Comparative study of reservoir operations using TLBO, PSO and DE optimization techniques: an experiment on the Hirakud reservoir, Odisha, India

Water resource management is a vital part of hydrology dealing with socioeconomic aspects. In the upcoming decades, the effects of climate change on the temporal and spatial variability of precipitation may significantly diminish the availability of water (Rocha et al. 2020). It is anticipated that the effect of climate change on the temporal and spatial variability of river water supply may result in less water available for agriculture, hydropower generation, industrial use, etc. (Orkodjo et al. 2022). In this scenario, it is crucial to manage the limited water resource from the accessible storage reservoirs, particularly in the non-monsoon season for many uses like industrial, hydroelectric and agricultural purposes. Thus, controlling a water reservoir to function during the non-monsoon season is a critical concern for all stakeholders involved. Controlled discharge of water from the reservoir for water supply, irrigation and hydropower demand is a difficult task during the non-monsoon compared with the monsoon period. Under climate-change scenarios, to enhance the management of reservoirs in water-scarce locations is to create a novel method of reservoir management based on rule curves and dynamic evaluation of water demands (Beça et al. 2023). A flexible reservoir management system, along with a reduction in water usage and losses from reservoirs, can help achieve good resilience to climate change (Aibaidula et al. 2023).

However, with climate change, managing reservoir water is a highly challenging issue, because it is intended to serve a variety of purposes, such as meeting non-monsoon demands (irrigation, hydropower, etc.) and the monsoon demand (lowering the risk of flood). Hence, reservoir operation is made more difficult to address these goals (Badr et al. 2023).

Therefore, optimization techniques are necessary to facilitate the planner and stakeholders appropriately in handling the operation of multipurpose reservoirs. More study needs to be done on optimization strategies because classical models, LP (Linear Programming), NLP (Non-Linear Programming) and DP (Dynamic Programming) have certain limitations. They are complex and hard to implement effectively, can only find a local optimum and may be vulnerable to numerical noise. They struggle to solve discrete optimization issues. As the problem size and dimensionality rise, they could become too big and complex to handle successfully. LP is unable to manage constraints with non-linear relationships, while NLP often yields a ‘local optimal solution,’ and DP suffers from the ‘curse of dimensionality’.

In the current decade, substantial research has been done using optimization techniques to establish optimal and suitable reservoir-operating policies (Lai et al. 2022). Researchers have used metaheuristic algorithms (MHAs) to optimize reservoir operation. Different MHA-based optimization schemes, such as evolutionary-based CRO (Coral Reefs Optimization), swarm-based PSO, human-based TLBO, bio-based IWO (Invasive Weed Optimization) and DE (Differential Evolution) algorithms, have been developed (Nguyen et al. 2022).

Of different techniques, Afshar (2012) used partially constraint-based PSO and fully constraint-based PSO in the Dez reservoir located in Iran and the outcomes so obtained were compared with GA and unconstrained PSO. The approaches were able to locate near-optimum solutions and convergence characteristics better than the original PSO and genetic algorithm (GA). Bashiri-Atrabi et al. (2015) used the Harmony Search Algorithm (HS) for the Narmab reservoir, Iran, and found encouraging outcomes compared with other methods like Honey-Bee Mating Optimization (HBMO) and a global optimization model (LINGO 8.0 NLP solution). Asgari et al. (2015) used the Weed Optimization Algorithm (WOA) for reservoir operation and compared it with GA and found that WOA had quick convergence toward the solution and the result was nearer to global optimal solutions than GA. According to Wan et al. (2018), PRA-PSO, which combines the PRA (Progressive Reservoir Algorithm) with the PSO, was superior to PSO and EMPSO (Elitist Mutated-PSO). Chen et al. (2020) used PSO combined with the ARIW (Adaptive Random Inertia Weight) approach known as ARIW-PSO and the results were superior to that of PSO and GA in flood control operations. Sharifi et al. (2021) introduced five algorithms in the Halilrood multi-reservoir system, Moth Swarm Algorithm (MSA), Seagull Optimization Algorithm (SOA), Sooty Tern Optimization Algorithm (STOA), Tunicate Swarm Algorithm (TSA) and the Harris Hawks Optimization Algorithm (HHO) for improving the operation policy of the reservoir. Motlagh et al. (2021) used GWO (Grey Wolf Optimization) for water allocation in Taleghan dam and compared the result of optimal water allocation with the GA and found that GWO was superior. Lai et al. (2022) investigated the effectiveness of the combination of three unique MHAs: the WOA (Whale Optimization Algorithm), HHO (Harris Hawks Optimization) algorithm and LFWOA (Levy-Flight WOA) and it was found that the HHO offered the best performance.

