Optimal operation of reservoir for sustainable water management using multi-criteria decision-making approach Open Access

Water scarcity in cities is a major challenge due to limited resources, pollution, and increasing demand due to industrial growth, population, and living standards. Unequal distribution of water resources leads to disputes and calls for resource optimization. Because they store and redistribute available natural resources, reservoirs are crucial to the development of water resource systems. The decision-making process for managing water in multipurpose reservoirs is complicated and involves many goals that are frequently at odds with one another and suggest rivalry between stakeholders and water users. Therefore, the optimal allocation of the available water to various sectors/functions from the reservoir is crucial as it requires performing multiple functions simultaneously. It depends upon various social, economic, and environmental factors, among others.

In recent years, multi-objective algorithms have been used for optimizing multi-reservoir systems due to their great efficiency and rapid convergence. However, every reservoir has different problems and objectives, which pose new challenges for optimal reservoir operation.

Over the years, there has been extensive research on reservoir operation optimization using conventional and evolutionary methods. The conventional methods included research on problem statements using linear programming (LP), non-linear programming, and dynamic programming, which have proven to be useful in solving different optimization problems by being stable and derivative-based. However, these standard methods suffered from various disadvantages: limited exploration, certain types of objective functions, the complexity of the problem, and others (Lai et al. 2021). In recent decades, researchers have come across numerous meta-heuristic algorithms (MHAs) inspired by natural systems. These MHAs can be divided into three distinct categories, viz. evolution, physics, and swarm intelligence. Among them, multi-objective genetic algorithms (MOGAs), being the evolutionary algorithms, have proved well suited to solving reservoir operation problems of complex systems owing to their faster convergence and diversity of solutions (Wang et al. 2022). Numerous researchers have used different variants of genetic algorithms for optimization. Wardlaw & Sharif (1999) proposed a simple genetic algorithm (GA) to evaluate different formulations for reservoir systems to be used in real-time operations. Several researchers continued studying and exploring the model in this field, such as Jothiprakash & Shanthi (2006), Reddy & Kumar (2006), Cheng et al. (2008), and many others. Chen et al. (2016) proposed a computational strategy involving the parallel populations concept with a non-dominating sorting genetic algorithm (NSGA II), which enhanced the quality of the solution concerning convergence and diversity. Heydari et al. (2016) used NSGA II to solve the optimization model for two reservoir systems, and considerable decisions on the problem were taken. Later, Dai et al. (2017) used NSGA II for modeling reservoirs using Pareto optimal solutions. The results indicated that the model had the potential to improve the comprehensive benefits of the reservoirs. Another application of NSGA II was presented by Hojjati et al. (2018) for optimal reservoir operation to maximize power generation and flood control capacity. Also, the results were compared with the multi-objective particle swarm optimization (MOPSO) model and were found to be superior with better convergence. Furthermore, Wang et al. (2022) represented three variants of GA, NSGA II, NSGA III, and Reference Vector Guided Evolutionary Algorithm (RVEA), for the optimization of a multi-reservoir system. The results emphasized the significance of selecting the appropriate algorithm for the given problem. Chen et al. (2017) proposed an improved NSGA III to optimize flood control operation and it was found that the model produced well-distributed Pareto optimal solutions. Another application of NSGA III was used by Ni et al. (2019) to analyze power generation, flood control, and ecological maintenance. Non-inferior scheduling strategies were obtained with better convergence and more uniformity. Later, Zhang & Huang (2021) applied NSGA III to optimize the flow and water level of a river basin to restore ecological health. Dabral et al. (2024) employed Metaheuristics algorithms – GA, NSGA II, NSGA III, and Eps MOEA – to optimize the objective function for maximization of storage along with a different set of constraints and performed sensitivity analyses on all algorithms to calibrate different evaluation parameters. So far, NSGA III has been widely applied in the field of water resources. Besides, in recent years, numerous research studies has been conducted on complex reservoir operations employing MOPSO. Reddy & Kumar (2007) presented MOPSO to generate Pareto optimal solutions for reservoir operation. The results indicated that MOPSO can be used as a viable alternative for solving complex water resources problems. Another variant of MOPSO was again proposed by Reddy & Kumar (2009), i.e. elitist mutation multi-objective particle swarm optimization, and the model developed was concluded to be an effective aid for water resources management. Later, Fallah Mehdipour et al. (2011) used the MOSPO model to optimize multi-reservoir system operations and were found to be successful in finding an optimal Pareto front. Furthermore, Rahimi et al. (2013) applied the MOPSO model with time-variant inertia and acceleration coefficients for the derivation of optimal operating policies for the chosen reservoir system. Mansouri et al. (2022) applied MOPSO to minimize the violation of allowed capacity and maximize the supply, and it was found that the model was able to provide 20–35% more supply in dry months. These multi-objective algorithms can be further explored using a multi-criteria decision-making (MCDM) approach to analyze the decisions made. Although there has been less literature presenting the application of MCDM techniques in reservoir operation, several studies have applied them successfully to complex problems. Zhu et al. (2016) proposed an MCDM model for flood control operation using an improved entropy weight method. In the same area of flood control operation, Zhu et al. (2017) proposed another MCDM technique based on a back propagation neural network, which also was proved as an effective tool. Later, Yang et al. (2019) used an efficient MCDM technique based on a technique for order preference by similarity to the ideal solution (TOPSIS), gray correlation, and a combination weighted method, providing more reliable solutions. To address the uncertainties of reservoir operation problems, Zhu et al. (2020) proposed a stochastic MCDM framework based on stepwise weight information, which indicated that risk-informed decisions could be made with more reliability. Furthermore, Zhang et al. (2020) developed another MCDM model that could facilitate decision-makers to make balanced decisions considering the past and future.

