Abstract
Water resource management is a complex engineering problem, due to the stochastic nature of inflow, various demands and environmental flow downstream. With the increase in water consumption for domestic use and irrigation, it becomes more challenging. Many more difficulties, such as nonconvex, nonlinear, multiobjective, and discontinuous functions, exist in real life. From the past two decades, heuristic and metaheuristic optimization techniques have played a significant role in managing and providing better performance solutions. The popularity of heuristic and metaheuristic optimization techniques has increased among researchers due to their numerous benefits and possibilities. Researchers are attempting to develop more accurate and efficient models by incorporating novel methods and hybridizing existing ones. This paper's main contribution is to show the stateoftheart of heuristic and metaheuristic optimization techniques in water resource management. The research provides a comprehensive overview of the various techniques within the context of a thorough evaluation and discussion. As a result, for water resource management problems, this study introduces the most promising evolutionary and swarm intelligence techniques. Hybridization, modifications, and algorithm variants are reported to be the most successful for improving optimization techniques. This survey can be used to aid hydrologists and scientists in deciding the proper optimization techniques.
HIGHLIGHTS
This paper reviews the different evolutionary algorithms and their applications.
This paper reviews the different swarm intelligence algorithms and their applications.
It identifies the importance and demerits of different heuristic and metaheuristic algorithms.
It highlights some of the observations on the challenges and needs.
It highlights the stateoftheart of water resources management and planning.
INTRODUCTION
Scarcity of water sources and increasing demand as a result of population increase and effects of climate change have always been difficult and critical problems for many river planners and managers (Lun et al. 2021). In the last few decades, many projects have been implemented. However, it is difficult to construct more and more water resource projects owing to the high investments involved and the land acquisition problems (Kumar & Yadav 2019). In this regard, planning, design, development and operational activities of projects need a solution based on qualitative procedures (Mohammed et al. 2017). Optimization and effectively managing the existing projects is an alternative solution to overcome these problems. Optimization techniques have been applied in the planning, operation and management of water resources for decades (Kumar & Yadav 2020b).
Conventional optimization techniques include linear (LP), nonlinear (NLP) and dynamic (DP) programming. Kantorovich (1960) introduced LP in 1939; the technique was developed during World War II to plan and reduce army expenses. It is one of the most popular and simplest optimization techniques. Later, it was implemented in other fields, including water resources. Despite the advantages, it has certain limitations too (Azizipour et al. 2016). It can be applied only when the objective functions, equations and constraints are linear. The technique is unable to deal with the uncertainty problem (Hossain & Elshafie 2013). NLP was developed to overcome the shortcomings of LP, and it is capable of solving nonlinear problems. NLP has been successfully applied in hydropower, reservoir operation and other water resource contexts. However, the technique fails when the dimensionality of the problem increases; it gets stuck in the local optimal solution and is unable to achieve a global solution (Hossain & Elshafie 2013). DP was developed to solve stochastic and nonlinear problems. The problem arises when multiple state variables are present. DP also has a few limitations, especially when the scale of the problem increases (Ahmadianfar et al. 2017). It requires more memory and suffers from an exponential increase in computational time. DP is also known as the curse of dimensionality (Kumar & Yadav 2020a). Therefore, these conventional optimization techniques do not guarantee global optimum performance and have led to the quest for new methods.
Heuristic and metaheuristic optimization techniques were developed in the late ‘70 s to overcome the drawbacks of LP, NLP and DP (Rao & Keesari 2018). A heuristic is a technique aimed to solve a problem faster when traditional techniques are too slow. A metaheuristic is a higherlevel technique or heuristic that seeks, generates, or selects a heuristic that may provide a sufficiently good solution to an optimization problem (Attea et al. 2021). These newer techniques were developed to address problems such as nonlinearity, multiobjective, uncertainty and so on (Fayaed et al. 2013). Broadly, they are classified into populationbased algorithms and neighbourhoodbased algorithms. Populationbased algorithms are evolutionary computation and swarm intelligence (Rao & Pawar 2020). These techniques are flexible and are capable of providing a global solution with more ease. The results depend on the initial population, which is randomly generated to obtain the global solution based on probabilistic theory. Evolutionary computations include genetic algorithm (GA), differential evolution (DE), genetic programming (GP), evolutionary programming (EP), and evolutionary strategies (ES) (Du & Swamy 2016). Swarm intelligencebased algorithms include ant colony optimization (ACO), harmony search (HS), particle swarm optimization (PSO), cuckoo search (CS), artificial bee colony (ABC), firefly algorithm (FA), bat algorithm (BA), honey bee mating optimization (HBMO), and shuffled frog leaping algorithm (SFLA). Neighbourhoodbased algorithms include simulated annealing (SA) and tabu search (TS) (Kumar & Yadav 2021). Figure 1 shows the flow chart of different algorithms.
Several heuristics and metaheuristic techniques have been applied to solve water resource problems successfully. For example, various algorithms have been used to solve reservoir operation problems such as GA (Khadr & Schlenkhoff 2021), PSO (Chen et al. 2020; BozorgHaddad et al. 2021), ABC (Moeini & Soghrati 2020), DE (Ahmadianfar et al. 2021), shark algorithm (SA) (Mohammed et al. 2017), and CS (Ming et al. 2015). To solve optimal cropping and water allocation problems GA (Dutta et al. 2016), nondominated sorting genetic algorithm (NSGAII) (Lalehzari et al. 2016), DE (Adeyemo & Otieno 2010), and PSO (Davijani et al. 2016) have been used. For water distribution network problems, for instance, PSO (Torkomany et al. 2021) DE (Pant & Snasel 2021), ABC (Li & Feng 2020), ACO (Mehzad et al. 2020). Reservoir flood control operation and management problems, for example, evolutionary algorithm (Qi et al. 2017), DE (Jia et al. 2016), PSO (JahandidehTehrani et al. 2020), immune algorithm (Luo et al. 2015) and NSGAII (Lei et al. 2018). Groundwater system management can be implemented by GA (Fowe et al. 2015), surface water and groundwater using FA (KazemzadehParsi et al. 2015a), GA (Ayvaz & Elçi 2018), agricultural land allocation using ACO (Mi et al. 2015), evapotranspiration modelling using FA (Tao et al. 2018).
Most of the algorithms have their advantages and limitations. For example, GA is one of the oldest EAs that has been successfully applied in the water resources field. It can provide multiple solutions to a problem. However, it requires a proper tuning of algorithmspecific parameters such as mutation, crossover and reproduction. Besides, the computational time is high when it comes to simulationoptimization based links and it is timeconsuming to fully understand the art (Zheng et al. 2017). GP is a simple, robust, flexible, and effective algorithm, which requires less computational time and provides accurate results. However, it necessitates internal parameters such as crossover and mutation probability (Rao & Pawar 2020). DE can handle nondifferentiable, nonlinear and multimodal functions. Nonetheless, careful selection of algorithmspecific parameters is needed – for instance, the scaling factor and crossover rate. When the system dimensions are increased, DE convergence ability and flexibility are affected. It could be observed that it may easily drop to the local optimal solution (Rao et al. 2011). ACO is robust enough to solve nonuniform, complex and nonlinear problems, and it is capable of achieving quick convergence. Nevertheless, its computation gets affected when the problem is of the explicit or implicit stochastic type. Further, it needs tuning parameters such as relative pheromone trail, heuristic information, and evaporation (Chen et al. 2017b). PSO is simple to code, provides fast convergence, and involves low computational cost. But, tuning of parameters such as inertia weight, social, and cognitive parameters is required. If the parameters are set correctly, the algorithm can achieve a global solution (Rezaei et al. 2017). ABC is flexible, simple, robust, easy to implement and capable of performing a global search. However, it is quite slow in sequential processing and requires tuning parameters such as scout, onlooker and employed bees (Li & Feng 2020).
While HS has fewer mathematical necessities and does not need the initial value to set the decision variables, it requires many parameters, such as memory size and pitch adjustment. Moreover, the rate of choosing the memory and neighbouring values is important (Jung et al. 2018). FA is useful in finding both global and local solutions synchronically and effectively. FA is useful for parallel implementation as different fireflies can work independently. However, the tuning of randomization parameter, attractiveness and absorption coefficient is needed (Wang et al. 2018). CS uses Levy flights, a process that helps the search space to explore more effectively. CS provides an efficient and global convergence solution. Furthermore, it requires lesser tuning parameters, such as probability factor, and the results are not very sensitive to these parameters (Sheikholeslami et al. 2015). BA is flexible, simple, and easy to implement. It yields the best solution in less time, has fast convergence at the early state, and later the convergence rate decreases. The convergence is affected if the proper tuning of parameters such as wavelength and emission coefficient is not done (Gandomi et al. 2013). SFL is faster in searching the space. However, too many internal parameters need to be set, including the number of memeplexes, frogs in each memeplex and submemeplex, and the step size (MoraMelia et al. 2016). The advantage of the HBMO algorithm is its robust, adaptive, simple, and scalable nature. The limitations include the necessity for tuning mating flights, size of the hive, number of accepted solutions and trial solutions, and constant parameters such as queen's energy and initial speed (Niknam et al. 2011). The tuning parameters are called algorithmspecific parameters, which need to be entered before running the algorithm. Their improper tuning affects the overall performance of the algorithm and may result in a local optimum solution. With practice, one can understand the way to tune these parameters to obtain a global optimum solution.
The main aim is to show the stateoftheart of heuristic and metaheuristic optimization techniques in water resource management. The research provides a comprehensive overview of various evolutionary and swarm intelligence techniques such as GA, DE, GP, ACO, POS, ABC, HS, FA, CS, BA, and SFLA in water resource management. This survey can be used to aid hydrologists and scientists in deciding the proper optimization techniques.
EVOLUTIONARY ALGORITHM
The most powerful metaheuristics technique for optimization is the evolutionary algorithm (EA), which is a natureinspired technique used for stochastic global optimization. The algorithm refers to a major approach in the field of optimization to build adaptive systems (Whitley et al. 1996). The technique is quite simple; yet, it can reach the nearoptimum or global optimum (maximum or minimum) solution. EA is especially useful when a conventional calculusbased method is not able to solve or is difficult to implement. EA can be applied to complex problems in multireservoir, multiobjective, noncontinuous, and nondifferentiable contexts. The most popular EA is a genetic algorithm (GA). The steps involved in EA are population generation, fitness selection and choice of the basic operators, namely crossover, mutation and selection. A few of the best EAs are given as follows.
Genetic algorithm (GA)
GA is an EA based on the mechanism of genetics and is derived from the natural evolution and selection process. It is a metaheuristic technique developed by Holland (1975). GA is used in optimization and search problems. The algorithm comprises four basic units, namely gene, bit, chromosome and gene pool. First, the initial population is selected for participation in the reproduction process. The second one is the crossover, in which the two strings exchange building blocks to create new ones. The next one is a mutation, where the new strings to the population are added and the best fitness selection is done. The strings are repeated until an optimal solution is obtained. Figure 2 shows the pseudocode of the genetic algorithm. The details of GA can be found in Savic & Walters (1997).
GA was utilized in water resources in the early 1990s. Goldberg & Kuo (1987) employed GA to obtain an optimal pipeline system. Dandy et al. (1996) proposed an improved version of GA by using variable power scaling as the fitness function and creeping mutation for obtaining an optimal pipe network. Sharif & Wardlaw (2000) made use of the technique for multireservoir system operation. The results obtained by GA were quite close to the optimum solution. Deb et al. (2002) proposed a multiobjective (MO) EA called Nondominated Sorting Genetic Algorithm II (NSGA II); it was tested with difficult test problems and the results were superior. Reddy & Kumar (2006) used a multiobjective genetic algorithm (MOGA) to operate the optimum Bhadra reservoir system and presented the efficiency and utility of the MOGAs in the development of multiobjective operating strategies in reservoirs. Kim et al. (2008) used NSGA II to operate the operating rules of a single reservoir. Results indicate that different inflow series would be handled by the developed operating rule. Nicklow et al. (2010) provided a stateoftheart for GA in water resources planning and management. The paper covered pertinent work related to water distribution, freshwater, sewer, hydrologic, and groundwater systems. Haghighi & Bakhshipour (2012) used an adaptive GA for the optimal design of sewer networks. The result revealed that the model is effective in terms of reliability and time. Tabari & Soltani (2013) used NSGA II to address the multiobjective model of reservoir operation and compared the outcomes with sequential genetic algorithms (SGA). NSGA II has been discovered to decrease the calculation burden significantly compared to SGA. Deb & Jain (2014) developed modifiedGA, a multiobjective optimization algorithm known as NSGA III. NSGA III has an advantage over Paretofront and convergence optimal solution. Although NSGA III is good, there is scope for development. Kalteh (2015) studied waveletbased GAsupport vector regression (SVR) for forecasting the monthly flow. The results were more promising than those obtained with normal GASVR. Zheng et al. (2017) proposed NSGA II with improved search behaviour using five crossover operators to obtain improved results in the water distribution system. The findings ascertain that simplex and simulated binary crossovers have an enhanced ability to find Paretofront solutions. Chen et al. (2017a) improved the NSGA III for enabling reservoir flood control operation. The observations were compared with NSGA II and original NSGA III and superior performance was witnessed. Table 1 provides the summary of the application of GA to water resource planning and management.
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

