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Over the past few years, several evolutionary algorithms have been developed and applied to solving reservoir optimization problems (Table 1).

Table 1

Literature review of the application of well-known evolutionary algorithms in the operation of reservoirs

Evolutionary algorithmReferencesProblem definitionResults
Genetic algorithm (GA) Sharif & Wardlaw (2000)  
  • Optimization of a multi-reservoir system in Indonesia by GA and discrete differential dynamic programming (DP)

 
  • ✓ The GA results are very close to the optimum, it does not need trial state trajectories to initiate the search and it does not need discretization of state variables, in contrast to DP.

 
Chang et al. (2005)  
  • Using GA to derive operating rule curves for the Shih-Men reservoir in Taiwan

 
  • ✓ GA provides an effective way for searching the rule curves.

 
Garousi-Nejad et al. (2016)  
  • Optimal operation of reservoirs for irrigation supply and hydropower generation using GA and FA

 
  • ✓ FA is superior in terms of convergence and variance of the results.

 
Genetic programming (GP) Fallah-Mehdipour et al. (2013a, 2013b) 
  • Extraction of optimal operation rules in an aquifer-dam system with developed version of GP in comparison with GA

 
  • ✓ Developed GP is more flexible and effective in determining optimal rule curves for a conjunctive aquifer-dam system.

 
Fallah-Mehdipour et al. (2012)  
  • Application of GP for real-time operation of reservoir

 
  • ✓ The GP-based rule is effective in determining optimal rule curves.

 
Ashofteh et al. (2015)  
  • Using multi-objective GP for evaluation of the climatic change impacts on multi-objective reservoir operation

 
  • ✓ Reservoir-operating rules that take into account changing climate would lead to improvements in reservoir performance in the order of 29–32% relative to operating rules based on baseline climatic conditions.

 
Fallah-Mehdipour et al. (2013a, 2013b) 
  • Developing operational decision rules of multi-purpose reservoirs by GP, GA and linear, integer, nonlinear, and global optimization (LINGO)

 
  • ✓ The objective function value is significantly enhanced by GP.

  • ✓ The GP-based operational rule is effective in determining optimal rule curves for reservoirs.

 
Ant colony optimization (ACO) Jalali et al. (2006)  
  • Optimal operation of Dez reservoir with ACO

 
  • ✓ ACO is quite sensitive to setup parameters, and provides better and more comparable results with known global optimum results.

 
Kumar & Reddy (2006)  
  • Derivation of operating policies for the Hirakud multi-purpose reservoir system using ACO and GA

 
  • ✓ ACO outperforms GA in terms of power production, irrigation demands and flood control restrictions.

 
Moeini & Afshar (2013)  
  • Optimal operation of multi-reservoir systems by ACO and constrained ACO

 
  • ✓ Constrained ACO was better than conventional ACO.

 
Mohammed et al. (2018)  
  • Optimization of Darbandikhan reservoir operation using a developed version of ACO

 
  • ✓ Developed ACO showed a high performance in exploring the optimum solutions for the operation of the Darbandikhan reservoir.

 
Particle swarm optimization (PSO) Afshar (2013)  
  • Using PSOs for optimal operation of multi-reservoir systems

 
  • ✓ PSOs are very effective in locating optimal solutions and very efficient in terms of the convergence rate.

 
 Ghimire & Reddy (2013)  
  • An elitist-mutated PSO (EMPSO) is applied for weekly operation policies of the Upper Seti Hydro-Power Reservoir for wet, dry and normal water years

 
  • ✓ The EMPSO can generate 3% more hydropower than the planned hydropower production with a sustainability index of 0.75.

 
 Afshar (2012)  
  • Using constrained PSOs (CPSO) for optimization of large reservoir operation compared to GA and conventional PSO

 
  • ✓ CPSOs were superior to conventional PSO and GA in locating near-optimal solutions and convergence characteristics.