Myo Lin et al. (2020) presented a multi-objective model predictive control scheme incorporating NSGA II and MCDM techniques to optimize existing reservoirs. Another MCDM technique based on a payoff matrix, objective weights, fuzzy technique, and compromise programming was used by Ramani & Umamahesh (2024) for designing three water distribution networks optimally. However, most existing studies lack an integrated approach that combines MCDM with multi-objective optimization algorithms such as NSGA-II, NSGA-III, and MOPSO. Our study bridges this gap by integrating the entropy method and compromise programming (EMCP) with multi-objective optimization techniques to achieve a comprehensive evaluation of reservoir operations.

Multi-objective evolutionary algorithms (MOEAs) such as NSGA-II, NSGA-III, and MOPSO have been widely applied in reservoir optimization due to their ability to handle conflicting objectives. However, each algorithm has its own strengths and limitations, as shown in Table 1.

Relevant studies by Husain & Shrivastava (2020), Ma et al. (2023), and Hosseini Dehshiri et al. (2023) have demonstrated the applicability of these algorithms in water resource management, reinforcing their selection for this research.

In the present study, NSGA II is used to optimize the given reservoir operation problem and evaluate the results based on optimal solutions and certain indicators, which are then compared with NSGA III and MOPSO for validation. Furthermore, to analyze the Pareto optimal solutions, the concept of the EMCP was used with the chosen algorithms to implement the MCDM approach in reservoir operation problems (Ramani & Umamahesh 2024). The novelty of the paper lies in the fact that the EMCP approach has not been used for reservoir operation problems, and in the present research work, the EMCP approach has been applied to NSGA II, NSGA III, and MOPSO algorithms, and a detailed comparison has been carried out based on the results obtained.

Ravishankar Sagar Reservoir (RSSR), located in Chhattisgarh, India, serves as a vital water resource for irrigation, drinking water supply, and hydropower generation. However, the reservoir faces several operational challenges, including seasonal water scarcity, conflicting water demands, and ecological sustainability concerns.

The selection of RSSR for this study is based on the following factors:

• Multi-purpose utility: RSSR supports irrigation, drinking water, and hydropower, making optimization crucial for sustainable management.

• Hydrological variability: The reservoir experiences significant seasonal inflow variations, requiring robust optimization strategies.

• Environmental concerns: Maintaining environmental flow (E-flow) requirements while meeting water demand is a key challenge.

These complexities make RSSR an ideal case study for developing and testing multi-objective optimization strategies aimed at sustainable water resource management. RSSR is built on the river Mahanadi, which originates in Pharsia village of Raipur (Madhya Pradesh, India). It is situated in the Dhamtari district within the geographical coordinates of 20° 34′ latitude and 81° 34′ longitude. The reservoir was mainly constructed for irrigation purposes and partially hydel, but at present, it serves many purposes, including municipal and industrial as well as domestic demands, with a catchment area of 3670 km². RSSR is used to satisfy the Municipal and Industrial and Irrigation demands, with municipal demands to be fulfilled at the first priority level.

The study focuses on using the MCDM technique for optimal reservoir operation utilizing NSGA II, NSGA III, and MOPSO algorithms.

NSGA II has been widely used in various engineering problems, including optimal reservoir operation. NSGA II is an important enhancement of the standard GA proposed by Deb et al. (2022). In addition to the basic concept of the GA, an elite strategy based on the crowding distance was introduced in NSGA II to explore the sampling space to a greater extent, thereby increasing the speed and robustness of the algorithm. The proposed algorithm is explained as follows:

• (i) Random generation of the initial population and initialization of parameters.

• (ii) Classification of the first generation based on non-dominated sorting and genetic operations.

• (iii) Sort the new merged population, i.e. the parent population and the sub-population, on the basis of crowding distance to generate a new parent population.