Goldberg & Kuo (1987)  GA  Application of GA for pipeline optimization.  Benchmark problem  The results showed that the algorithm doesn't depend on the search space's underlying continuity and requires no information except the payoff values. 
Dandy et al. (1996)  Improved GA  Application of GA for pipeline network optimization.  New York City water supply problem  The findings showed that improved GA solutions are less costeffective than the standard GA. 
Sharif & Wardlaw (2000)  GA  Application of GA for the multireservoir system.  Brantas basin, East Java, Indonesia  The results of this research have proved GA's effectiveness in optimizing the multireservoir system, but the probability of the optimal results being reduced when the chromosomes are very long. 
Deb et al. (2002)  NSGAII  Developed NSGAII to help improve computational complexity.  Difficult test problems  The proposed NSGAII is capable of finding a much wider range of solutions and better convergence. 
Reddy & Kumar (2006)  MOGA  MOGA is used to generate a set of optimal operation policies.  Bhadra reservoir system, in India  This research shows how MOGA can be used to solve a reallife multiobjective reservoir operator with a variety of alternative policies. 
Kim et al. (2008)  NSGAII  Reservoir operation using NSGAII  Soyanggang dam basin, North Han River  The results show that the operating rule developed can handle a variety of inflow series. 
Haghighi & Bakhshipour (2012)  Adaptive GA  Proposed to design sewer network design  Benchmark sewer network  The adaptive constraint handling method is shown to be more effective in terms of speed and reliability computation time. 
Tabari & Soltani (2013)  NSGAII  To address the multiobjective model of reservoir operation  Karaj reservoir  The results of singleobjective and multiobjective model operation show that using the NSGAII model to assess optimum quantities reduces the time it takes to get to the optimal quantity of decision variables and the exchange curve between objectives. 
Deb & Jain (2014)  NSGAIII  Developed NSGAIII to handle manyobjective optimization problem  Test problems  This research shows that NSGA III has an advantage over Paretofront and convergence optimal solutions. 
Zheng et al. (2017)  Improved NSGAII  Applied to different water distribution system design problems  Test problems  Offers guidance for selecting appropriate operators for reallife water resources problems. 
Chen et al. (2017a)  Improved NSGAIII  Application of improved NSGAIII for the reservoir flood control operation  Three Gorges reservoir  The results of the simulation indicate that this method can produce optimal Pareto solutions that are well distributed. 
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

