm is employed. This algorithm is coupled with the WEAP model by utilizing a VBScript developed in the MATLAB environment. In the coupled model structure, in each iteration of the MOPSO algorithm, the decision parameters are imported to the WEAP environment as parameters of the reservoir operation. The WEAP model uses these variables and after zoning the reservoir applies the hedging rules for the optimal operation of the reservoir. After the implementation of the WEAP model, the results of the system simulation are brought to the environment of the optimization algorithm in MATLAB and these results are evaluated by the objective functions. If the objective functions are not satisfactory, new parameters are generated and the simulation-optimization cycle continues until the best response is achieved. After achieving the optimal solution in the last iteration of the algorithm, the final results are stored in both simulator and optimizer environments.

Multi-objective particle swarm algorithm
The particle swarm optimization (PSO) algorithm is one of the methods of swarm intelligence algorithms, which was introduced in 1955 by Kennedy and Eberhart to solve single-objective problems. In the PSO algorithm, each answer is considered as a particle that moves towards the optimal point based on the velocities of particles and the whole set in the decision space. The problem is being searched in the environment. The motion of each particle in this process is influenced by three factors: the current position of the particle, the best position the particle has ever reached (Pbest), and the best position that the best member of the set has ever reached (Gbest). In each iteration corresponding to each particle, a target function is  calculated. In the first iteration, the initial position of each particle is selected as Pbest and the particle corresponding to the best value of the target function is selected as Gbest. In subsequent iterations, if the value of the new objective function of each particle is better than the previous value, the position of the new particle is selected as Pbest, otherwise, the position of the particle in the previous iteration is known as Pbest. In the case of Gbest, a similar calculation is performed, except that this time a comparison is made between all particles of the set in all iterations. In the evolutionary process of this algorithm, each particle develops its social behavior according to the behavior of other particles and moves towards the optimal destination. The basic form of the PSO algorithm used by Kennedy and Eberhart in 1997 is in accordance with Eqs. (1) and (2). If in a next D problem we display the position of the ith particle of the population by X i = (x i1 , x i2 , … , x id ) T , the particle velocity by V i = (v i1 , v i2 , … , v id ) T and the number by n, then we have: Shihand Eberhart changed the above relations in 1998 to improve the convergence of the PSO algorithm as follows: where the parameter χ is called the shrinkage constant to control the size of the velocity, so that its large values increase the decision space, and vice versa. c1 and c2 are fixed and positive coefficients called weighting factors and are usually considered to be between 1.5 and 2.5. The larger the value of these coefficients, the faster the convergence, and vice versa. r1 and r2 are random numbers with uniform distribution in the range (1, 0). The parameter w is named the weight of inertia, which controls the effect of previous velocities on the convergence of the algorithm and establishes a balance between the optimal general and local values. In other words, it can be said that convergence strongly depends on this parameter, and the higher the parameter w, the higher the overall search, and on the other hand, as the value decreases, the local search volume increases. The value of w in each iteration is calculated according to Eq. (5): (1) V n+1 id = V n id + c 1 r n 1 pbest n id − X n id + c 2 r n 2 gbest n [w.V n id + c 1 r n 1 pbest n id − X n id + c 2 r n 2 gbest n d − X n id (4) X n+1 id = X n id + V n id (5) w= w max − (w max − w min ) × n Iter max where W max is the weight of inertia at the beginning of the search, W min is the weight of inertia at the end of the search, n is the current number of iterations, and Iter max is the total number of iterations. Also, to prevent divergence of the PSO algorithm, it is necessary to limit the final particle velocity value to the range [− Vmax, Vmax]. The MOPSO algorithm was later developed based on its one-objective structure. A multi-objective function is employed to evaluate the quality of the answers in each iteration of the optimization algorithm. The first objective is to maximize the percentage of supplying all needs of the system and the second goal is to minimize the penalty for violating the allowed capacity of the reservoir through the entire operation time frame.