• (iv) Perform genetic operations on the new parent population to produce a child population for the next iterations.

NSGA III is another enhancement of the GA based on the NSGA II framework and was proposed by Deb & Jain (2013). The main feature of NSGA III is that it replaces the concept of crowding distance for the selection mechanism with a uniformly distributed reference point concept to improve solution diversity. The algorithm is explained as follows:

• (i) Random generation of the initial population and initialization of parameters.

• (ii) For each individual reference points are generated to determine the mating parent and then selected.

• (iii) Offspring populations are formed on the basis of crossover and mutation operations.

• (iv) Parent and offspring populations are merged through non-dominated sorting.

• (v) New individuals are selected on the basis of reference point operation to enter the next generation population.

The particle swarm optimization algorithm is another evolution-based technique inspired by the movement of birds and was introduced by Eberhart & Kennedy (1955), for multi-objective problems. The Particle Swarm Optimization (PSO) algorithm considers every solution as a particle moving with some velocity toward optimality. The position and velocities of the particle and the whole population set are updated with every iteration to evolve and move toward the optimal destination. The algorithm is explained as follows:

• (i) Initialization of population with velocity and position vectors.

• (ii) Simulate the movement of the particles individually and globally.

• (iii) Update the population to form new solutions toward optimality.

• (iv) Perform mutating operations on the new population to produce optimal solutions for the next iterations.

Once the formulated set of equations for the multi-objective problems has been optimized using the soft computing algorithms, a set of best possible solutions known as Pareto fronts can be found for the given optimization problem. It becomes important to choose the preferred solution among these based on quality. To perform this task, the MCDM technique is used for performance evaluation of the obtained solutions through multiple criteria. For this decision-making process, several MCDM methods are available, like the weighted sum method, TOPSIS, Visekriterijumsko Kompromisno Rangiranje, and fuzzy analytic network process, mentioned by Taherdoost & Madanchian (2023). Other methods, viz. weightage allocation criteria and compromise programming, were used by Ramani & Umamahesh (2024).

The simple stepwise procedure of the adopted methodology is given as follows:

• 1. On the basis of an extensive literature review, the proposed models were adopted for the given formulated problem.

• 2. The data collected was analyzed and prepared to form input to the models developed.

• 3. The models were then run with specified parameter values, which were selected after performing sensitivity analysis; objective function, and constraints to obtain Pareto optimal solutions.

• 4. Once the solutions were obtained, the EMCP approach was incorporated to identify the best solutions. The EMCP is used to rank Pareto optimal solutions by considering the relative importance of objectives. The methodology follows these steps:

• • • Normalize the objective function values using the min–max normalization method.

  • • Compute entropy weights for each criterion to reflect their relative importance.

  • • Apply compromise programming to select the solution closest to the ideal point based on the weighted Euclidean DM.

• 5. It is this structured approach that ensures an unbiased selection of the best reservoir operation strategy while balancing tradeoffs among conflicting objectives.

The objective here is the minimization of the squared deviation between releases and demands subjected to various constraints.

The final models were then run to minimize the objective functions, duly satisfying the given constraints using NSGA II, NSGA III, and MOPSO models in MATLAB. In the present study, the first priority is given to the E-flow condition, and then the next priority is to meet first the municipal demand, secondly the irrigation demand, and then the industrial demand.

The most commonly used performance measuring indicators for reservoir operation are reliability, vulnerability, and resilience (Anusha et al. 2017).

Based on the problem formulation, results were obtained using the three evolutionary algorithms, which were then run in MATLAB for RSSR. The inputs used for the models were the monthly inflows and demands. The first priority in the formulated problem was to fulfill the E-flow criteria followed by the municipal, irrigation, and industrial demand. The given set of equations was applied to the proposed models NSGA II, NSGA III, and MOPSO to fulfill the given demands.

Model parameters play a crucial role in governing the function of the algorithm, as each parameter has its contribution to the process. To validate the rationality of parameter settings, a sensitivity analysis was conducted by varying key algorithm parameters such as population size, mutation rate, and crossover probability, and with various simulations (Vojinovik et al. 2003), the parameter values were obtained. The following tests were performed, as shown in Tables 3–5.

The key parameters of the models are shown in Table 6.

After running the models for the respective number of iterations, several solution sets were obtained, from which the decision had to be made using the MCDM technique to reduce the large solution set to a smaller number of solutions.

Optimal operating policies for any reservoir involve forming rule curves that specify how much water to store at different periods in a year while maintaining specific storage levels. In the present study, after obtaining the best solution from the EMCP approach, the rule curves are derived from the three selected algorithms as discussed in the following section.

In the case of the Himalayan rivers, the CWC recommends the E-flow conditions as follows: the minimum E-flow should be greater than 2.5% of the 75% dependable annual flow. E-flow when calculated from the Weibull method is equal to 6.4 MCM.

