Four-reservoir System Research Articles

Introducing improved atom search optimization (IASO) algorithm: Application to optimal operation of multi-reservoir systems

Nowadays, optimal reservoir operation is regarded as one of the most important issues in water resources management. In this regard, several optimization algorithms have been used to evaluate the issue of optimal reservoir operation. To increase the accuracy and proximity of the solutions to the absolute optimal solution, the improved atom search optimization (IASO) algorithm was introduced with a mutation strategy to improve its global search capability, as an important factor in preventing trapping in a locally optimal solution. This article implemented the atom search optimization (ASO) algorithm and its improved model to improve the results of the objective function in multi-reservoir systems. Comparing the IASO algorithm with the basic ASO algorithm on the mathematical benchmark functions revealed good accuracy and the superiority of the IASO algorithm. Then, sensitivity analysis was performed on the effective coefficients of both algorithms, in which alpha and beta, as the depth and weight coefficients used in the calculation of atoms acceleration, were considered 50 and 0.5, respectively. The results showed the relatively good accuracy of the ASO algorithm in the case of multi-reservoir systems, but implementing and comparing the results of the improved algorithm, showed improvement so that the best IASO results were improved from 95.33% to 99.99% as close to the global four-reservoir system response of 308.29 and from 89.67 to 94.36% with the solution of the ten-reservoir system in the amount of 1194.44.

Improved progressive optimality algorithm and its application to determination of optimal release trajectory of long-term power generation operation of cascade reservoirs

Dynamic programming (DP) is an effective method for solving multi-stage decision-making problems and has been extensively applied to the optimization of reservoir operations. However, the method is limited by the dimensionality problem; hence, it cannot be directly applied to optimizing the operations of a reservoir system with more than three reservoirs at current computing power. The progressive optimality algorithm (POA) is a classic variant of DP and has been widely used for optimizing multi-reservoir operations. Despite the use of a static variable decoupling strategy to ease DP's dimensionality problem, the POA's performance is reduced by an inherent drawback of the blind search of the static variable decoupling strategy and the dimensionality problem in two-stage solutions. To enhance the POA's performance, we propose an improved version of the POA known as the dipole optimization procedure (DOP) for optimizing cascade reservoir operations. In the improved algorithm, we use a dynamic variable decoupling strategy to obtain search directions that are more targeted than those of the POA so as to improve the quality of the solutions. The dynamic decoupling of variables was achieved by constructing and solving a dipole optimization problem using a DP model developed in this study. Moreover, a perturbation mechanism was introduced to address the POA's dimensionality problem so that the algorithm can be extended to larger reservoir systems. The results of the simulation of a hypothetical four-reservoir system and a real-world cascade reservoir system showed the superiority of the DOP over the POA and other five available alternatives. The comparison was based on the quality of solutions and solving efficiency. The results indicate that the DOP is rational and feasible and has the potential to be applied to optimizing the operation of large-scale multi-reservoir systems with numerous reservoirs.

Multi-objective risk analysis for flood control operation of a complex reservoir system under multiple time-space correlated uncertainties

Many uncertainties are involved in flood control operation of a multi-reservoir system and result in risks for the system. Risk analysis for reservoir flood control operation is essential for decision making. Traditional flood control risk analysis only takes flood forecast error as the main risk source, ignoring the influence of dynamic control of flood-limited water level on reservoir initial water level for flood regulation. In this study, the spatial correlation of reservoir initial water level errors and the spatiotemporal correlation of flood forecast errors are identified via copula function. A risk analysis model considering both upstream and downstream is established for multi-objective flood control operation of a complex reservoir system, coupling multi-dimensional uncertainties of reservoir initial water levels, flood forecast errors, reservoir capacity curve errors, reservoir discharge curve errors and river flood routing errors. The impact of multiple risk sources with spatiotemporal correlations on reservoir flood control operation is then evaluated and the competitive tradeoff between flood control risks in upstream and downstream analyzed. The model is applied to a mixed four-reservoir system in Pi River Basin in China. Results indicated that 1) there is a strong correlation between the reservoir initial water level errors in space and also between the flood forecast errors in space and time, which can be effectively described by copula function, and ignoring the correlations will underestimate the flood control risk; 2) the two objective values of upstream and downstream show a clear competitive relationship, and the solution that prefers one objective has low risk marginal benefit, thus choosing a compromise solution can balance risks; 3) coupling the initial water level uncertainty reduces the flood control risk caused by the flood forecast errors to a certain extent, but also lead to the increase of extreme risk loss.