Objective functions
1.-Maximizing the total coverage percentage for all system needs The structure of the MOPSO algorithm used in this research has been developed to find the values of the minimum objective functions. Therefore, Eq. (6) is rewritten as Eq. (7): In this formula: COV zdt : Percentage of supplying the demand d in the zone z in each of the periods t TDW zdt : Total water supplied to the demand d in the zone z in each period t MD zdt : The amount of water required for the demand d (the amount of water needed for the demand d) in the zone z in each of the periods t 2.-Second Objective: Minimizing the amount of penalties due to violation of the authorized capacity of the reservoir: where: S tR : The amount of water storage volume in the dam reservoir R in each of the periods t (6)  In the body of the MOPSO algorithm, the number of decision variables is 24. There are 12 variables related to the reservoir volume at the gedging level and 12 variables related to the coefficient or percentage of hedging which are defined in the system on a monthly basis. To evaluate the performance of the system, two managerial scenarios comprising the reference scenario (RS) (the continuation of the current situation) and the optimal scenario (OS) are considered. The results obtained from each of these scenarios are compared for the entire operation period.
In the RS, the operation years based on the current situation are from October 1990 to September 2019. The SOP operation method is used. The priority of allocation for drinking, environment and agriculture is considered as numbers 1, 2 and 3, separately. The OS is defined based on the RS and the number of operation years, allocation priorities, and the inflow to the system are taken into account in the same way. In this scenario, to optimal (9) TAW tzs = RS tzs , t = 1, … , m × y, z = 1, … , nz s = 1, … , ns (10) operate the system, the optimized values of the hedging level and the hedging coefficient in different months are employed.

Results and discussion
The system optimization is obtained by considering the particle population equal to 48 and the implementation of the MOPSO algorithm up to 1000 iterations and the set of optimal solutions in the last iteration. Other parameters such as c1r1 and c2r2 coefficients are considered equal to 1.5 and 2, respectively, for better convergence of the algorithm. The last solutions are shown on the optimal exchange curve of goals (Pareto graph1) between the goals F 1 and F 2 (Fig. 4). In the MOPSO algorithm, similar to NSGA-II, in each iteration, the best responses are chosen based on the Crowding-Distance function and stored as the Pareto front to move to the next optimization stage. The points shown on the Pareto front are a set of 24 optimal solutions extracted by the algorithm, and the axes of the Pareto graph represent the target functions F 1 and F 2 .
By selecting answer number 1 from the set of answers shown on the Pareto front, the values of the coverage and penalty functions will have the lowest and highest amounts, respectively. Therefore, this answer is desirable in terms of the first objective function, but is undesirable considering the second objective function. Answer number 24 is a good answer in terms of the penalty function, but it is undesirable considering the coverage function. Therefore, according to the values of the objective functions, the answer that has the most desirable value for both objective functions in comparison with other answers is chosen as the best solution. In this research, according to the Pareto Fig. 4 Pareto curve (Pareto front) at last optimization iteration graph, answer number 16 has this feature and is considered as the best answer. The optimal decision parameters resulting from Solution 16 are entered into the WEAP model and the system behavior under this solution is analyzed. The values of the reliability of providing the needs and the percentage of supplying the demands of each of the different uses in the RS and OS are shown in Figs. 5 and 7. Figure 5 shows that in the RS, the needs of Konjan Cham and Amirabad have the lowest amount of reliability (about 87.5 and 90.8). The reliability of these needs in the OS is about 80 and 82.5%, respectively. The reason for the decrease in the reliability of meeting the needs in the implementation of the OS is the application of the reservoir hedging rules. According to the hedging policy implemented in the optimization scenario, only part of the downstream needs are released through the wet months and the other part is stored in the reservoir to be released during the dry months. This method increases the level of providing the demands in the low water and critical months and prevents the occurrence of months with a percentage of supply close to zero. This policy decreases the level of providing the needs in the wet months and to some extent reduces the overall reliability of all uses, but due to the increase in the supplying percentage in critical periods (dry and low water seasons), the duration of failure period and the severity of failure in these months are mitigated to prevent the social and economic consequences of severe water shortages.
