Verification of FPA and PSO algorithms for rule curve extraction and optimization of single- and multi-reservoir systems' operations considering their specific purposes

Abstract The optimal operation of reservoirs is known as a complex issue in water resources management, which requires consideration of numerous variables (such as downstream water demand and power generation). For this optimization, researchers have used evolutionary and meta-heuristic algorithms, which are generally inspired by nature. These algorithms have been developed to achieve optimal/near-optimal solutions by a smaller number of function evaluations with less calculation time. In this research, the flower pollination algorithm (FPA) was used to optimize: (1) Aidoghmoush single-reservoir system operation for agricultural water supply, (2) Bazoft single-reservoir system operation for hydropower generation, (3) multi-reservoir system operation of Karun 5, Karun 4, and Bazoft, and (4) Bazoft single-reservoir system for rule curve extraction. To demonstrate the effectiveness of the FPA, it was first applied to solve the mathematical test functions, and then used to determine optimal operations of the reservoir systems with the purposes of downstream water supply and hydropower generation. In addition, the FPA was compared with the particle swarm optimization (PSO) algorithm and the non-linear programming (NLP) method. The results for the Aidoghmoush single-reservoir system showed that the best FPA solution was similar to the NLP solution, while the best PSO solution was about 0.2% different from the NLP solution. The best values of the objective function of the PSO were approximately 3.5 times, 28%, and 43% worse than those of the FPA for the Bazoft single-reservoir system for hydropower generation, the multi-reservoir system, and the Bazoft single-reservoir system for rule curve extraction, respectively. The FPA outperformed the PSO in finding the optimal solutions. Overall, FPA is one of the new evolutionary algorithms, which is capable of determining better (closer to the ideal solution) objective functions, decreasing the calculation time, simplifying the problem, and providing better solutions for decision makers.

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Multi-Objective Joint Optimal Operation of Reservoir System and Analysis of Objectives Competition Mechanism: A Case Study in the Upper Reach of the Yangtze River

Water ◽

10.3390/w11122542 ◽

2019 ◽

Vol 11 (12) ◽

pp. 2542 ◽

Cited By ~ 2

Author(s):

Mufeng Chen ◽

Zengchuan Dong ◽

Wenhao Jia ◽

Xiaokuan Ni ◽

Hongyi Yao

Keyword(s):

Power Generation ◽

Water Supply ◽

Yangtze River ◽

Water Resource Management ◽

Flood Control ◽

Optimal Operation ◽

Total Power ◽

The Yangtze River ◽

Multi Objective ◽

Reservoir System

The multi-objective optimal operation and the joint scheduling of giant-scale reservoir systems are of great significance for water resource management; the interactions and mechanisms between the objectives are the key points. Taking the reservoir system composed of 30 reservoirs in the upper reaches of the Yangtze River as the research object, this paper constructs a multi-objective optimal operation model integrating four objectives of power generation, ecology, water supply, and shipping under the constraints of flood control to analyze the inside interaction mechanisms among the objectives. The results are as follows. (1) Compared with single power generation optimization, multi-objective optimization improves the benefits of the system. The total power generation is reduced by only 4.09% at most, but the water supply, ecology, and shipping targets are increased by 98.52%, 35.09%, and 100% at most under different inflow conditions, respectively. (2) The competition between power generation and the other targets is the most obvious; the relationship between water supply and ecology depends on the magnitude of flow required by the control section for both targets, and the restriction effect of the shipping target is limited. (3) Joint operation has greatly increased the overall benefits. Compared with the separate operation of each basin, the benefits of power generation, water supply, ecology, and shipping increased by 5.50%, 45.99%, 98.49%, and 100.00% respectively in the equilibrium scheme. This study provides a widely used method to analyze the multi-objective relationship mechanism, and can be used to guide the actual scheduling rules.

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

Water Science & Technology Water Supply ◽

10.2166/ws.2019.005 ◽

2019 ◽

Vol 19 (5) ◽

pp. 1396-1404 ◽

Cited By ~ 4

Author(s):

Edris Ahmadebrahimpour

Keyword(s):

Genetic Algorithm ◽

Water Resources Management ◽

Simple Structure ◽

Search Algorithm ◽

Global Optimum ◽

Optimal Operation ◽

Resources Management ◽

Reservoir System ◽

Hydropower Plants ◽

Reservoir Systems

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.