Crop pattern optimization in a multi-reservoir system by combining many-objective and social choice methods

Crop pattern determination is an essential step toward proper water resources management in irrigated agricultural development, especially in arid and in semi-arid regions. In this paper, we propose a method for determining short-term optimal crop pattern by developing a suitable model for a four-reservoir system in the Karun basin including Karun 1, 3, and 4, and Gotvand reservoirs in Iran. The model satisfies multiple objectives including hydropower, municipal, industrial, agricultural, and environmental purposes. To achieve this goal, we examined two heuristic many-objective algorithms including SPEA2 and NSGA-III. Many-objective algorithms provide a Pareto front of optimal solutions. However in practice we need to know an exact solution of crop pattern. To overcome this problem, a novel application of social choice (SC) is accomplished. The results indicate the superiority of NSGA-III over SPEA2. Comparison of the results for the minimization objective functions shows that the average values of municipal, agricultural, environmental and hydropower obtained with the NSGA-III algorithm are 0.22, 6.73, 0.49 and 1.72, respectively, whereas in SPEA2 they are 0.72, 9.47, 2.05 and 4.72. This finding also emphasizes the importance of improvements necessary in solution algorithms for complicated water resources problems.

Integrated real-time flood risk identification, analysis, and diagnosis model framework for a multireservoir system considering temporally and spatially dependent forecast uncertainties

Uncertainties in flood forecasts that result from error propagation in meteorological–hydrological simulation processes present spatial and temporal dependences that are the principal sources of risk to real-time flood control in a multireservoir system. Risk analysis models that neglect such dependences potentially yield biased results regarding flood control operations. To enhance the accuracy of flood risk analysis and inform decision making regarding real-time flood control for a multireservoir system, this study proposed an integrated flood risk identification, analysis, and diagnosis model framework that incorporates the multidimensional dependences of forecast uncertainties. The framework includes an uncertainty identification model that uses the copula function to characterize the joint probability function of the mixed dependent uncertainties. It also incorporates a real-time flood risk analysis module that couples simulation and optimization to convert the complex multiobjective operation under uncertainty into a tractable model capable of flexibly evaluating individual and joint flood risks. The third component is a risk diagnosis module that calculates risk contributions using conditional probability, and identifies stable and vulnerable reservoirs within the system to alter operational decisions toward risk reduction. Methodologies were verified through application to a mixed four-reservoir system in the Pi River Basin, China. The principal findings were as follows. (1) Positive-dominated dependences of forecast uncertainties were identified because of error propagation through the meteorological and rainfall–runoff forecasts within the spatial and temporal continuity connection, and the copula function accurately described and quantified the multidimensional temporal and spatial dependences of the uncertainties. (2) In neglecting the spatial dependences of forecast uncertainties, the joint flood risk of the reservoir system was underestimated; in ignoring high-order temporal dependences, individual flood risk was underestimated owing to biased estimation in error variance. (3) Systematic reorganization of the operational strategies of diagnosed stable and vulnerable reservoirs could provide guidance for reduction and homogenization of flood risks. The proposed framework could be used to improve the accuracy of flood risk analysis and support reliable real-time flood control operation of a multireservoir system.