Goldberg & Kuo (1987)  GA  Application of GA for pipeline optimization.  Benchmark problem  The results showed that the algorithm doesn't depend on the search space's underlying continuity and requires no information except the payoff values. 
Dandy et al. (1996)  Improved GA  Application of GA for pipeline network optimization.  New York City water supply problem  The findings showed that improved GA solutions are less costeffective than the standard GA. 
Sharif & Wardlaw (2000)  GA  Application of GA for the multireservoir system.  Brantas basin, East Java, Indonesia  The results of this research have proved GA's effectiveness in optimizing the multireservoir system, but the probability of the optimal results being reduced when the chromosomes are very long. 
Deb et al. (2002)  NSGAII  Developed NSGAII to help improve computational complexity.  Difficult test problems  The proposed NSGAII is capable of finding a much wider range of solutions and better convergence. 
Reddy & Kumar (2006)  MOGA  MOGA is used to generate a set of optimal operation policies.  Bhadra reservoir system, in India  This research shows how MOGA can be used to solve a reallife multiobjective reservoir operator with a variety of alternative policies. 
Kim et al. (2008)  NSGAII  Reservoir operation using NSGAII  Soyanggang dam basin, North Han River  The results show that the operating rule developed can handle a variety of inflow series. 
Haghighi & Bakhshipour (2012)  Adaptive GA  Proposed to design sewer network design  Benchmark sewer network  The adaptive constraint handling method is shown to be more effective in terms of speed and reliability computation time. 
Tabari & Soltani (2013)  NSGAII  To address the multiobjective model of reservoir operation  Karaj reservoir  The results of singleobjective and multiobjective model operation show that using the NSGAII model to assess optimum quantities reduces the time it takes to get to the optimal quantity of decision variables and the exchange curve between objectives. 
Deb & Jain (2014)  NSGAIII  Developed NSGAIII to handle manyobjective optimization problem  Test problems  This research shows that NSGA III has an advantage over Paretofront and convergence optimal solutions. 
Zheng et al. (2017)  Improved NSGAII  Applied to different water distribution system design problems  Test problems  Offers guidance for selecting appropriate operators for reallife water resources problems. 
Chen et al. (2017a)  Improved NSGAIII  Application of improved NSGAIII for the reservoir flood control operation  Three Gorges reservoir  The results of the simulation indicate that this method can produce optimal Pareto solutions that are well distributed. 
Genetic programming (GP)
Fogel et al. (1966) initiated the concept of GP. Later, Koza (1990) extended the work and developed GP. In brief, GP is modified from GA (Harris et al. 2003). Metagenetic programming is a method developed by the genetic programming system. The initial population is randomly generated, and a termination criterion is assigned for the problem. GP uses specified inputs and various operators (+, −, *, /). Each population is assigned a fitness evaluator to help in solving the problem. The new generation is derived based on the operators and the fitness (selection). The reproduction process consists of crossover and mutation. The algorithm is repeated until an optimal solution is reached. The details about the algorithm can be found in Koza (1992). The application of GP in water resource problems started in the early 2000s. Savic et al. (1999) were the first researchers to apply the GP in water resources to develop the weights' matrix for the ANN to study the rainfallrunoff. Guven & Kisi (2013) used linear GP (LGP) for the modelling of monthly pan evaporation and compared the results with fuzzy genetics, ANN, adaptive neurofuzzy inference systems. The results suggested that LGP outperformed the other techniques. AkbariAlashti et al. (2015) applied fixedlength gene GP (FLGGP) in hydropower reservoir operation. The results were compared with GA and NLP, and FLGGP was discerned to be more effective and powerful. FallahMehdipour et al. (2016) applied GP to solve flow routing in simple and compound channels. The results were compared with the Muskingum model and 1D coupled characteristic dissipative Galerkin. It was inferred that the GP model is effective in prediction and decreases the computational burden. Cobaner et al. (2016) studied groundwater levels using GP. Five different models of artificial intelligence were used, namely radial basis neural network, multilayer perceptron, multigene GP, multilinear and nonlinear regression models. The multigene GP model provided more accurate predictions than the other methods. Heřmanovský et al. (2017) studied GP to analyze the runoff models for 176 catchment areas. The results of GP were compared with three conceptual models, and it was found that GP was satisfactory and can be used in runoff modelling. Ravansalar et al. (2017) used a new approach known as hybrid wavelet linear GP for the prediction of monthly streamflow. The results were compared with linear GP, hybrid waveletANN and multilinear regression models. The data indicated that the hybrid wavelet linear GP could help in streamflow prediction. Table 2 provides the summary of the application of GP to water resource planning and management.
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

Savic et al. (1999)  GP  Applied GP over rainfallrunoff modelling  Kirkton catchment  The number of GP parameters (population size, crossover and probability of mutation) is much smaller and doesn't have to change for a runoff problem. 
Guven & Kisi (2013)  LGP  Applied LGP for monthly pan evaporation modelling  Mediterranean region  The findings showed that the LGP method can successfully model monthly pan evaporations. 
AkbariAlashti et al. (2015)  FLGGP  Application of FLGGP in hydropower reservoir operation  Karun 3 reservoir  The findings have shown that FLGGP is a powerful, efficient tool and can be used as an appropriate replacement for GP. 
FallahMehdipour et al. (2016)  GP  Application of GP to flow routing  Silakhor River case study and Treske channel case study  The results showed that in simple and compound channels differences are similar between GP predicted hydrographs and Muskingum modular hydrographs and CCDG1D methods. 
Cobaner et al. (2016)  GP  Application of GP for the estimation of groundwater level with surface observation  Upper Estonia Creek Basin in North Central Florida  GP produced more accurate predictions. 
Heřmanovský et al. (2017)  GP  Application of GP for runoff modelling  Model parameter estimation experiment project  The study indicated that the GP is flexible and easy to use and provides a quick and easy way to solve runoff modelling. 
Ravansalar et al. (2017)  Wavelet linear GP  Application of wavelet linear GP for the modelling of monthly streamflow  Beshar River, Iran  The model could be used to simulate the cumulative streamflow data forecast. 
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

Savic et al. (1999)  GP  Applied GP over rainfallrunoff modelling  Kirkton catchment  The number of GP parameters (population size, crossover and probability of mutation) is much smaller and doesn't have to change for a runoff problem. 
Guven & Kisi (2013)  LGP  Applied LGP for monthly pan evaporation modelling  Mediterranean region  The findings showed that the LGP method can successfully model monthly pan evaporations. 
AkbariAlashti et al. (2015)  FLGGP  Application of FLGGP in hydropower reservoir operation  Karun 3 reservoir  The findings have shown that FLGGP is a powerful, efficient tool and can be used as an appropriate replacement for GP. 
FallahMehdipour et al. (2016)  GP  Application of GP to flow routing  Silakhor River case study and Treske channel case study  The results showed that in simple and compound channels differences are similar between GP predicted hydrographs and Muskingum modular hydrographs and CCDG1D methods. 
Cobaner et al. (2016)  GP  Application of GP for the estimation of groundwater level with surface observation  Upper Estonia Creek Basin in North Central Florida  GP produced more accurate predictions. 
Heřmanovský et al. (2017)  GP  Application of GP for runoff modelling  Model parameter estimation experiment project  The study indicated that the GP is flexible and easy to use and provides a quick and easy way to solve runoff modelling. 
Ravansalar et al. (2017)  Wavelet linear GP  Application of wavelet linear GP for the modelling of monthly streamflow  Beshar River, Iran  The model could be used to simulate the cumulative streamflow data forecast. 
Differential evolution (DE)
DE is a heuristic optimization technique. Storn & Price (1996) introduced DE as an effective method for optimizing multimodel objective problems. It has only a few controlling points; it is easy to use, robust and can solve complex engineering problems. The first step in DE is to generate a random vector for the population. After initialization, a mutation process is carried out for each vector. Once the mutation phase is over, a crossover operation is applied to increase the diversity. The last one is the selection operation; if the termination criteria are satisfied, the algorithm provides an optimum solution, else it gets repeated. Storn & Price (1997) presented DE and tested it with the minimizing continuous space problem. The results were compared with adaptive simulated annealing (ASA), GA, annealed Nelder and Mead approach (ANM) (Press et al. 1993) and, stochastic differential equations (SDE). DE outperformed all the techniques. Figure 3 shows the pseudocode of differential evolution. The details of DE can be referred from Storn & Price (1997).
Application of DE in water resource engineering was first attempted by Reddy & Kumar (2007b), which used multiobjective (MO) DE in reservoir operation, compared the results with NSGA II, and they found that MODE exhibited superior performance. Vasan & Simonovic (2010) used DE for the optimization of water distribution network design. The result proved that DE can be an alternative tool for the planning and management of water distribution networks as it is economical and reliable. Regulwar et al. (2010) used DE for the optimal operation of a multipurpose reservoir in hydropower generation. The results were compared with GA, and DE was concluded to be a suitable alternative method for achieving an optimal operation. Zheng et al. (2012) compared the use of DE, dither DE, GA and creep mutation GA in water distribution system optimization. The result established that variants of DE significantly outperformed GA. Raju et al. (2012) applied MODE to irrigation planning problems. It was concluded that selecting a suitable parameter is required for the proper implementation of the algorithm.
Nwankwor et al. (2013) proposed hybrid DE and PSO to identify the optimal hydrocarbon reservoir well. The result showed that the hybrid algorithm outperformed the ordinary DE and PSO, apart from being capable of solving other reservoir problems. Gurarslan & Karahan (2015) used DE to identify the sources of groundwater pollution. The results obtained from DE were better than those derived from other models in the literature. Moosavian & Lence (2017) applied a nondominated sorting differential evolution algorithm (NSDE) and rankingbased mutation (NSDERMO) to solve a problem in a looped water distribution system. The results were compared with NSGAII, and it was found that both NSDE and NSDERMO were similar and better than NSGAII in their performance. Ahmadianfar et al. (2017) introduced an enhanced DE to frame optimal hydropower policies. The applicability of the algorithm applicability was checked using different benchmark problems. The results were effective and robust. Table 3 provides the summary of the application of DE to water resource planning and management.
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