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

Water Science & Technology Water Supply ◽

10.2166/ws.2017.217 ◽

2017 ◽

Vol 18 (4) ◽

pp. 1484-1496 ◽

Cited By ~ 5

Author(s):

Afshin Mansouri ◽

Babak Aminnejad ◽

Hassan Ahmadi

Keyword(s):

Genetic Algorithm ◽

Optimization Algorithm ◽

Real World ◽

Global Optimum ◽

Optimal Operation ◽

The Other ◽

Reservoir System ◽

Search Optimization ◽

Real World Problem ◽

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.

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

Water Science & Technology Water Supply ◽

10.2166/ws.2020.368 ◽

2020 ◽

Author(s):

Saeid Akbarifard ◽

Mohammad Reza Sharifi ◽

Kourosh Qaderi ◽

Mohamad Reza Madadi

Keyword(s):

Harmony Search ◽

Imperialist Competitive Algorithm ◽

Complex Problem ◽

Global Optimum ◽

Optimal Operation ◽

Metaheuristic Algorithms ◽

Reservoir System ◽

Optimal Value ◽

Reservoir Systems ◽

Cpu Usage

Abstract In this study, the capability of recently introduced Moth Swarm Algorithm (MSA) was compared with two robust meta-heuristics of harmony search (HS) algorithm and imperialist competitive algorithm (ICA). First, the performance of these algorithms was assessed by seven benchmark functions having 2–30 dimensions. Next, they were compared in optimization of complex problem of 4-reservoir and 10-reservoir systems operation. Furthermore, the results of these algorithms were compared with nine other metaheuristic algorithms developed by several researchers. Sensitivity analysis was performed to determine the appropriate values of the algorithms parameters. The statistical indices of R2, RMSE, MAE, MSE, NMSE, MAPE, and Willmott's index of agreement were used to compare the algorithms performance. The results showed that the MSA was the superior algorithm in solving all benchmark functions in terms of obtaining the optimal value and saving the CPU usage. ICA and HS were placed in the next orders, respectively. It was found that by increasing the dimensions of the problem, the performance of ICA and HS dropped but the MSA has still performed extraordinary. In addition, the minimum CPU usage and the best solutions for optimal operation of four-reservoir system were obtained by MSA algorithm with values of (269.7s and 308.83) which are very close to the global optimum solution. Corresponding values for ICA and HS were (486.73, 306.47) and (638.61s, 264.61) respectively, which put them in the next ranks. Similar results were observed for ten-reservoir system; the CPU time and optimal value obtained by MSA were (722.5s, 1,195.58) while for ICA and HS were (1,421.62s, 1,136.22) and (1,963.41s, 1,060.76), respectively. The values of R2 and RMSE achieved by MSA were (0.951, 0.528) and (0.985, 0.521) for 4-reservoir and 10-reservoir systems which demonstrated the outstanding performance of this algorithm in optimal operation of multi-reservoir systems. In a general comparison, it was concluded that among the twelve investigated algorithms, MSA was the best, and it is recommended as a robust promising tool in optimal operation of multi-reservoir systems.

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Comparative analysis of some evolutionary-based models in optimization of dam reservoirs operation

Scientific Reports ◽

10.1038/s41598-021-95159-4 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Mohammad Reza Sharifi ◽

Saeid Akbarifard ◽

Kourosh Qaderi ◽

Mohamad Reza Madadi

Keyword(s):

Objective Function ◽

Optimization Algorithm ◽

Optimal Operation ◽

Engineering Problem ◽

Performance Criteria ◽

Reliable Technique ◽

Reservoir System ◽

Dam Reservoirs ◽

Reservoir Systems ◽

Swarm Algorithm

AbstractDeriving optimal operation policies for multi-reservoir systems is a complex engineering problem. It is necessary to employ a reliable technique to efficiently solving such complex problems. In this study, five recently-introduced robust evolutionary algorithms (EAs) of Harris hawks optimization algorithm (HHO), seagull optimization algorithm (SOA), sooty tern optimization algorithm (STOA), tunicate swarm algorithm (TSA) and moth swarm algorithm (MSA) were employed, for the first time, to optimal operation of Halilrood multi-reservoir system. This system includes three dams with parallel and series arrangements simultaneously. The results of mentioned algorithms were compared with two well-known methods of genetic algorithm (GA) and particle swarm optimization (PSO) algorithm. The objective function of the optimization model was defined as the minimization of total deficit over 223 months of reservoirs operation. Four performance criteria of reliability, resilience, vulnerability and sustainability were used to compare the algorithms’ efficiency in optimization of this multi-reservoir operation. It was observed that the MSA algorithm with the best value of objective function (6.96), the shortest CPU run-time (6738 s) and the fastest convergence rate (< 2000 iterations) was the superior algorithm, and the HHO algorithm placed in the next rank. The GA, and the PSO were placed in the middle ranks and the SOA, and the STOA placed in the lowest ranks. Furthermore, the comparison of utilized algorithms in terms of sustainability index indicated the higher performance of the MSA in generating the best operation scenarios for the Halilrood multi-reservoir system. The application of robust EAs, notably the MSA algorithm, to improve the operation policies of multi-reservoir systems is strongly recommended to water resources managers and decision-makers.