A hybrid constrained coral reefs optimization algorithm with machine learning for optimizing multi-reservoir systems operation

The continuous growing demand for water, prolonged periods of drought, and climatic uncertainties attributed mainly to climate change mean surface water reservoirs more than ever need to be managed efficiently. Several optimization algorithms have been developed to optimize multi-reservoir systems operation, mostly during severe dry/wet seasons, to mitigate extreme-events consequences. Yet, convergence speed, presence of local optimums, and calculation-cost efficiency are challenging while looking for the global optimum. In this paper, the problem of finding an efficient optimal operation policy in multi-reservoir systems is discussed. The complexity of the long-term operating rules and the reservoirs' upstream and downstream joint-demands projected in recursive constraints make this problem formidable. The original Coral Reefs Optimization (CRO) algorithm, which is a meta-heuristic evolutionary algorithm, and two modified versions have been used to solve this problem. Proposed modifications reduce the calculation cost by narrowing the search space called a constrained-CCRO and adjusting reproduction operators with a reinforcement learning approach, namely the Q-Learning method (i.e., the CCRO-QL algorithm). The modified versions search for the optimum solution in the feasible region instead of the entire problem domain. The models’ performance has been evaluated by solving five mathematical benchmark problems and a well-known continuous four-reservoir system (CFr) problem. Obtained results have been compared with those in the literature and the global optimum, which Linear Programming (LP) achieves. The CCRO-QL is shown to be very calculation-cost-effective in locating the global optimum or near-optimal solutions and efficient in terms of convergence, accuracy, and robustness.

Optimal operation of multi-reservoir systems: comparative study of three robust metaheuristic algorithms

Abstract In this study, the capability of the recently introduced moth swarm algorithm (MSA) was compared with two robust metaheuristic algorithms: the harmony search (HS) algorithm and the imperialist competitive algorithm (ICA). First, the performance of these algorithms was assessed by seven benchmark functions having 2–30 dimensions. Next, they were compared for optimization of the complex problem of four-reservoir and 10-reservoir systems operation. Furthermore, the results of these algorithms were compared with nine other metaheuristic algorithms. Sensitivity analysis was performed to determine the appropriate values of the algorithms’ parameters. The statistical indices coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), mean square error (MSE), normalized MSE (NMSE), mean absolute percentage error (MAPE), and Willmott’s index of agreement (d) were used to compare the algorithms’ performance. The results showed that MSA was the superior algorithm for solving all benchmark functions in terms of obtaining the optimal value and saving CPU usage. ICA and HS were ranked next. When the dimensions of the problem were increased, the performance of ICA and HS dropped but MSA has still performed extremely well. In addition, the minimum CPU usage and the best solutions for the optimal operation of the four-reservoir system were obtained by MSA, with values of 269.7 seconds and 308.83, which are very close to the global optimum solution. Corresponding values for ICA were 486.73 seconds and 306.47 and for HS were 638.61 seconds and 264.61, which ranked them next. Similar results were observed for the 10-reservoir system; the CPU time and optimal value obtained by MSA were 722.5 seconds and 1,195.58 while for ICA they were 1,421.62 seconds and 1,136.22 and for HS they were 1,963.41 seconds and 1,060.76. The R2 and RMSE values achieved by MSA were 0.951 and 0.528 for the four-reservoir system and 0.985 and 0.521 for the 10-reservoir system, which demonstrated the outstanding performance of this algorithm in the optimal operation of multi-reservoir systems. In a general comparison, it was concluded that among the 12 algorithms investigated, MSA was the best, and it is recommended as a robust and promising tool in the optimal operation of multi-reservoir systems.