  • ✓ CPSOs were more insensitive to the swarm size and initial swarm.

 
 Al-Aqeeli & Agha (2020)  
  • Optimal operation of Mosul and Badush reservoirs system for hydropower production using PSO

 
  • ✓ PSO has high performance in real-time operation of single- and multi-reservoir systems.

 
Harmony search (HS) Bashiri-Atrabi et al. (2015)  
  • Application of HS for optimization of the Narmab reservoir operation for flood management

 
  • ✓ HS has high convergence rate, it can be effectively used for operation of reservoirs for flood management.

 
Kougias & Theodossiou (2013)  
  • Application of HS for optimum operation of a four-reservoir system over 24 hours

 
  • ✓ HS has high potential for the optimization of multi-reservoir systems.

 
Mirbeyk et al. (2020)  
  • Using HS for optimal operation of Dez reservoir

 
  • ✓ HS has the ability to solve real large reservoir problems.

 
Water cycle algorithm (WCA) Bozorg Haddad et al. (2015)  
  • Comparison of WCA and GA for optimal operation of Karon-4 reservoir in Iran

 
  • ✓ The results demonstrate the high efficiency and reliability of WCA in solving reservoir operation problems.

 
Qaderi et al. (2018)  
  • Optimal operation of Golestan and Voshmgir consecutive dams by WCA

 
  • ✓ WCA excellently calculated the annual deficit of the Golestan–Voshmgir multi-reservoir system.

 
Honey-bee mating optimization (HBMO) Bozorg Haddad et al. (2011)  
  • HBMO was compared with linear programming (LP), DP, differential DP, discrete differential DP and GA in the optimal operation of multi-reservoir systems

 
  • ✓ The high efficiency and rapid convergence rate of HBMO compared to other algorithms make it a robust tool for the optimal operation of reservoirs.

 
Soghrati & Moeini (2020)  
  • Performance of HBMO for optimization of Dez hydropower reservoir operation was compared with artificial bee colony (ABC) algorithm, GA, improved particle swarm optimization (IPSO) algorithm, ACO and GSA

 
  • ✓ Using ABC gave the best results with low computational costs.

 
Gravity search algorithm (GSA) Bozorg-Haddad et al. (2016)  
  • Application of GSA to optimization of multi-reservoir operation

 
  • ✓ GSA requires few parameters for implementation, and reaches the optimal solution in few functional evaluations.

 
Imperialist competitive algorithm (ICA) Afshar et al. (2015)  
  • Optimizing water supply and hydropower reservoir operation rule curves by ICA for Dez reservoir in Iran

 
  • ✓ ICA converged to near-optimal solutions efficiently in the case study. It performed quite well in reservoir operation optimization.

 
Hosseini-Moghari et al. (2015)  
  • Optimal operation policy of the Karun4 reservoir using ICA, GA, cuckoo optimization algorithm (COA), and nonlinear programing (NLP).

 
  • ✓ Both COA and ICA showed high performance in extraction of optimal operation policies of Karun4.

 
Rahimi et al. (2020)  
  • Optimization of hydropower energy and flood control for a real multi-objective multi-reservoir system by ICA

 
  • ✓ ICA has a fast convergence rate and a high adaptability to the problem constraints.

 
Spider monkey algorithm (SMA) Ehteram et al. (2018)  
  • Investigating the capability of SMA compared to well-known optimization algorithms in the optimization of the Golestan and Voshmgir dam operations

 
  • ✓ The SMA, with its high convergence rate, is suggested as an appropriate tool for optimizing the operation policy of cascade reservoirs.

 
Bat algorithm (BA) Ahmadianfar et al. (2016)  
  • An improved version of BA was used to optimize hydropower generation through two multi-reservoir benchmark problems

 
  • ✓ The improved BA indicated a high performance in hydropower optimization.