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Modeling the Physical Nexus across Water Supply, Wastewater Management and Hydropower Generation Sectors in River–Reservoir Systems

Water ◽

10.3390/w11040822 ◽

2019 ◽

Vol 11 (4) ◽

pp. 822 ◽

Cited By ~ 1

Author(s):

Dedi Liu ◽

Jiayu Zhang ◽

Yujie Zeng ◽

Youjiang Shen

Keyword(s):

Water Quality ◽

Boundary Conditions ◽

Water Supply ◽

Water Inflow ◽

Wastewater Management ◽

Hydropower Generation ◽

Reservoir System ◽

River Reservoir ◽

Protection And Utilization ◽

Wastewater Pollutants

Most water supply and hydropower generation is obtained from the river–reservoir system, and wastewater pollutants are also dumped into the system. Increasing water demand and consumption have caused the water supply, wastewater pollutant management and hydropower generation sectors to be interlinked and to reinforce each other in the system. A physical nexus across water supply, wastewater management and hydropower generation sectors for a river–reservoir system was developed based on the analytical water quality and hydropower generation equations. Considering the Jinghong hydropower reservoir, located in the middle and lower reaches of the Lancangjiang River Basin, as a case study, both the wastewater pollutant management target and water inflow from the upstream as the external and boundary conditions, were employed to establish the effects of the external and boundary conditions on the nexus. It was demonstrated that the nexus of water supply and hydropower generation sectors does not vary with the water quality indicators and its protection target, without the separation of environmental flow in hydropower generation flow. In addition, the amount of hydropower generation decreases with increasing water supply. However, the lapse rates of allowable wastewater pollutants–water supply differ based on the water inflow and the wastewater pollutant management sectors, while the efficiency of hydropower generation and the sensitivity of allowable wastewater pollutants per amount of water supply are considered to be unrelated to the water inflow and wastewater pollutant management target conditions. The quantitative nexus developed through the proposed equation not only contributes to a more complete understanding of the mechanism of cross-connections, but also in creation of specific water protection and utilization measures, which is also the focus of the water–energy nexus.

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Application of Cellular Automata in Bi-Objective Operation of Multi Reservoir Systems

Water ◽

10.3390/w13192740 ◽

2021 ◽

Vol 13 (19) ◽

pp. 2740

Author(s):

Mohammad Hadi Afshar ◽

Reza Hajiabadi

Keyword(s):

Simulated Annealing ◽

Cellular Automata ◽

Water Resource Management ◽

Computational Cost ◽

Search Space ◽

Optimal Operation ◽

Reservoir System ◽

Conflicting Objectives ◽

Reservoir Systems ◽

Southwestern Iran

Optimal operation of multi-reservoir systems is one the most challenging problems in water resource management due to their multi-objective nature and time-consuming solving process. In this paper, Multi-Reservoir Parallel Cellular Automata-Simulated Annealing (MPCA-SA), a hybrid method based on cellular automata and simulated annealing is presented for solving bi-objective operations of multi-reservoir systems problems. The problem considers the bi-objective operation of a multi-reservoir system with the two conflicting objectives of water supply and hydropower generation. The MPCA-SA method uses two single-objective cellular automata acting in parallel to explore the problem search space and find the optimal solutions based on the probabilistic interaction with each other. Bi-objective operation of the Dez-Gotvand-Masjed Soleyman three-reservoir system, as a real-world system in southwestern Iran for a period of 60 months, is considered in order to evaluate the ability of the proposed method. In addition, a Non-dominated Sorting Genetic Algorithm (NSGAII) is also used to solve the problems and the results are compared with those of MPCA-SA, indicating the capabilities of the proposed MPCA-SA method. The results show that the MPCA-SA method is able to produce solutions comparable to those of NSGAII with a much-reduced computational cost equal to 1.2% of that required by the NSGAII, emphasizing the efficiency and practicality of the proposed method.