Optimizing operating rules for multi-reservoir hydropower generation systems: An adaptive hybrid differential evolution algorithm

The optimization of hydropower multi-reservoir systems is one of the most challenging reservoir management problems due to the complex dynamic nonlinear influencing variables such as reservoir active storage volume, released water discharge rate, and water pressure head available for hydropower generation. To optimize such a complex problem in an efficient way, the development of a high-precision meta-heuristic algorithm are of essential significance. This paper develops an adaptive differential evolution with particle swarm optimization (A-DEPSO) algorithm to derive optimal operating rules for multi-reservoir systems with the purpose of hydropower production. A-DEPSO algorithm uses novel mutation and crossover mechanisms to improve global and local search capabilities, respectively. The application of the proposed method is verified to solve a complex four-reservoir hydropower generation system, located in the southwest of Iran. The results achieved indicate that the A-DEPSO reduced the value of the objective function by an average of 57% compared with other well-known optimizers in the literature. Furthermore, the total power generated from the four-reservoir system using the proposed method increased by an average of 11% compared to the other methods. Finally, the results obtained in this study confirm that the A-DEPSO can be used efficiently to solve complex multi-reservoir hydropower generation systems.

Generation of Clean Hydropower Energy in Multi-Reservoir Systems Based on a New Evolutionary Algorithm

Lingering droughts and shortage of water sources signify the importance of optimal utilization of water reservoirs such as multi-reservoir systems. These systems could be employed not only as a storage system to manage the water utilization but also as a power generation system. To rise the generated power besides the management of water utilization, an optimization algorithm should be used. In this study, the kidney algorithm in three different scenarios, namely the wet, normal, and dry years is employed to fulfill such an engineering operation in a four-reservoir system in China. Simulations show well compatibility of the water level inside the reservoir with real statistical indices in terms of RMSE and MAE. Results also reveal that using the kidney algorithm not only reduces the required calculation but also increases the convergence pace with respect to other algorithms that have been used (bat, shark, abundance of particles, and genetic algorithms). Moreover, it increases the amount of the generated energy by a factor of 2.2–3.2 with respect to the aforementioned algorithms. Results indicate the capability of the kidney algorithm in the management of water sources and engineering operations.

Optimal operation of reservoir systems using the Wolf Search Algorithm (WSA)

Abstract Optimizing hydropower plants is complex due to nonlinearity, complexity, and multidimensionality. This study introduces and evaluates the performance of the Wolf Search Algorithm (WSA) for optimizing the operation of a four-reservoir system and a single hydropower system in Iran. Results indicate WSA could reach 99.95 and 99.91 percent of the global optimum for the four-reservoir system and single reservoir system, respectively. Comparing the results of WSA with a genetic algorithm (GA) also indicates WSA's supremacy over GA. Thus, due to its simple structure and high capability, WSA is recommended for use in other water resources management problems.

Gradient Evolution Optimization Algorithm to Optimize Reservoir Operation Systems

Population growth, environmental destruction, and climate change have all led to water scarcity on the available water resources. In this regard, reservoir systems have an important role to manage water resources. Thus, it is essential to optimize the management of water resources. Optimizing reservoir systems involves complications such as nonlinear functions, large number of sizing variables and numerous constraints. To solve complicated optimization problems, meta-heuristic optimization algorithms are reliable and powerful methods. Hence, the present paper applies gradient evolution (GE) algorithm to optimize reservoir operation systems. This algorithm is extracted from a gradient-based optimizer. In fact, the main novelty of this study is the application of GE algorithm to optimize single- and multi-reservoir systems. Accordingly, the GE is employed to optimize a four-reservoir system, the Khersan-1 reservoir and the Dez reservoir in Iran. The results confirm the high capacity of the GE to optimize the single and multi-reservoir systems as it can obtain solutions 99.99, 96 and 94% of global optimum for the four-reservoir, Khersan-1 reservoir and Dez reservoir operation problems respectively. The results of the GE are compared with those solutions calculated with linear programming (LP), non-linear programming (NLP) and genetic algorithm (GA), which corroborate the superior ability of GE to reach global optimum solution of reservoir operation systems.