Mezenner et al. (2023) used Principal Components Analysis-based simulation models and GA to lower the water deficit by optimized reservoir operation. Beiranvand & Rajaee (2023) used the WCA (Water Cycle Algorithm) and Dash et al. (2023) used the SWAT-HEC-ResSim-GA model to enhance the performance of the Eyvashan reservoir and Kangsabati reservoir, respectively to take into account the uncertainty of future supply and demand under a climate-change scenario. In Feizi et al. (2024), the efficacy of the DE, GA and TLBO algorithms was compared to determine the best way to operate the Mahabad dam reservoir. The results showed that DE performed better than the other two.

Shared-type and independent-type rule curves were the two main forms that were analyzed and compared using the parameter-simulation-optimization framework, which specifically used the NSGA-II algorithm (Tang et al. 2024).

From the various works, it was found that the majority of the works primarily concentrated on developing an optimization model for the monthly operation of the reservoir for the entire year. Since the release rule for a multipurpose reservoir differs for the monsoon and non-monsoon periods, in this work an attempt was made to develop a release rule for the non-monsoon period using available data on a ten-day basis. An expert committee constituted for the optimal operation of the Hirakud dam reservoir devised a rule curve in 1988 which time and again has been, especially, used for the monsoon period (June to October). The operation during non-monsoon is completely heuristic for which in many years either there is a surplus or deficit toward the end of the non-monsoon season. This is revealed if we go for the status of the reservoir in the year 2024 in which there is a surplus amount of storage at the end of the non-monsoon period resulting in the loss of valuable stored water, whereas for several years, there has been a deficit resulting in the distress of populations due to non-production of hydropower and scarcity in supply to industry and irrigation. Due to various limits, such as the construction of multiple barrage systems in the upper Mahanadi Basin and water disputes among the states of Odisha and Chhatisgarh (Rath 2019), the existing rule curve is unable to meet the water demand during non-monsoon. This scenario urgently necessitates the development of a rule curve which will guide engineers to reap optimal benefits for the Hirakud dam reservoir during the non-monsoon season. This concept is one of the innovative contributions to the optimal use of reservoir water. The use of a supercomputer to devise the operational guideline with a short-term flow forecast saves a lot of computational time. The PARAM Shavak supercomputer, a small, affordable and customized supercomputing system that provides a ready-to-use supercomputing-in-a-box solution based on commercial off-the-shelf HPC hardware resources was used to simulate the optimization models. The computational times for one iteration using TLBO, PSO and DE are 2 min 02 s, 2 min 17 s and 2 min 56 s, respectively, on the 64-GB RAM, Ubuntu operating system and 28 logical core processor PARAM Shavak supercomputer. In contrast, developed programs are executed on a 4-GB RAM, 64-bit operating system, quad-core processor and the computational times for one iteration of TLBO, PSO and DE are 40 min 12 s, 45 min 23 s and 48 min 78 s, respectively.

From an extensive survey of the literature, it is revealed that the operation of dam reservoirs is done using various metaheuristic methods. The characteristics and objectives differ greatly across reservoir systems. Therefore, there is not a specific algorithm that needs to be used to run the system. The objective function, limitations, data accessibility, system features and other factors influence the solution model. Although many metaheuristic optimization techniques have been developed and applied on different reservoirs, in this study, three optimization metaheuristic techniques, PSO, TLBO and DE have been experimented with because in each algorithm the common parameters, such as population size and number of iterations, are required to be updated. Other evolutionary algorithms require the control of common parameters and the control of algorithm-specific parameters. In contrast to other heuristic algorithms, the TLBO algorithm is straightforward, easy to explain and simple to apply. The TLBO algorithm also exhibits strong robustness in optimization problems, good convergence performance, high accuracy and fewer parameters. As a result, in recent years, professionals and academics have given it a lot of attention. Not only has the TLBO algorithm been extensively enhanced but it has also seen widespread use (Xue & Wu 2020). Hence, based upon the above facts, the experimentation was done to evaluate the non-monsoon performance of the Hirakud reservoir using TLBO and comparing it with DE and PSO. Using this more efficient and suitable metaheuristic technique for water reservoir management, befitting the given multipurpose project under consideration, reservoir managers/engineers will be better equipped to optimize the benefits from the water released for different objectives, thereby reducing the expenditure and risk of surplus or deficit of supply. Most importantly, the major multipurpose reservoirs are managed by government bodies, in which transfer and superannuation/retirement is a frequent phenomenon. If an expert reservoir manager is retired or transferred to a different location, a vacuum is created if sufficiently trained persons are not in place. In such cases and in general, these metaheuristic techniques will provide suitable guidance for the reservoir operation at times when expert presence is a must but it is not available.