Maintaining E-flow constraints is crucial for sustaining aquatic ecosystems and ensuring social well-being. The results indicate that NSGA-II outperformed NSGA-III and MOPSO in minimizing E-flow violations, ensuring greater compliance with ecological requirements. The practical significance of this finding is that optimized reservoir operation strategies must consider municipal, irrigation, and industrial demands along with downstream ecological needs, which include:

• Biodiversity conservation: Ensuring adequate water levels for aquatic habitats.

• Fisheries management: Supporting livelihoods dependent on reservoir fisheries.

• Community water access: Balancing ecosystem conservation with water supply to rural communities.

This study underscores the need for a balanced water management strategy that integrates ecological sustainability into decision-making. The comparison of e-flow criteria satisfied by different algorithms and original policy is shown in Table 7.

For performance assessment of the proposed models, the basic indices, viz. reliability, vulnerability, resilience, and Root Mean Square Error (RMSE) were estimated and are shown in Table 8. The release policies and rule curves obtained using NSGA II are more reliable than the other two models. For NSGA II, the resilience index is closer to one, indicating higher resilience and less vulnerability.

While this study presents an efficient reservoir optimization framework, certain limitations must be acknowledged, which are discussed as follows.

The application of NSGA-II, NSGA-III, and MOPSO requires significant computational resources, especially for large-scale reservoirs. The soft computing techniques applied in this study require considerable computational resources. The complexity grows with increasing population sizes, more iterations, and additional objectives, leading to longer computation times and less flexibility in trying more complex configurations. High computational demand leads to increased processing time, high dependance on advanced hardware, and a lack of scalability for more significant systems or real-time applications. In this line of thought, this study also highlights the need for strategies to overcome such challenges by using parallel computing to reduce processing times, integrating data-driven models for approximating objective functions, and refining algorithms to eliminate redundant computations.

One major limitation of this study is the lack of a real-time decision-making framework, mainly because real-time data are unavailable. Reservoir operations are very dynamic, given the changing patterns of inflows, demands for water use, and E-flow requirements. However, this study had to rely on historical data to develop operational policies, which, although useful for long-term planning, lack the responsiveness required for real-time scenarios.

Each reservoir is influenced by its unique hydrological inputs. The specific characteristics of the reservoir influence modeling. The performance of the algorithms and approaches presented may vary when applied to other reservoirs with different inflow patterns, catchment characteristics, and operational constraints.

Reservoir operation plays a crucial role in water resources management. The goal of optimizing reservoir operations is to lower risks and maximize reservoir benefits without compromising the reservoir's objective functions and constraints.

The present study employs three multi-objective algorithms, NSGA-II, MOPSO, and NSGA-III, to optimize the RSSR located in Chhattisgarh, India.

A detailed comparative analysis was executed for the proposed models. Based on the Pareto front solutions, rule curves, release policies, monthly deficits, E-flow criteria, and performance indices, NSGA II outperforms the other algorithms and produces the most reliable results across a variety of objectives due to its diverse solutions and Pareto fronts handling. The dynamic behavior of NSGA II enhances the potential of the model to manage the reservoir operation rules in a better way. NSGA III performs adequately, especially in handling higher-dimensional objective problems. However, it does not outperform NSGA-II in terms of overall solution quality. In some other studies, NSGA III does not necessarily outperform NSGA II; it also depends on the type of problem (Ishibuchi et al. 2016). MOPSO shows a lower degree of variety and convergence than NSGA II and NSGA III. However, it provides logical solutions for the reservoir operation issue.

Based on the results, the following recommendations are proposed for policymakers and reservoir managers:

• Adopt NSGA-II for operational decision-making: Given its superior reliability and resilience performance, NSGA-II can serve as a baseline algorithm for optimizing reservoir operations.

• Implement dynamic water allocation strategies: Flexible reservoir release schedules should be designed to accommodate seasonal variations in water demand while maintaining ecological balance.

• Incorporate stakeholder perspectives: Decision-making processes should involve local communities, agricultural stakeholders, and environmental agencies to ensure equitable water distribution.

• Enhance climate resilience in water management: Future policies must consider climate-adaptive reservoir operation strategies, integrating real-time hydrological forecasting.

These insights provide a roadmap for sustainable reservoir management while balancing competing water-use priorities.

The authors have given consent and approved for manuscript submission.

All authors contributed to the study's conception and design. Methodology development was done by R.D., application, and data analysis were done by R.D., and data collection and conceptualization were done by H.A.S Sandhu. Draft preparation and review were done by M.T. and C.C.

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

The authors declare that they have no conflict of interest.

All data used during the study were provided by a third party. Direct requests for these materials may be made to the provider.