 
Evolutionary algorithmReferencesProblem definitionResults
Genetic algorithm (GA) Sharif & Wardlaw (2000)  
  • Optimization of a multi-reservoir system in Indonesia by GA and discrete differential dynamic programming (DP)

 
  • ✓ The GA results are very close to the optimum, it does not need trial state trajectories to initiate the search and it does not need discretization of state variables, in contrast to DP.

 
Chang et al. (2005)  
  • Using GA to derive operating rule curves for the Shih-Men reservoir in Taiwan

 
  • ✓ GA provides an effective way for searching the rule curves.

 
Garousi-Nejad et al. (2016)  
  • Optimal operation of reservoirs for irrigation supply and hydropower generation using GA and FA

 
  • ✓ FA is superior in terms of convergence and variance of the results.

 
Genetic programming (GP) Fallah-Mehdipour et al. (2013a, 2013b) 
  • Extraction of optimal operation rules in an aquifer-dam system with developed version of GP in comparison with GA

 
  • ✓ Developed GP is more flexible and effective in determining optimal rule curves for a conjunctive aquifer-dam system.

 
Fallah-Mehdipour et al. (2012)  
  • Application of GP for real-time operation of reservoir

 
  • ✓ The GP-based rule is effective in determining optimal rule curves.

 
Ashofteh et al. (2015)  
  • Using multi-objective GP for evaluation of the climatic change impacts on multi-objective reservoir operation

 
  • ✓ Reservoir-operating rules that take into account changing climate would lead to improvements in reservoir performance in the order of 29–32% relative to operating rules based on baseline climatic conditions.

 
Fallah-Mehdipour et al. (2013a, 2013b) 
  • Developing operational decision rules of multi-purpose reservoirs by GP, GA and linear, integer, nonlinear, and global optimization (LINGO)

 
  • ✓ The objective function value is significantly enhanced by GP.

  • ✓ The GP-based operational rule is effective in determining optimal rule curves for reservoirs.

 
Ant colony optimization (ACO) Jalali et al. (2006)  
  • Optimal operation of Dez reservoir with ACO

 
  • ✓ ACO is quite sensitive to setup parameters, and provides better and more comparable results with known global optimum results.

 
Kumar & Reddy (2006)  
  • Derivation of operating policies for the Hirakud multi-purpose reservoir system using ACO and GA

 
  • ✓ ACO outperforms GA in terms of power production, irrigation demands and flood control restrictions.

 
Moeini & Afshar (2013)  
  • Optimal operation of multi-reservoir systems by ACO and constrained ACO

 
  • ✓ Constrained ACO was better than conventional ACO.

 
Mohammed et al. (2018)  
  • Optimization of Darbandikhan reservoir operation using a developed version of ACO

 
  • ✓ Developed ACO showed a high performance in exploring the optimum solutions for the operation of the Darbandikhan reservoir.

 
Particle swarm optimization (PSO) Afshar (2013)  
  • Using PSOs for optimal operation of multi-reservoir systems

 
  • ✓ PSOs are very effective in locating optimal solutions and very efficient in terms of the convergence rate.

 
 Ghimire & Reddy (2013)  
  • An elitist-mutated PSO (EMPSO) is applied for weekly operation policies of the Upper Seti Hydro-Power Reservoir for wet, dry and normal water years

 
  • ✓ The EMPSO can generate 3% more hydropower than the planned hydropower production with a sustainability index of 0.75.

 
 Afshar (2012)  
  • Using constrained PSOs (CPSO) for optimization of large reservoir operation compared to GA and conventional PSO

 
  • ✓ CPSOs were superior to conventional PSO and GA in locating near-optimal solutions and convergence characteristics.

  • ✓ CPSOs were more insensitive to the swarm size and initial swarm.

 
 Al-Aqeeli & Agha (2020)  
  • Optimal operation of Mosul and Badush reservoirs system for hydropower production using PSO

 
  • ✓ PSO has high performance in real-time operation of single- and multi-reservoir systems.