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Mitigate water shortage by improving hydropower generation strategy of the cascade reservoir system in the Be River Basin, Vietnam

Water Science & Technology Water Supply ◽

10.2166/ws.2020.220 ◽

2020 ◽

Vol 20 (8) ◽

pp. 3216-3232

Author(s):

Nguyen Thi Thuy Linh ◽

Frederick N.-F. Chou

Keyword(s):

Water Resources ◽

Water Supply ◽

River Basin ◽

Water Resources Management ◽

Water Allocation ◽

Water Shortage ◽

Hydropower Generation ◽

Water Shortages ◽

Resources Management ◽

Reservoir System

Abstract To meet increasing water consumption with limited water resources, management approaches that transfer water between purposes must be improved for sustainable development. This entails an urgent requirement for appropriate water resources management within water–energy interaction if severe water shortage occurs occasionally. This study evaluates hydropower generation policies of a cascade reservoir system in the Be River Basin in terms of security of water supply and energy production. The Generalized Water Allocation Simulation Model (GWASIM) was applied to simulate the water use of a complex system of hydropower generation and water supply. Two water allocation scenarios and six alternatives defined by varying monthly generating hours were modeled and compared. The results demonstrate that a compromise between hydropower generation and water supply can be negotiated to reduce the severity of water shortages. Different monthly hours of hydropower generation among alternatives show an effect on improving power production and reliable water supply. This study provides overall insight into the performance of a multi-purpose cascade reservoir system. It will provide a foundation for improving future study of reservoir operations in meeting the increasing demands of water and energy in Vietnam.

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Optimizing the Management Strategies of a Multi-Purpose Multi-Reservoir System in Vietnam

Water ◽

10.3390/w12040938 ◽

2020 ◽

Vol 12 (4) ◽

pp. 938

Author(s):

Frederick N.-F. Chou ◽

Nguyen Thi Thuy Linh ◽

Chia-Wen Wu

Keyword(s):

Water Supply ◽

River Basin ◽

Management Strategies ◽

Water Shortage ◽

Hydropower Generation ◽

Water Shortages ◽

Global Trends ◽

Reservoir System ◽

System A

Resource shortages are having an increasingly severe impact as global trends like rapid population growth, urbanization, economic development, and climate change unfold. Moreover, rising living standards across many regions are also affecting water and energy resources. This entails an urgent requirement to improve water resources management. An important improvement is to transfer water between the different uses of the reservoir system. A compromise between the needs of hydropower generation and the water supply can be negotiated for the reservoir system to reduce the severity of water shortages. The Be River basin in Vietnam was selected as a case study to investigate. The combination of the generalized water allocation simulation model (GWASIM) and the bounded optimization by quadratic approximation (BOBYQA) algorithm was applied to optimize hydropower generation in various water shortage scenarios. The results present optimized hydropower generation policies for cascade reservoirs that would significantly improve the present operating policy in terms of both the water supply and hydropower generation. Moreover, multiple scenarios will provide flexibility to the reservoir operator by giving the relationship between water and energy. Given water supply conditions, the operator will be able to choose among several optimal solutions to ensure greater water resource efficiency in the Be River basin.

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Extended multi-objective firefly algorithm for hydropower energy generation

Journal of Hydroinformatics ◽

10.2166/hydro.2017.114 ◽

2017 ◽

Vol 19 (5) ◽

pp. 734-751 ◽

Cited By ~ 2

Author(s):

Omid Bozorg-Haddad ◽

Irene Garousi-Nejad ◽

Hugo A. Loáiciga

Keyword(s):

Firefly Algorithm ◽

Heuristic Algorithms ◽

Optimization Problems ◽

Hydropower Generation ◽

Local Optima ◽

Multi Objective ◽

Reservoir System ◽

Study Results ◽

Highly Nonlinear ◽

Matlab Programming

Classical methods have severe limitations (such as being trapped in local optima, and the curse of dimensionality) to solve optimization problems. Evolutionary or meta-heuristic algorithms are currently favored as the tools of choice for tackling such complex non-linear reservoir operations. This paper evaluates the performance of an extended multi-objective developed firefly algorithm (MODFA). The MODFA script code was developed using the MATLAB programming language and was applied in MATLAB to optimize hydropower generation by a three-reservoir system in Iran. The two objectives used in the present study are the maximization of the reliability of hydropower generation and the minimization of the vulnerability to generation deficits of the three-reservoir system. Optimal Paretos (OPs) obtained with the MODFA are compared with those obtained with the multi-objective genetic algorithm (MOGA) and the multi-objective firefly algorithm (MOFA) for different levels of performance thresholds (50%, 75%, and 100%). The case study results demonstrate that the MODFA is superior to the MOGA and MOFA for calculating proper OPs with distinct solutions and a wide distribution of solutions. This study's results show that the MODFA solves multi-objective multi-reservoir operation system with the purpose of hydropower generation that are highly nonlinear that classical methods cannot solve.

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