Reddy & Kumar (2007b)  MODE  MODE applied to multiobjective reservoir operation  Hirakud Reservoir project in Orissa state, India  The MODE performance for the reservoir system optimization problem is found to be better than NSGAII. 
Vasan & Simonovic (2010)  DE  Application of DE to optimize the water distribution network  New York Water Supply System & Hanoi Water Distribution Network  It has been found that the DE model can be combined with the EPANET simulation model. The test results indicated that the technique was robust and simple and could be an alternative method for the water distribution network. 
Regulwar et al. (2010)  DE  Application of DE for the reservoir operation  Jayakwadi project, Godavari River  The analysis indicates that DE can effectively be applied to the multiobjective reservoir operation problems. 
Zheng et al. (2012)  DE  Application of DE for the water distribution network  Benchmark problem  DE is suited better to optimize the water distribution network compared to GA 
Raju et al. (2012)  DE  Used DE for irrigation planning  Mahi Bajaj Sagar Project, Rajasthan, India.  The result demonstrated proper parameter selection is important for effective implementation for realworld problems. 
Nwankwor et al. (2013)  Hybrid DE & PSO  Application of Hybrid DE & PSO for optimal good placement  Test problems  The results indicated that the hybridized algorithm could be potential for reservoir operational problems. 
Gurarslan & Karahan (2015)  DE  Application of DE for the ground water pollution source identification  Test problems  The results obtained by the developed model were better than the literature. 
Moosavian & Lence (2017)  NSDE  Application of NSDE for the water distribution system  Benchmark problems  The optimal Pareto front of the NSDE algorithms dominated all other algorithms, showing optimal Pareto solutions more, distributed and converged earlier. 
Ahmadianfar et al. (2017)  Enhanced DE  Application of enhanced DE for reservoir operation problems  Benchmark problems  The outcome showed the highest performance. 
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

Reddy & Kumar (2007b)  MODE  MODE applied to multiobjective reservoir operation  Hirakud Reservoir project in Orissa state, India  The MODE performance for the reservoir system optimization problem is found to be better than NSGAII. 
Vasan & Simonovic (2010)  DE  Application of DE to optimize the water distribution network  New York Water Supply System & Hanoi Water Distribution Network  It has been found that the DE model can be combined with the EPANET simulation model. The test results indicated that the technique was robust and simple and could be an alternative method for the water distribution network. 
Regulwar et al. (2010)  DE  Application of DE for the reservoir operation  Jayakwadi project, Godavari River  The analysis indicates that DE can effectively be applied to the multiobjective reservoir operation problems. 
Zheng et al. (2012)  DE  Application of DE for the water distribution network  Benchmark problem  DE is suited better to optimize the water distribution network compared to GA 
Raju et al. (2012)  DE  Used DE for irrigation planning  Mahi Bajaj Sagar Project, Rajasthan, India.  The result demonstrated proper parameter selection is important for effective implementation for realworld problems. 
Nwankwor et al. (2013)  Hybrid DE & PSO  Application of Hybrid DE & PSO for optimal good placement  Test problems  The results indicated that the hybridized algorithm could be potential for reservoir operational problems. 
Gurarslan & Karahan (2015)  DE  Application of DE for the ground water pollution source identification  Test problems  The results obtained by the developed model were better than the literature. 
Moosavian & Lence (2017)  NSDE  Application of NSDE for the water distribution system  Benchmark problems  The optimal Pareto front of the NSDE algorithms dominated all other algorithms, showing optimal Pareto solutions more, distributed and converged earlier. 
Ahmadianfar et al. (2017)  Enhanced DE  Application of enhanced DE for reservoir operation problems  Benchmark problems  The outcome showed the highest performance. 
SWARM INTELLIGENCE
Swarm Intelligence (SI) was introduced by (Wang & Beni 1989) for simple cellular robotic systems. SI is an intelligent multiagent system that simulates the behaviour of social insects such as ants, bees, termites and cockroaches and also swarms such as a flock of birds, a school of fishes, and a herd of quadrupeds. Unlike EAs where the populations are competitive among themselves, the performance of SI is optimized by adapting to the environment. A few of the best SIs are given as follows.
Ant colony optimization (ACO)
The behaviours of ants were documented in the early 1970s. Later Dorigo et al. (1991) developed the behaviour into an optimization technique. Thereafter, Dorigo has published many reports on ant colony optimization such as (Dorigo & Di Caro 1999). ACO is a metaheuristic technique and applies to a wide range of problems. It works on the principle of identifying the shortest route between the food sources and the colonies. Figure 4 shows the pseudocode of ant colony optimization. The details about ACO can be referred from (Maniezzo 1996; Maier et al. 2003). The application of ACO to water resources began in the early 2000s. Abbaspour et al. (2001) estimated the hydraulic parameters of an unsaturated soil using ACO and obtained promising results in eight different applications. Later, many researchers have applied ACO for several water resource problems. Maier et al. (2003) studied ACO for designing water distribution systems. The main purpose of the study was to come up with an alternative to GA for tackling the problem. The results established that ACO outperformed GA in terms of its efficiency and ability to find the global optimal solution. Kumar & Reddy (2006) studied multipurpose reservoir operation using ACO. The results were compared with GA, and it was found that ACO was superior. LópezIbáñez et al. (2008) studied water distribution networks for the optimal control of pumps using ACO. It was found that ACO yielded better results than GA for small as well as large water network problems.
Hou et al. (2014) presented Pareto ACO for the optimal allocation of water resources in Henan Province, China. Commendable results were obtained from the Pareto ACO than ordinary ACO, MOGA. Afshar et al. (2015) presented the application of ACO in water resources and environmental management problems for both continuous and discrete domains. The paper presented the major advantages, disadvantages and opportunities related to different water resource problems. Tu et al. (2015) studied smallscale irrigation systems by using ACO. The results were compared with GA and it was found that ACO possessed greater reliability and efficiency. Nguyen et al. (2016) developed an improved version of ACO to derive optimal solutions to water and crop allocation problems and secured better results than with other ACO variants. Table 4 provides the summary of the application of ACO to water resource planning and management.
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