The details of the Hirakud dam and Hirakud reservoir are presented in Table 1. There are two powerhouses for this project: one at Chipilima, which is located 22.5 km downstream of the dam and the other at Burla, which is on the dam's right bank toe, with a total installed capacity for hydropower generation of 307 MW.

Additionally, this project protects 9,500 sq km of the delta of Mahanadi in the Cuttack and Puri districts from flooding. The maximum discharge at the Mahanadi delta head is limited to 26,897 cumecs (9.5 lakh (×10⁵) cusecs), excepting extreme emergencies, which is based on the regulation of the discharge through the Hirakud dam. The existing rule curve (graph between storage levels with respect to time) was created by a committee of the Central Water Commission convened in 1988 to control flooding during the monsoon and maintain reservoir operation (irrigation and electricity generation) after the monsoon. In accordance with the existing rule curve, the reservoir's storage level must be close to the dead storage between 1 July and 1 August or between 179.8 and 181.4 m (Supplementary Information, Figure S1). This will make flood protection easier; if there is a significant inflow into the reservoir, water can be held and released in a controlled manner.

In Equation (1), is the inertia weight, and are the PSO's social and cognitive parameters, respectively s, x is the constriction coefficient, are the decision variables, the index of best particle among the entire population is represented by g, Δt is taken as the time step (considered as 1) in the equation, n is considered as generation number, and represent uniformly produced arbitrary values within 0–1 and the index for the particle swarm population is represented by⁠, = size of particle swarm. The detailed flow diagram and pseudo-code of the algorithm are given in the Supplementary Information (Figures S2 and S3).

The TLBO algorithm (Rao et al. 2011; Satapathy et al. 2013) is inspired by the teaching–learning process in class, (i) via teacher guidance (referred to as the teacher phase) along with (ii) through peer interaction between learners (referred to as the learner phase).

In this step, teachers attempt, to the best of their abilities, to raise the class mean in the subject they are teaching. Assume there are m subjects (i.e., design variables) and n learners (i.e. represents the size of population) at every iteration i. represents the average result of the learners in a given subject, where j varies from 1 to m. The overall best solution, considered as taking into account each and every one of the subjects collectively achieved in the whole population, can be used to determine the best learner as⁠.

and r_i is an arbitrary number ranging from 0 to 1.

No algorithm-specific control parameters are needed for this algorithm; the only universal control parameters are the population size n and number of iterations⁠. The flow diagram and pseudo-code of the algorithm are given in the Supplementary Information (Figures S4 and S5).

The DE is a population-based algorithm and employs operators, such as crossover, mutation and selection, much like genetic algorithms. The search is directed toward potential locations in the search space through the algorithm using selection and mutation operations (Vasan & Raju 2007). The recombination (crossover) operator successfully rearranges information regarding successful combinations by building trial vectors from the elements of the current population, searching for an improved space of solution. An optimization assignment with D parameters can be presented through a D-dimensional vector. First, a population of NP solution vectors is generated at random. A general procedure and pseudo-code of the algorithms are given in the Supplementary Information (Figures S6 and S7).

The governing equations for the entire algorithm process are as follows.

Initial parameter values for every parameter by lower bound and upper bound are typically uniformly selected at random within the interval [⁠,].

In the above equation F is a scaling factor regarded as a constant, whose value varies from 0 to 2.

is a random integer from (1,2,…, D) with where D is the dimension of the solution or the number of control variables. It is guaranteed by that ⁠.

The trial vector and the target vector are compared and the vector with the higher fitness value is promoted for the following iteration.

All three processes – mutation, recombination and selection – are maintained until the stopping point is reached.

Three objective functions make up the problem's overall goal function: maximizing power production, minimizing industrial water demand deficit and minimizing irrigation demand deficit.

Different constraints for the above objective function are storage constraints, release constraints for irrigation, power and industrial along with canal capacity constraints. The net storage of a reservoir at each time step is influenced by inflow, outflow and total losses (evaporation and seepage losses) that occur in the reservoir system (Chaudhuri 2018). All data were taken on ten-day basis.