Introducing modified version of penguins search optimization algorithm (PeSOA) and its application in optimal operation of reservoir systems

Abstract In the current study, modified version of the penguins search optimization algorithm (PeSOA) was introduced, and its usage was assessed in the water resources field. In the modified version (MPeSOA), the Gaussian exploration was added to the algorithm. The MPeSOA performance was evaluated in optimal operation of a hypothetical four-reservoir system and Karun-4 reservoir as a real world problem. Also, genetic algorithm (GA) was used as a criterion for evaluating the performance of PeSOA and MPeSOA. The results revealed that in a four-reservoir system problem, the PeSOA performance was much weaker than the GA; but on the other hand, the MPeSOA had better performance than the GA. In the mentioned problem, PeSOA, GA, and MPeSOA reached 78.43, 97.46, and 98.30% of the global optimum, respectively. In the operation of Karun-4 reservoir, although PeSOA performance had less difference with the two other algorithms than four-reservoir problem, its performance was not acceptable. The average values of objective function in this case were equal to 26.49, 23.84, and 21.48 for PeSOA, GA, and MPeSOA, respectively. According to the results obtained in the operation of Karun-4 reservoir, the algorithms including MPeSOA, GA, and PeSOA were situated in ranks one to three in terms of efficiency, respectively.

Applications of the anarchic society optimization (ASO) algorithm for optimizing operations of single and continuous multi-reservoir systems

To address the related water resources management issues, different evolutionary and heuristic algorithms have been developed in recent years. In this paper, a new algorithm is introduced for optimizing the operation of reservoir systems. Specifically, the anarchic society optimization (ASO) algorithm is applied to solve water resources management problems for the first time. In these problems, the operations of a single-reservoir hydropower system (Karun-4 reservoir) and a four-reservoir system with the objective of maximizing the profits of releases are optimized. The objective function values of the ASO algorithm and the genetic algorithm (GA) for Karun-4 reservoir are 1.254 and 1.535, respectively. The objective function value from the ASO algorithm is very close to the global optimum (1.213) from the non-linear programming (NLP). The optimal solution of the ASO algorithm for the four-reservior system covers 93.88% of the NLP value while the GA model only accounts for 91.86% of the global optimum, indicating that the ASO algorithm does have better performance. The applications of the ASO algorithm for three benchmark mathematical functions and the single- and multi-reservoir systems and the comparisons with the GA method demonstrate its acceptable performance and applicability to real, complex engineering problems.

Optimal Operation of the Multireservoir System in the Seine River Basin Using Deterministic and Ensemble Forecasts

This article investigates the improvement of the operation of a four-reservoir system in the Seine River basin, France, by use of deterministic and ensemble weather forecasts and real-time control. In the current management, each reservoir is operated independently from the others and following prescribed rule-curves, designed to reduce floods and sustain low flows under the historical hydrological conditions. However, this management system is inefficient when inflows are significantly different from their seasonal average and may become even more inadequate to cope with the predicted increase in extreme events induced by climate change. In this work, a centralized real-time control system is developed to improve reservoirs operation by exploiting numerical weather forecasts that are becoming increasingly available. The proposed management system implements a well-established optimization technique, model predictive control (MPC), and its recently modified version that can incorporate uncertainties, tree-based model predictive control (TB-MPC), to account for deterministic and ensemble forecasts respectively. The management system is assessed by simulation over historical events and compared to the no-forecasts strategy based on rule-curves. Simulation results show that the proposed real-time control system largely outperforms the no-forecasts management strategy, and that explicitly considering forecast uncertainty through ensembles can compensate for the loss in performance due to forecast inaccuracy.

Biogeography-Based Optimization Algorithm for Optimal Operation of Reservoir Systems

AbstractThe optimal operation of reservoir systems to meet water demand is a complex and nonlinear problem. This paper applies the biogeography-based optimization (BBO) algorithm to solve reservoir operation problems. The BBO algorithm is first verified with the minimization of three mathematical benchmark functions (Sphere, Rosenbrock, and Bukin6). In addition, the BBO algorithm was applied to a single reservoir system and a four-reservoir system. The performance of the BBO algorithm was compared with that of the genetic algorithm (GA) in solving the three optimization problems. The results show that the BBO algorithm minimized the benchmark functions accurately, and outperformed the GA in this respect. In the case of the single-reservoir hydropower optimization problem the BBO reached a near-optimal solution. The values of the objective function averaged 1.228 and 1.746 with the BBO and GA, respectively. The global solution of this problem with the nonlinear programming method equals 1.213. In the four-...