Maier et al. (2003)  ACO  Application of ACO for the design of systems for water distribution  Test problems  The finding showed that the ACO is better able to find global solutions in the terms of computational efficiency and capability. 
Kumar & Reddy (2006)  ACO  Application of ACO for reservoir operation  Hirakud reservoir  ACO has performed better for annual power generation while satisfying irrigation requirements. 
LópezIbáñez et al. (2008)  ACO  Application of ACO for water distribution network  Test problems  The overhead computational effort of the ACO algorithm operation is very small. 
Hou et al. (2014)  Pareto ACO  Application of Pareto ACO for the allocation of water resources  Henan Province, China  The algorithm is appropriate for optimizing the complex spatial distribution of water resources at a large scale. 
Tu et al. (2015)  ACO  Use of ACO to develop smallscale irrigation systems  Jiangsu University, Zhenjiang, China  The ACO developed could be a useful tool for optimizing irrigation systems. 
Nguyen et al. (2016)  Improved ACO  Developed improved ACO for crop and irrigation water allocation  Loxton, South Australia  The improved ACO makes it possible to reduce the size of the search space and to investigate better regions of the search area. 
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

Maier et al. (2003)  ACO  Application of ACO for the design of systems for water distribution  Test problems  The finding showed that the ACO is better able to find global solutions in the terms of computational efficiency and capability. 
Kumar & Reddy (2006)  ACO  Application of ACO for reservoir operation  Hirakud reservoir  ACO has performed better for annual power generation while satisfying irrigation requirements. 
LópezIbáñez et al. (2008)  ACO  Application of ACO for water distribution network  Test problems  The overhead computational effort of the ACO algorithm operation is very small. 
Hou et al. (2014)  Pareto ACO  Application of Pareto ACO for the allocation of water resources  Henan Province, China  The algorithm is appropriate for optimizing the complex spatial distribution of water resources at a large scale. 
Tu et al. (2015)  ACO  Use of ACO to develop smallscale irrigation systems  Jiangsu University, Zhenjiang, China  The ACO developed could be a useful tool for optimizing irrigation systems. 
Nguyen et al. (2016)  Improved ACO  Developed improved ACO for crop and irrigation water allocation  Loxton, South Australia  The improved ACO makes it possible to reduce the size of the search space and to investigate better regions of the search area. 
Particle swarm optimization (PSO)
PSO is a swarm intelligence based optimization technique proposed by Eberhart & Kennedy (1995), which depends on natural grouping and resembles bird flocking. It is a populationbased algorithm and provides the optimal solution according to individual and social behaviour (Baltar & Fontane 2008). The initialization is similar to GA, and the population is generated using random solutions; however, the difference is that each potential solution is assigned with a randomly generated velocity. The potential solutions are called particles, which flow in the hyperspace for the best solution, and each particle maintains its track in the search space. The best solution progresses to better positions and helps other swarm particles to update their velocity and position towards the best solution. Once the termination criteria are satisfied, the optimal solution is reached. Figure 5 shows the pseudocode of particle swarm optimization. The details about the algorithm can be obtained from Eberhart & Kennedy (1995).
Application of PSO in water resources was attempted in the mid2000s and various water resource problems were solved using this technique, such as the design of water distribution networks (Suribabu & Neelakantan 2006), stage predictions (Chau 2007), water resources management and planning (Zarghami & Hajykazemian 2013), groundwater management (Gaur et al. 2011), irrigation water allocation and planning (Morankar et al. 2016), rainfallrunoff (Taormina & Chau 2015) and reservoir operation (Kumar & Yadav 2021).
Reddy & Kumar (2007a) proposed an elitist mutation (EM) EMPSO optimal solution for reservoir operation, which was discerned to be efficient and served as an alternative method to arrive at the optimal solution. Ostadrahimi et al. (2012) presented an optimal rule cure for the operation of a multireservoir system using a multiswarm version of PSO merged with the wellknown HECResPRM model. The result indicated that multiswarm PSO outperformed the implicit stochastic optimization method. Afshar (2012) proposed two different models, namely partial and fully constrained PSO to solve two different problems in water supply and hydropower operation. The results were compared with GA and PSO. The models were found superior to GA and PSO. Noory et al. (2012) compared LP and continuous PSO for optimizing water allocation and solving multicrop planning problems. Moreover, a mixedinteger linear (MIL) model and discrete (D) PSO were developed. DPSO algorithm revealed that it was a more feasible tool for solving water allocation and multicrop planning problems.
Zarghami & Hajykazemian (2013) developed a modified PSO by coupling the mutation process. The results of the model were better when compared with those derived from other models for urban water reservoir planning. Sudheer et al. (2013) predicted streamflow using hybrid model support vector machine–quantum behaved PSO (SVMQPSO). PSO was used to minimize the normalized mean square error. Later, the model was compared with other forecasting models. The result from SVMQPSO was more acceptable in terms of monthly streamflow prediction. Rezaei et al. (2017) tried to improve surface and groundwater management using a hybrid algorithm, namely fuzzy MOPSO, and the latter outperformed MOPSO. Bai et al. (2017) optimized cascade reservoir operation by fusing the feasible search space (FSS) with PSO and compared the results with classical and chaos PSO. The results indicated that the proposed algorithm was more effective and easier to implement. Table 5 provides the summary of the application of PSO to water resource planning and management.
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

Reddy & Kumar (2007a)  EMPSO  Application of EMPSO for the optimal reservoir operation  Malaprabha Reservoir system Krishna Basin  The proposed model can be used efficiently to make optimal use of the water resources available in a multicrop irrigation reservoir. 
Ostadrahimi et al. (2012)  Multiswarm PSO  Application of reservoir operation using multiswarm PSO  Columbia River Basin  The result indicated that multiswarm PSO outperformed the implicit stochastic optimization method. 
Afshar (2012)  Adapted versions PSO  Adapted versions PSO is used for the reservoir operation  Dez reservoir in Iran  The algorithm proposed is insensitive to the swarming dimension and the initial swarm, and can be extended further to multireservoir systems. 
Noory et al. (2012)  Discrete PSO  Use of discrete PSO for water allocation and crop planning  Case Study Central Iran  The results show that the algorithm is promising for a realworld irrigation system and could be used for multiple purposes. 
Zarghami & Hajykazemian (2013)  Modified PSO  Used for urban water management  Tabriz, Iran  The results were improved and suggested to solve the problem of multiobjective and nonlinear urban water problems. 
Ch et al. (2013)  SVMQPSO  SVMQPSO application for streamflow prediction  Krishna and Godavari Rivers  The results showed that the SVMQPSO offers a high degree of precision and reliability and can be used for the analysis of time series. 
Rezaei et al. (2017)  Fuzzy MOPSO  Used for the management of conjunctive water  Najafabad Plain in Iran  The algorithm proposed is in a position to find the single optimal solution on the Pareto front to facilitate decisions to address major optimization problems. 
Bai et al. (2017)  FSSPSO  PSO application for multiobjective optimization of the cascade reservoir  Yellow River basin  The results indicate that the FSSPSO is a promising tool for managing water resources problems. 
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