According to Figs. 6 and 7, in the OS with the implementation of solution number 16, due to the implementation of reservoir hedging rules, the level of providing the needs in dry periods compared to the RS has increased to some extent. In this scenario, due to the hedging policy, the number of months with zero supply has been reduced and heavy failures (failure intensity) in dry and low water months have been reduced. This achievement prevents heavy economic and social losses to the whole system during these months. The results demonstrate that in the OS, the average level of providing the needs in September and October is 81.1% and 81.4%, separately. The demand-supplying percentage in these months in comparison with the RS are improved by 3 and 4.4%, respectively. During the operation time, the optimization algorithm has the best performance in increasing the percentage of providing the water demands of low water months to prevent a complete breakdown in these months. The findings show that the method developed in this research, in addition to maximizing the supply percentage, especially in the dry months, by properly implementing the hedging policy prevents the emptying of the reservoir in such months.
Changes in the water volume stored in the Ilam Dam reservoir during the 360-month operation period are shown in Fig. 8. Figure 8 displays that in the optimization scenario in wet months, some of the inflow is stored in the dam reservoir to be released in dry months. Also, considering the penalty for violating the permitted capacity of the dam in the second target function prevents the reservoir from being emptied and the water level in the reservoir may not be lower than the minimum operation level. According to Fig. 8, in the RS, due to the use of standard operation policy, the water level in the reservoir during the 360-month operational period in many low water months reaches the dead level of the reservoir. But in the OS, due to the implementation of the hedging rules, in the whole system operation period, the reservoir water level never reaches the dead level.
The results show that due to the implementation of the optimization scenario, during the 360-month planning period, except for a few months, the water level in the reservoir is not fallen below the minimum operation level of the dam. This method leads to better and more principled management of the reservoir in severe drought conditions. The implementation of the water hedging policy with the help of the optimization algorithm in arid and semi-arid areas, in addition to achieving the desired and acceptable reliability, reduces the number of months of failure and the severity of failure in such months in periods of severe water shortage. This is well proved in the Ilam Dam reservoir using the coupled simulator (WEAP) and optimizer (MOPSO) and determining the optimal values of the hedging parameters. Utilizing this technique, by zoning the reservoir on the basis of the hedging policy, the dam role curve can be optimized in dry and low water areas.

Conclusions
In this research, by linking the MOPSO multi-objective algorithm and the WEAP simulation model, a new method was developed to manage the reservoir operation in arid and semi-arid regions. This approach, by applying the reservoir hedging rules, has a good capability and efficiency in finding optimal solutions and extracting the optimal role curve for the principled release of flow from the dam reservoir. The results showed that by optimizing the system and extracting the optimal variables of the reservoir hedging, as well as maintaining the reliability of the system within an acceptable range, the level of providing most demands, especially in dry and low water periods, increases in comparison with the RS. The utilization of this structure causes in addition to the operation of the reservoir with the minimum penalty due to violation of the allowed capacities, the duration of the failure period and the severity of failure in low water and dry seasons to be significantly reduced. The method developed in this research can be used to extract the optimal role curve for the principled operation of reservoirs in dry climates. The superiority of this method over other optimization models that do not consider the hedging policy is that by storing part of the flow in wet months and releasing it in dry months, it reduces the shortage in these months and also prevents the water level in the reservoir from reaching the dead level during the whole operation period. It can be said that in water resource operation systems, a high percentage of reliability alone cannot indicate the desirability of the system performance. Because the reliability equations are calculated based on the number of months with fully demand supply and do not pay attention to the amount of shortage, duration of the failure period and severity of failure in drought and water shortage conditions. The results of this study showed that in low water and dry regions, it is possible through flow release management under the hedging policy as well as maintaining the system reliability in an acceptable range with less water allocation to downstream uses in wet months and storing part of the flow in the reservoir to prevent sequence and severe failures and emptying the reservoir in low water years. In order to apply these solutions and implement the hedging rules in low-water areas, it is necessary to control the river withdrawal by local managers by establishing a cooperative of water users and defining the authorized water supply. The solutions proposed by the optimizer model can be implemented by installing instrumentation and Data Logger at the beginning of water withdrawal canals and water withdrawal sites from the river. Penalties should be imposed on local managers who exceed water withdrawals to support the implementation of these solutions.
Author contribution All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Sedighe Mansouri, Hossein Fathian, Alireza Nikbakht Shahbazi, Mehdi Asadi Lourm, and Ali Asareh. The first draft of the manuscript was written by Hossein Fathian and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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