 
Harmony search (HS) Bashiri-Atrabi et al. (2015)  
  • Application of HS for optimization of the Narmab reservoir operation for flood management

 
  • ✓ HS has high convergence rate, it can be effectively used for operation of reservoirs for flood management.

 
Kougias & Theodossiou (2013)  
  • Application of HS for optimum operation of a four-reservoir system over 24 hours

 
  • ✓ HS has high potential for the optimization of multi-reservoir systems.

 
Mirbeyk et al. (2020)  
  • Using HS for optimal operation of Dez reservoir

 
  • ✓ HS has the ability to solve real large reservoir problems.

 
Water cycle algorithm (WCA) Bozorg Haddad et al. (2015)  
  • Comparison of WCA and GA for optimal operation of Karon-4 reservoir in Iran

 
  • ✓ The results demonstrate the high efficiency and reliability of WCA in solving reservoir operation problems.

 
Qaderi et al. (2018)  
  • Optimal operation of Golestan and Voshmgir consecutive dams by WCA

 
  • ✓ WCA excellently calculated the annual deficit of the Golestan–Voshmgir multi-reservoir system.

 
Honey-bee mating optimization (HBMO) Bozorg Haddad et al. (2011)  
  • HBMO was compared with linear programming (LP), DP, differential DP, discrete differential DP and GA in the optimal operation of multi-reservoir systems

 
  • ✓ The high efficiency and rapid convergence rate of HBMO compared to other algorithms make it a robust tool for the optimal operation of reservoirs.

 
Soghrati & Moeini (2020)  
  • Performance of HBMO for optimization of Dez hydropower reservoir operation was compared with artificial bee colony (ABC) algorithm, GA, improved particle swarm optimization (IPSO) algorithm, ACO and GSA

 
  • ✓ Using ABC gave the best results with low computational costs.

 
Gravity search algorithm (GSA) Bozorg-Haddad et al. (2016)  
  • Application of GSA to optimization of multi-reservoir operation

 
  • ✓ GSA requires few parameters for implementation, and reaches the optimal solution in few functional evaluations.

 
Imperialist competitive algorithm (ICA) Afshar et al. (2015)  
  • Optimizing water supply and hydropower reservoir operation rule curves by ICA for Dez reservoir in Iran

 
  • ✓ ICA converged to near-optimal solutions efficiently in the case study. It performed quite well in reservoir operation optimization.

 
Hosseini-Moghari et al. (2015)  
  • Optimal operation policy of the Karun4 reservoir using ICA, GA, cuckoo optimization algorithm (COA), and nonlinear programing (NLP).

 
  • ✓ Both COA and ICA showed high performance in extraction of optimal operation policies of Karun4.

 
Rahimi et al. (2020)  
  • Optimization of hydropower energy and flood control for a real multi-objective multi-reservoir system by ICA

 
  • ✓ ICA has a fast convergence rate and a high adaptability to the problem constraints.

 
Spider monkey algorithm (SMA) Ehteram et al. (2018)  
  • Investigating the capability of SMA compared to well-known optimization algorithms in the optimization of the Golestan and Voshmgir dam operations

 
  • ✓ The SMA, with its high convergence rate, is suggested as an appropriate tool for optimizing the operation policy of cascade reservoirs.

 
Bat algorithm (BA) Ahmadianfar et al. (2016)  
  • An improved version of BA was used to optimize hydropower generation through two multi-reservoir benchmark problems

 
  • ✓ The improved BA indicated a high performance in hydropower optimization.