Reddy & Kumar (2007a)  EMPSO  Application of EMPSO for the optimal reservoir operation  Malaprabha Reservoir system Krishna Basin  The proposed model can be used efficiently to make optimal use of the water resources available in a multicrop irrigation reservoir. 
Ostadrahimi et al. (2012)  Multiswarm PSO  Application of reservoir operation using multiswarm PSO  Columbia River Basin  The result indicated that multiswarm PSO outperformed the implicit stochastic optimization method. 
Afshar (2012)  Adapted versions PSO  Adapted versions PSO is used for the reservoir operation  Dez reservoir in Iran  The algorithm proposed is insensitive to the swarming dimension and the initial swarm, and can be extended further to multireservoir systems. 
Noory et al. (2012)  Discrete PSO  Use of discrete PSO for water allocation and crop planning  Case Study Central Iran  The results show that the algorithm is promising for a realworld irrigation system and could be used for multiple purposes. 
Zarghami & Hajykazemian (2013)  Modified PSO  Used for urban water management  Tabriz, Iran  The results were improved and suggested to solve the problem of multiobjective and nonlinear urban water problems. 
Ch et al. (2013)  SVMQPSO  SVMQPSO application for streamflow prediction  Krishna and Godavari Rivers  The results showed that the SVMQPSO offers a high degree of precision and reliability and can be used for the analysis of time series. 
Rezaei et al. (2017)  Fuzzy MOPSO  Used for the management of conjunctive water  Najafabad Plain in Iran  The algorithm proposed is in a position to find the single optimal solution on the Pareto front to facilitate decisions to address major optimization problems. 
Bai et al. (2017)  FSSPSO  PSO application for multiobjective optimization of the cascade reservoir  Yellow River basin  The results indicate that the FSSPSO is a promising tool for managing water resources problems. 
Bee metaheuristics
Bees are insects that produce honey and wax. There are approximately 20,000 species of bees. Some of the common types are honey bees, bumblebees, and sweat bees. Each bee executes only a specific task in the hive. The entire colony performs the complex tasks of building the hives, searching for food and harvesting (Karaboga & Basturk 2007b). The colony survives based on the two principles of foraging and mating.
Bee foraging: Two groups of bees in the colony are involved in the harvesting of food; the first is the employed foragers and the second is the unemployed foragers. The latter includes both the onlookers and the scouts. Employed bees exploit a food source and after returning to the hive, share the information with a certain probability. Onlookers search for a better food source based on the information shared by the employed bee and make a choice. The scout bee randomly searches for new food sources (Du & Swamy 2016).
Bee mating: A bee colony consists of the queen, workers (female workers) and drones (male bees). Queen is only capable of laying the eggs (Haddad et al. 2006). Inspired by the behaviour of bees, several optimization techniques have been developed, such as bee colony optimization (Teodorovic & Dell’ Orco 2005), honey bee mating optimization (Haddad et al. 2006), bee algorithm (Pham et al. 2007), and artificial bee colony (Karaboga & Basturk 2007a).
Artificial Bee colony (ABC)
ABC is a swarmbased optimization technique proposed by Karaboga in 2005 (Karaboga 2005). Karaboga & Basturk (2007a) employed an extended version of ABC for solving constrained optimization problems. ABC works on the same principle as the behaviour of the bee and utilizes the food sources as the solution. The algorithm simulates the foraging process of the bees. The colony contains the onlooker, employed and scout bees. The food source is a symbol of a possible solution to the problem. The quality of a food source represents the fitness of the solution. Figure 6 shows the pseudocode of an artificial bee colony. The details of the algorithm can be found in Karaboga & Basturk (2007a). Application of ABC in water resources was attempted in the late 2010s. Liao et al. (2012) introduced an adaptive artificial bee colony (AABC) and implemented the algorithm for the hydropower reservoir system of the Three Gorges river of China. AABC performed better than a discrete differential dynamic program (DDDP) and PSO. Hossain & Elshafie (2014) applied ABC to optimize the reservoir release policy and it was found ABC performed better than GA. Ahmad et al. (2016) used ABC and gravitational search algorithm (GSA) to optimize the reservoir operation. The results showed the ABC's superiority to GSA in the quicker rates of convergence, stability, greater efficiency and reduced vulnerability, while the GSA's resilience measurement was much better. Choong et al. (2017) used an ABC algorithm for the optimization of multiple hydropower reservoirs operation. The tests showed that the weekly ABC optimization was superior to reliability and vulnerability, leading to a better release policy for optimal operation. Huo et al. (2018) proposed a parallel multicore (MPABC algorithm and utilized it to optimize the solution for four benchmark problems in the Heihe River Basin. Table 6(a) provides the summary of the application of ABC to water resource planning and management.
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

a) Artificial Bee Colony (ABC)  
Liao et al. (2012)  AABC  Application of AABC to the hydropower system  Three Gorges River of China  AABC was performing better than a DDDP and PSO program. 
Hossain & Elshafie (2014)  ABC  Application of ABC for the optimizing release policy of Aswan High Dam  Aswan High Dam of Egypt  The algorithm was able to achieve a total time period of 98 per cent of the release policy demands. 
Ahmad et al. (2016)  ABC  Application for optimization of the reservoir operation  Imah Tasoh Dam  Results indicated quicker rates of convergence, stability, greater efficiency and reduced vulnerability for ABC 
Choong et al. (2017)  ABC  Optimization of the reservoir operation  Chenderoh reservoir operation  Optimization for ABC was superior and a better release policy. 
Huo et al. (2018)  MPABC  Application of MPABC for the hydrological models  Heihe River Basin  The MPABC algorithm is an effective and feasible way to solve the problem of hydrological models. 
b) Honey Bee Mating Optimization (HBMO)  
Haddad et al. (2006)  HBMO  Proposed HBMO for the reservoir operation  Dez reservoir in southern Iran  The model performance is promising in a realworld reservoir operating problem. 
Sabbaghpour et al. (2012)  HBMO  Application for the water distribution network  Langarud city  The HBMO results are promising. 
Haddad et al. (2008)  HBMO  To obtain optimal rules of the reservoir  Dez reservoir in southern Iran  The proposal and rules are very promising and show that the HBMO algorithm proposed can solve the reservoir operation problem. 
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

a) Artificial Bee Colony (ABC)  
Liao et al. (2012)  AABC  Application of AABC to the hydropower system  Three Gorges River of China  AABC was performing better than a DDDP and PSO program. 
Hossain & Elshafie (2014)  ABC  Application of ABC for the optimizing release policy of Aswan High Dam  Aswan High Dam of Egypt  The algorithm was able to achieve a total time period of 98 per cent of the release policy demands. 
Ahmad et al. (2016)  ABC  Application for optimization of the reservoir operation  Imah Tasoh Dam  Results indicated quicker rates of convergence, stability, greater efficiency and reduced vulnerability for ABC 
Choong et al. (2017)  ABC  Optimization of the reservoir operation  Chenderoh reservoir operation  Optimization for ABC was superior and a better release policy. 
Huo et al. (2018)  MPABC  Application of MPABC for the hydrological models  Heihe River Basin  The MPABC algorithm is an effective and feasible way to solve the problem of hydrological models. 
b) Honey Bee Mating Optimization (HBMO)  
Haddad et al. (2006)  HBMO  Proposed HBMO for the reservoir operation  Dez reservoir in southern Iran  The model performance is promising in a realworld reservoir operating problem. 
Sabbaghpour et al. (2012)  HBMO  Application for the water distribution network  Langarud city  The HBMO results are promising. 
Haddad et al. (2008)  HBMO  To obtain optimal rules of the reservoir  Dez reservoir in southern Iran  The proposal and rules are very promising and show that the HBMO algorithm proposed can solve the reservoir operation problem. 
Honey Bee mating optimization (HBMO)
Abbass (2001) proposed the mating process of the honey bees as an optimization approach and Haddad et al. (2006) presented HBMO inspired by the bee mating process. Honeybee colonies mostly start in two ways: The first one is a ‘solitary colony’; that is, a colony begins with one or more queens without family (Du & Swamy 2016). The second method is ‘swarming’, in which one or more queens form a new colony encompassing the workers of the original colony. The working process and details of the algorithm can be found in Afshar et al. (2007). Numerous researchers have successfully studied and applied HBMO in various water resource problems such as reservoir operation (Haddad et al. 2006) the water distribution system (Sabbaghpour et al. 2012), and optimal operation rules for the reservoir (Haddad et al. 2008). Table 6(b) provides the summary of the application of HBMO to water resource planning and management.
Other Bee algorithms
Other methods derived from bee metaheuristics are available. Bee colony optimization (BCO) proposed by Teodorovic & Dell’ Orco (2005) is a metaheuristic technique inspired by the foraging behaviour of bees. BCO is good at exploration but weak at exploitation. To overcome this drawback, Moayedikia et al. (2015) proposed weighted bee colony optimization (wBCO) to improve the exploitation aspects. The bee algorithm proposed by Pham et al. (2007) mimics the foraging nature of the bees. Here, the bees search for food in the neighbourhood using random search. Bee swarm optimization (BSO) proposed by Akbari et al. (2010) is also similar to BA; however, the difference is that the bees can adjust their flying trajectory.
A harmony search (HS)
Geem et al. (2001) developed an HS algorithm to solve water distribution network problems. It is a heuristic optimization technique that tries to mimic the musical process related to searching for a better polish tone. It works on the principle of a musician trying to identify a state of pleasing harmony and continuing to play the pitches to seek better harmony (Lee & Geem 2004). The algorithm is fit to solve both discrete and continuous problems. The HS has three compulsory control parameters and two optional ones (Du & Swamy 2016). Figure 7 shows the pseudocode of harmony search. The details of the algorithm can be referred from (Geem et al. 2001).
Many variants and improved versions of HS are available. Omran & Mahdavi (2008) proposed the globalbest harmony search (GBHS) based on the concept of swarm intelligence. The performance of the GBHS was compared with HS, and it was inferred that GBHS was superior in dealing with ten different benchmark problems. Wang & Huang (2010) proposed selfadaptive HS to overcome the problem of tuning parameters since it is difficult to select the control parameter. Zou et al. (2011) introduced a global harmony search (GHS) consisting of two operations, namely genetic mutation and position updates with a small probability. Khalili et al. (2014) proposed the global dynamic HS by enhancing the key tuning parameters into a dynamic mode so that they need not be predefined. Numerous researchers have successfully studied and applied HS in various water resource problems. Geem et al. (2001) proposed HS and used the algorithm to solve benchmark problems in the water distribution network. Later, Geem et al. (2002) applied HS to solve the pipe network design problem and Geem (2006) to come up with an optimal design for the water distribution network. BashiriAtrabi et al. (2015) used HS to optimize the reservoir operation, compared the results with HBMO and ascertained the algorithm's effectiveness. Table 7(a) provides the summary of the application of HS to water resource planning and management.
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