Rainfall, runoff, reservoir capacity, inflow, industrial demand, municipal water supply demand, evaporation, irrigation release, power release data, spill and surplus of reservoir, power generation, downstream water demand, reservoir level, rule curve, canal carrying capacity, reservoir storage (dead storage, live storage, maximum storage level, minimum storage level), power capacity, turbine capacity, reservoir level, tailwater level and annual average yield were collected from the Water Resources Department, Secha Sadan, Bhubaneswar and the Office of the Basin Manager (Chief Engineer), Upper Mahanadi, Burla. The data were collected on a ten-day basis from the year 1990 to 2016 and the statistics are given in Table 2. Table 2 shows that the average inflow value to the reservoir is approximately 815.71 MCM, while the average outflow value is approximately 815.415 MCM. Based on these observations, it is possible to forecast that the average inflow value will be higher than the average outflow value (the average outflow value is the sum of average irrigation, power, evaporation and spillway). Kurtosis shows how much data are contained in the tails. It appears that the tails are drawn closer to the mean in distributions with a high kurtosis because they contain more tail data than normal distributed data. There are fewer tail data in distributions with low kurtosis and the bell curve's tails appear to be pushed away from the mean. A distribution is considered platykurtic if its kurtosis is negative, indicating that its tails are thinner and its peak is flatter than in a normal distribution. This only indicates that a greater proportion of data values are found close to the mean and a lower proportion are found near the tails. So from the statistics table, it is found that irrigation and power release data produce negative kurtosis. The difference between data points and the mean is measured by variance. As per the source, the variance is the extent to which a collection of data or numbers deviates from its mean or average value. Finding the expected difference in variation from the actual value is known as variance. If the data are more dispersed from the mean, the higher the variance value, and if the variance value is small or zero, the data are less dispersed from the mean. So, it is found the inflow data and outflow have greater variance than the others and irrigation release has the least variance from the rest of the data series. The level of asymmetry shown in a probability distribution is known as skewness. A bell curve is skewed when its data points are not equally distributed to the left and right of the median. Distributions may be left- or right-skewed, positive or negative. A negatively skewed distribution, sometimes referred to as a left-skewed distribution in statistics, is a distribution type in which the left tail of the distribution graph is longer and more values are concentrated on the right side or tail of the distribution graph. The table shows that irrigation release is negatively skewed. Also important in statistics is the degree of data dispersion with respect to the mean, expressed as a standard deviation. Data with a small standard deviation are closely grouped around the mean, whereas data with a large standard deviation are widely dispersed. From the statistics, it is found that inflow has more standard deviation and irrigation release has the least standard deviation.

The target function for monitoring irrigation, hydropower generation and industrial release is formulated using Equation (15). Three constants — ⁠, ⁠, and — are employed in the objective function depending on the priority of the objectives. Numerous combinations are examined and explained below to obtain the precise values of ⁠, and _, as shown in Table 3. To determine the final values that would give the best release for industries, power production and irrigation, a variety of trial values for⁠, and were obtained.

The optimum values declined after = 0.5, = 0.4 and = 0.1 values. Because irrigation is prioritized above hydropower generation along with industrial release, a constant weight of 0.5, 0.4 and 0.1 is assigned to irrigation release, power generation and industrial release, respectively. Using DE, PSO and TLBO, tests are carried out to determine the ideal release values. The results of the experiments are presented.

DE depends on three factors at first: the iteration number, the lower and upper bounds of the scaling factor F (beta_min and beta_max) and the probability of crossover (pCR). The two control parameters, the crossover rate (pCR) and the scaling factor (F), are essential for maintaining the right balance between the exploration and exploitation processes. The parameter pCR is responsible for the perturbation in the new solutions, whereas F is responsible for the step size throughout the solution search.

The first three parameters are arbitrarily defined. The optimal values are obtained by varying the values of beta_min, beta_max and pCR. Water releases for industry, power and irrigation are calculated for various values of beta_min, beta_max and pCR (million cubic metres), respectively and the efficiencies (in percentage terms). The results obtained using DE for various demands and corresponding efficiencies for the current study with the varying scaling factor F (lower bound as beta_min and upper bound beta_max) are given in Table 4 . The pCR value was taken as 0.2 for the whole iteration process. The parametric variation and corresponding efficiencies for various releases are given in the Supplementary Information (Figures S8, S9 and S10).

The best outcome is achieved by applying 0.8, 0.2 and 0.2 respectively, as the scaling factor's upper bound, lower bound and crossover probability. The range of its fitness value is 201.419–7.791. Its fitness value converges to 7.791 after the 110th iteration.