 
They are considered to be very effective alternatives for solving complex optimization problems with either single or multiple objectives. These algorithms offer an expanded capability to systematically select the optimal solutions given the objectives and constraints (Labadie 2004). Garousi-Nejad et al. (2016) applied the firefly algorithm (FA) to optimal operation of reservoirs used for irrigation supply and hydropower production. The results demonstrated the superior performance of FA compared to genetic algorithms (GA) in terms of the convergence rate and obtaining optimal value. Qaderi et al. (2018) used a water cycle algorithm (WCA) to derive operating policy for a multi-reservoir system. They reported a high performance of WCA compared to other well-known algorithms. Ehteram et al. (2017) used the GA-krill hybrid for the optimization of multi-reservoir systems operation and showed that it outperformed the traditional nonlinear programming models. Ehteram et al. (2018) successfully used the spider monkey algorithm (SMA) to optimize a multi-reservoir system with the aim of decreasing irrigation deficiencies. Asadieh & Afshar (2019) used the charged system search (CSS) algorithm to optimize water-supply and hydropower reservoir operation. The results demonstrated the robustness and superiority of the CSS algorithm in solving long-term reservoir operation problems, compared to alternative methods. Feng et al. (2019) proposed the k-means clustering method and extreme learning machine based on particle swarm optimization (PSO) for the operation rule derivation for two hydropower reservoirs in China. They reported the satisfactory performance of proposed method in real-world cases. Mohammadi et al. (2019) reported the high performance of the hybrid whale-genetic algorithm in the optimal operation of multi-reservoir benchmark systems. Using the long-term data of Hongjiadu reservoir in China, Niu et al. (2019) evaluated the capability of four methods: multiple linear regression (MLR), artificial neural network (ANN), extreme learning machine (ELM), and support vector machine (SVM) in deriving the operation rule of the hydropower reservoir. They reported that the three artificial intelligence algorithms (ANN, SVM, and ELM) showed better performances than the conventional MLR and scheduling graph method. Ehteram et al. (2019) proposed the crow algorithm (CA) for optimizing hydropower generation in multi-reservoir systems. They documented the high potential of the proposed CA for achieving optimal solutions to complex optimization problems associated with dam and reservoir operations. Zhou et al. (2019) identified efficient operating rules for hydropower reservoirs using the system dynamics approach. The Three Gorges Reservoir in central China was used as a case study. The results showed that the system dynamics simulation is an efficient way to simulate a complicated reservoir system using feedback and causal loops. Dehghani et al. (2019) applied the grey wolf optimization (GWO) method coupled with an adaptive neuro-fuzzy inference system (ANFIS) to forecast hydropower generation. The results indicated that the hybrid GWO-ANFIS model was capable of predicting hydropower generation satisfactorily. Soghrati & Moeini (2020) proposed an improved artificial bee colony (ABC) algorithm to solve the single-reservoir operation optimization problem. They documented the capability of proposed algorithms to solve large reservoir operation optimization problems. Moeini & Babaei (2020) applied a hybrid of the constrained version of the improved particle swarm optimization (CIPSO) algorithm with a support vector machine (SVM) called the hybrid SVM-CIPSO method for the optimal operation of reservoirs for uncertain water inflow conditions. They reported the acceptable accuracy of this model in predicting the optimal water release for future conditions. Feng et al. (2020) proposed adaptive mutation sine cosine algorithm (ASCA) to optimize multiple hydropower reservoir operation. In this algorithm, they used the elite mutation strategy to increase individual diversity, the simplex dynamic search strategy to improve solution accuracy, and the neighborhood search strategy improve the convergence rate. The simulations of 25 test functions and a real-world hydropower system in China indicated the superiority of ASCA over several existing methods. Al-Aqeeli & Agha (2020) successfully employed PSO for the optimal operation of a multi-reservoir system (Mosul and Badush reservoirs in Iraq) for hydroelectric generation. Azizipour et al. (2020) employed the hybrid cellular automata-simulated annealing approach for optimal hydropower operation of multi-reservoir systems. The case study was a three-reservoir system in the USA. The results indicated that the proposed method was much more efficient than existing algorithms. Bozorg-Haddad et al. (2020) applied the flower pollination algorithm (FPA) to optimize single- and multi-reservoir systems. They reported the superiority of FPA over PSO and nonlinear programming method (NLP) in finding the optimal solutions.

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