a) Harmony Search (HS)  
Geem et al. (2001)  HS  The HS algorithm for the pipeline network design problem  Test problem & pipeline network  HS has exceeded existing mathematical and heuristic approaches. 
Geem et al. (2002)  HS  Application of pipe network design  Test problem  The results of HS were almost optimal. 
Geem (2006)  HS  Design of the water distribution network for the optimal design of costs  Test problem  The results demonstrate that the HS model is suitable for the design of a water network. 
BashiriAtrabi et al. (2015)  HS  Application of HS for the reservoir operation  Narmab Reservoir  For the operation of the reservoir for flood management, the HS algorithm can effectively be used. 
b) Firefly Algorithm (FA)  
Tahershamsi et al. (2014)  Hybrid FS & HS  For the design of a water distribution network  Benchmark problem  The suggested algorithm shows good solution quality performance. 
KazemzadehParsi et al. (2015a)  Modified FS  For the design of unconfined contaminated aquifers  Example problem  For effective management of contaminated aquifers, the proposed method can be used. 
GarousiNejad et al. (2016)  FS  FS application for the reservoir operation  Aydoghmoush Reservoir  FA has achieved better solutions with faster convergence. 
c) Cuckoo Search (CS)  
Wang et al. (2012)  CS  CS was used for the optimization of the water distribution network  Benchmark problems  Compared to NSGAII, multiobjective CS showed overall excellence in achieving a wide range of solutions. 
Chaowanawatee & Heednacram (2012)  CS  CS application to train the neural network to forecast floods  Little Wabash River  This problem is better suited to the Polyharmonic function than to the Gaussian function. 
Shamshirband et al. (2016)  CS  CS application to train the neural network to estimate reference evapotranspiration  Serbia  The optimized ANFIS version with CSA delivers better results in training and testing stages than the ANFIS model. 
Mohammadrezapour et al. (2017)  COA  To optimize the allocation of water and crop planning  Qazvin plain, Iran  COA's simple structure, excellent search efficiency and strong robustness make it very promising in the field of crop optimization. 
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

a) Harmony Search (HS)  
Geem et al. (2001)  HS  The HS algorithm for the pipeline network design problem  Test problem & pipeline network  HS has exceeded existing mathematical and heuristic approaches. 
Geem et al. (2002)  HS  Application of pipe network design  Test problem  The results of HS were almost optimal. 
Geem (2006)  HS  Design of the water distribution network for the optimal design of costs  Test problem  The results demonstrate that the HS model is suitable for the design of a water network. 
BashiriAtrabi et al. (2015)  HS  Application of HS for the reservoir operation  Narmab Reservoir  For the operation of the reservoir for flood management, the HS algorithm can effectively be used. 
b) Firefly Algorithm (FA)  
Tahershamsi et al. (2014)  Hybrid FS & HS  For the design of a water distribution network  Benchmark problem  The suggested algorithm shows good solution quality performance. 
KazemzadehParsi et al. (2015a)  Modified FS  For the design of unconfined contaminated aquifers  Example problem  For effective management of contaminated aquifers, the proposed method can be used. 
GarousiNejad et al. (2016)  FS  FS application for the reservoir operation  Aydoghmoush Reservoir  FA has achieved better solutions with faster convergence. 
c) Cuckoo Search (CS)  
Wang et al. (2012)  CS  CS was used for the optimization of the water distribution network  Benchmark problems  Compared to NSGAII, multiobjective CS showed overall excellence in achieving a wide range of solutions. 
Chaowanawatee & Heednacram (2012)  CS  CS application to train the neural network to forecast floods  Little Wabash River  This problem is better suited to the Polyharmonic function than to the Gaussian function. 
Shamshirband et al. (2016)  CS  CS application to train the neural network to estimate reference evapotranspiration  Serbia  The optimized ANFIS version with CSA delivers better results in training and testing stages than the ANFIS model. 
Mohammadrezapour et al. (2017)  COA  To optimize the allocation of water and crop planning  Qazvin plain, Iran  COA's simple structure, excellent search efficiency and strong robustness make it very promising in the field of crop optimization. 
Firefly algorithm (FA)
FA is a swarmbased metaheuristic algorithm introduced by Yang (2009), and it is inspired by the fireflies. The insects have the ability to emit light through the biochemical process called bioluminescence. Nonetheless, its purpose is still not ascertained (Fister et al. 2013). The two fundamental functions are to attract potential prey and mating partners. In addition, the flashing light also protects the fireflies from other predators. Three basic assumptions or rules were idealized while developing the firefly algorithm (Yang 2009). First, all the fireflies are unisex. Second, the brightness of the flash is directly proportional to the attractiveness of the fly. Third, the brightness diminishes as the distance increases (Du & Swamy 2016). Figure 8 shows the pseudocode of the firefly algorithm. The details of the algorithm can be found in Yang (2009). Many variations and improvements of FA have been observed in the past. The application of FA in water resources engineering is quite new. Tahershamsi et al. (2014) used hybrid FA and HS to solve problems in water distribution systems. KazemzadehParsi et al. (2015b) combined FA with the finite element simulation method (FEM) to optimize the pump design and groundwater treatment remediation systems. GarousiNejad et al. (2016) applied FA for the optimization of reservoir operation for irrigation and power generation. Table 7(b) provides the summary of the application of FS to water resource planning and management.
Cuckoo search (CS)
CS is a swarmbased metaheuristic search algorithm proposed by Yang & Deb (2009) for global optimization following the behaviour of cuckoos. The bird lays its eggs in the nest of others and also removes the eggs of the host bird. If the Cuckoo egg resembles that of the host bird and the latter is unable to differentiate between the two, the egg will be well taken care of (Arsenault et al. 2014). However, if the host bird discovers that the eggs are not its own, it pushes them out or abandons the nest. The probability of being discovered by the host bird is between 0 and 1 (Yang & Deb 2009). Yang & Deb (2010) studied the design of spring and welded bean, and compared the results with GA and PSO. CS was discerned to be better than the other two algorithms. Figure 9 shows the pseudocode of cuckoo search. The detailed methodology can be found in Yang & Deb (2009, 2010). Li & Yin (2015) modified CS by considering the selfadaptive parameters to control the population diversity. The cuckoo optimization algorithm (COA) proposed by Rajabioun (2011) is another metaheuristic populationbased algorithm inspired by the bird.
Numerous researchers have successfully studied and applied CS as well as its variants in various water resource problems. Wang et al. (2012) used MOCS to obtain an optimal water distribution network. The findings indicate that MOCS are superior to NSGAII in terms of convergence and diversity, providing more alternatives for high quality. Chaowanawatee & Heednacram (2012) combined CS with a radial basis function neural network for determining the flood water level. Shamshirband et al. (2016) studied the ability of CS to optimize the weights from ANN and the adoptive neurofuzzy interface system (ANFIS) to estimate the reference evapotranspiration. Mohammadrezapour et al. (2017) made use of COA for the optimization of water allocation and crop planning. Table 7(c) provides the summary of the application of CS to water resource planning and management.
Bat algorithm (BA)
BA is a swarmbased metaheuristic algorithm developed by Yang (2010) which is inspired by the echolocation of bats and is capable of obtaining a global optimum solution. Among the mammals, other than bats, only a few communities of squirrels can fly. It is estimated that nearly 996 species of bats exist. Different species have varied echolocation capabilities through which they can emit a very short and loud sound pulse of up to 100 dB in the ultrasonic region and receive the sound in the form of an echo reflected from the surrounding objects. The bat analyzes the echo, discriminates the pathway, and categorizes the obstacles and prey (Yang & Hossein Gandomi 2012). This phenomenon is formulated into an optimization technique for engineering problems. The echolocation of microbats is characterized by three rules based on which the bat algorithm has been developed. First, bats use the process to sense the distance and differentiate between the food and obstructions in their pathway. Second, bats fly at a random speed at position with a fixed frequency , varying wavelength and loudness to hunt for the prey. To target the prey, the bat can adjust the frequency or wavelength depending on its proximity. Third, the loudness echo can be changed from a constant minimum value to a large one (Wang & Guo 2013). BA was designed based on these rules. Figure 10 shows the pseudocode of the bat algorithm. The detailed methodology can be checked in Gandomi et al. (2013); Yang (2010; 2012).
The application of BA in water resources is quite new. BozorgHaddad et al. (2015) used the BA for the optimization of reservoir operation. In comparison with conventional optimization techniques, the BA was able to achieve the best alternatives. Ahmadianfar et al. (2016) presented a hybrid of BA and DE to solve multireservoir operational problems. The results obtained were 99.9% close to the global optimum solution. Kuok et al. (2018) combined BA with ANN to forecast the rainfall, and the results indicated that BANN was capable of avoiding the local trap. Ethteram et al. (2018) used BA for the Aydoghmush dam and Karun 4 dam reservoir operation. It has been found that the bat algorithm with the thirdorder rule curve is better than the other order rules curves. Table 8(a) provides the summary of the application of BA to water resource planning and management.
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