The variation in the production of hydropower during the non-monsoon season between 2000 and 2016 is shown in Figure 3(b). The simulation period was taken as 27 years for 1990–2016 on a ten-day basis (Supplementary Information, Figure S12). Here, the powerhouse's installed electricity generation capacity is 235.5 MW. The storage can also be used to generate electricity if it is at a dead storage level. Because less water is available in the reservoir before the advent of monsoon, less power is generated in May and June. However, the reservoir fills up completely in October, and because of the high reservoir level, more electricity is generated during that period.

The industrial release for operations on a ten-day basis through the non-monsoon period of 1990–2016 is given in the Supplementary Information (Figure S13). Figure 3(c) represents the industrial release for the non-monsoon period from 2000 to 2016. Consequently, the provision of water to industries is given increasing importance. The industrial release is almost approximately the same every month as demand is taken as constant for the entire monsoon period, but it is slightly less in June as in the data period taken up to 20 June in every year the reservoir is at the dead storage level.

Initially⁠, the personal learning coefficient and⁠, the global learning coefficient along with the number of iterations are selected at random. The maximum of optimality can be obtained by periodically varying the values of and ⁠. Table 5 shows different values of the coefficients and and different releases for various demands and corresponding efficiencies using the PSO algorithm. From the datasets for and ⁠, maximum release and corresponding good efficiencies for different releases are achieved for the values and ⁠. So, using these two parameters, and further iterations were done to get the best fitness value for the optimization problem. The sensitivity analyses for PSO for various releases are given in the Supplementary Information (Figures S14–S16).

Initially, the number of iterations is selected at random. The maximum optimality can be periodically achieved by altering the iterations. Water release for industry, power and irrigation was calculated for several iterations (measured in million cubic metres) and the related efficiencies were established. From Table 6, it is observed at the 300th iteration the efficiencies for irrigation, power generation and industrial release are greater and after that the value remains constant with further increase in the number of iterations. The graphical variations of efficiency with iterations for TLBO are given in the Supplementary Information (Figures S17–S19).

In Tables 7–9, the comparative study results of irrigation release, power generation and industrial release are shown for the Hirakud reservoir system from year 1990 to 2016 during the non-monsoon season using DE, PSO and TLBO techniques for ten-day time-steps. From the tables, it is observed that release for irrigation can be obtained up to 137.26 MCM using TLBO, which is approximately equal to the maximum demand of 138 MCM.

As a result, compared with policies made using other techniques, the strategy produced by this method is better. The target is kept so that the water level in the reservoir will reach up to dead storage level to accommodate the high inflow during monsoon. Based on that, the release rule applied for ten-day basis time-steps is obtained and presented in Table 10 for the non-monsoon period.

Table 10 illustrates the release policy which will ensure that the reservoir's water is optimally released for irrigation, hydropower generation and industrial use during the non-monsoon period and which will also ensure the end-of-season reservoir water storage. The adoption of this policy and its intermittent upgrading every five years or so will help the reservoir managers/engineers to operate the reservoir with more confidence as the present heuristic operation based on experience may be possible only for a few persons who may not be available for all time to come or at the time of need as the major multipurpose water reservoirs in India are state-owned and the transfer and superannuation of engineers are obvious.

The experimentation on the Hirakud reservoir has proved that the TLBO technique gives better solutions for non-monsoon seasons. The results obtained in the process revealed that irrigation release from the reservoir as suggested by DE, PSO and TLBO is 132.13, 134.30 and 137.26 million m³, respectively; hydropower to be generated is 187.33, 189.52 and 207.32 MW, respectively; and the industrial releases are 73.175 million m³, 78.481 million m³ and 82.156 million m³. The irrigation release efficiency is 95.7%, 97.3% and 99.5%, respectively; the efficiency of hydropower generation is 98.5%, 98.9% and 99.6%, respectively and the efficiency for industrial water release is 86.1%, 92.3% and 97.0%, respectively. The techniques used in this research work should not be used for other reservoirs but can be extended to derive release or operation policies of different reservoirs while taking into account the unique characteristics of those reservoirs. All other reservoir constraints such as maximum and minimum storage constraints, outflow constraints and all indicators of reservoir performance will also be the scope of further work. The weekly/ten-day reservoir operation strategies that were designed for this study can be used to derive daily reservoir operation during the non-monsoon season.

No funding was provided for this research from any Institute or Organization.

Every author agrees to take part in this activity.

Every author agrees to publish.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.