Development and Application of the Bat Algorithm for Optimizing the Operation of Reservoir Systems

AbstractOptimal utilization of water resources by means of water transfers and reservoirs in semiarid and arid regions is used to mitigate natural water scarcity. In this context, metaheuristic algorithms for optimum reservoir system operation have become an attractive alternative to traditional operations research algorithms such as linear programming (LP), nonlinear programming (NLP), and dynamic programming (DP). This paper presents the metaheuristic bat algorithm (BA) and its application to the optimal operation of the Karoun-4 reservoir system in Iran and to a hypothetical four-reservoir system. The merits of the performance of the BA in the optimization of reservoir operation are demonstrated by comparison to those of LP, NLP, and genetic algorithm (GA) in terms of the convergence to global optima and of the variance of results about global optima for reservoir optimization problems.

Application of the Water Cycle Algorithm to the Optimal Operation of Reservoir Systems

AbstractWater resources, in time, place, and quantity, are often poorly matched to the needs of humanity. This disparity tends to be more accentuated in arid and semiarid regions, predominant in Iran. Reservoir systems are a common means to control and manage water resources. Due to limited resources and the increasing demands for water, these systems must be optimally operated to maximize the efficiency of water use. Evolutionary optimization algorithms provide reliable and simple methods for solving complex optimization problems. One of those methods, the water cycle algorithm (WCA), is used in this paper to find optimal operation strategies for the Karon-4 reservoir and a four-reservoir system in Iran. The results demonstrate the high efficiency and reliability of the WCA in solving reservoir operation problems.

Application of the Harmony Search optimization algorithm for the solution of the multiple dam system scheduling

During the last few years Harmony Search Algorithm (HSA), a new optimization technique, has been used effectively in solving large scale problems. In this paper along with a brief presentation of HSA, an application on classic Dam Scheduling problem is presented. This application concerns the optimum operation of a four-reservoir system over 24 hours. The water released from each dam is used for hydropower generation and irrigation. The objective is to maximize the daily benefits gained from the reservoir system over 12 (two-hour) time steps.

Computational improvement for dynamic programming models by diagnosing infeasible storage combinations

A dynamic programming (DP) optimization model is developed for long term planning of multiple-reservoir operations. To overcome the well-known dimensionality problem associated with such a model, a heuristic approach is used to narrow the needed search algorithm within the state space of the DP model. This method can recognize many infeasible transitions from the initial to the final state of the DP stages. By diagnosing these infeasible transitions in advance and removing them from further computations, significant improvement in computational load is achieved so that the computer time for solving the model is reduced more than 50 times for the reservoir system under study. This methodology is applied to a four-reservoir system located in Iran.

Optimal Operation of Reservoir Systems using Simulated Annealing

A stochastic search technique, simulated annealing (SA), is used to optimize the operation of multiple reservoirs. Seminal application of annealing technique in general to multi-period, multiple-reservoir systems, along with problem representation and selection of different parameter values used in the annealing algorithm for specific cases is discussed. The search technique is improved with the help of heuristic rules, problem-specific information and concepts from the field of evolutionary algorithms. The technique is tested for application to a benchmark problem of four-reservoir system previously solved using a linear programming formulation and its ability to replicate the global optimum solution is examined. The technique is also applied to a system of four hydropower generating reservoirs in Manitoba, Canada, to derive optimal operating rules. A limited version of this problem is solved using a mixed integer nonlinear programming and results are compared with those obtained using SA. A better objective function value is obtained using simulated annealing than the value from a mixed integer non-linear programming model developed for the same problem. Results obtained from these applications suggest that simulated annealing can be used for obtaining near-optimal solutions for multi-period reservoir operation problems that are computationally intractable.