a) Bat Algorithm (BA)  
BozorgHaddad et al. (2015)  BA  Use of BA on operation of the reservoir  Benchmark problem  In comparison to conventional optimization methods, the BA was able to reach better solutions in reservoir operations. 
Ahmadianfar et al. (2016)  Hybrid BA & DE  Hybrid BA & DE application for a multireservoir operation  Benchmark problem  The proposed method provides very promising solutions and significantly improves performance with the best known global results. 
Kuok et al. (2018)  BatNN  Application of BatNN for the forecast of rainfall  Kuching city  The results indicated that BatNN can optimize and accurately predict longterm rainfall. 
Ethteram et al. (2018)  BA  BA was used for reservoir operation  Aydoughmoush dam and Karoun 4 dam in Iran  The bat algorithm can be seen as a suitable optimization model for operation in the reservoir. 
b) Shuffled Frog Leaping Algorithm (SFLA)  
Eusuff & Lansey (2003)  SFLA  Applied to the water distribution network  Benchmark problem  SFLA has found optimal solutions in fewer iterations than GA and simulated annealing. 
Eusuff et al. (2006)  SFLA  Applied to the problem of groundwater model and the water distribution system  Test problem  SFLA is very suitable for parallelization and can be investigated for other water resources problems. 
Sun et al. (2016)  SFLA  Used for the reservoir operation  Cascade reservoirs  The model has been discovered to have better search capabilities and quicker convergence, and parallel calculation can efficiently cut down the time required. 
Fang et al. (2018)  MODE Chaos SFLA  Used for optimizing the allocation of water resources  Northern China  MODE Chaos SFLA possesses the capacity to solve complex water resources optimization problems. 
Li et al. (2018a)  Improved SFLA  Used for reservoir operation  Cascade reservoirs  Improved SFLA has been discovered to be better than SFLA, PSO, immune SFLA and cloud SFLA. 
Yang et al. (2019)  CNSFLA  For the multiobjective reservoir operation  Cascade reservoirs  CNSFLA's performance analysis checks its efficient search capability for high quality and stability. 
Case study reference .  Algorithm .  Applications .  Catchment/study area .  Contribution . 

a) Bat Algorithm (BA)  
BozorgHaddad et al. (2015)  BA  Use of BA on operation of the reservoir  Benchmark problem  In comparison to conventional optimization methods, the BA was able to reach better solutions in reservoir operations. 
Ahmadianfar et al. (2016)  Hybrid BA & DE  Hybrid BA & DE application for a multireservoir operation  Benchmark problem  The proposed method provides very promising solutions and significantly improves performance with the best known global results. 
Kuok et al. (2018)  BatNN  Application of BatNN for the forecast of rainfall  Kuching city  The results indicated that BatNN can optimize and accurately predict longterm rainfall. 
Ethteram et al. (2018)  BA  BA was used for reservoir operation  Aydoughmoush dam and Karoun 4 dam in Iran  The bat algorithm can be seen as a suitable optimization model for operation in the reservoir. 
b) Shuffled Frog Leaping Algorithm (SFLA)  
Eusuff & Lansey (2003)  SFLA  Applied to the water distribution network  Benchmark problem  SFLA has found optimal solutions in fewer iterations than GA and simulated annealing. 
Eusuff et al. (2006)  SFLA  Applied to the problem of groundwater model and the water distribution system  Test problem  SFLA is very suitable for parallelization and can be investigated for other water resources problems. 
Sun et al. (2016)  SFLA  Used for the reservoir operation  Cascade reservoirs  The model has been discovered to have better search capabilities and quicker convergence, and parallel calculation can efficiently cut down the time required. 
Fang et al. (2018)  MODE Chaos SFLA  Used for optimizing the allocation of water resources  Northern China  MODE Chaos SFLA possesses the capacity to solve complex water resources optimization problems. 
Li et al. (2018a)  Improved SFLA  Used for reservoir operation  Cascade reservoirs  Improved SFLA has been discovered to be better than SFLA, PSO, immune SFLA and cloud SFLA. 
Yang et al. (2019)  CNSFLA  For the multiobjective reservoir operation  Cascade reservoirs  CNSFLA's performance analysis checks its efficient search capability for high quality and stability. 
Shuffled frog leaping algorithm (SFLA)
SFLA is a memetic metaheuristic swarm intelligencebased algorithm proposed by Eusuff & Lansey (2003), which is inspired by the social behaviour of frogs. Frogs search for their food in a group. The swamp has many stones and at each one a different quantity of food is present. Frogs try to locate the stone with maximum food sources. To reduce the time spent searching for food, frogs develop their memes by exchanging information. The frogs change their leaping based on the previous memes' conversation. Thus, they are directed towards the position with more food sources. Based on this concept, the SFLA was developed, and the algorithm has three stages, namely partitioning, local search and shuffling. The algorithm combines the deterministic and random approaches and is capable of solving continuous and discrete optimization problems (Du & Swamy 2016). Figure 11 shows the pseudocode of the Shuffled Frog Leaping Algorithm. The details of the algorithm are given in Eusuff et al. (2006); Eusuff & Lansey (2003).
Eusuff & Lansey (2003) proposed SFLA, applied the algorithm in the water distribution network and obtained promising results. Eusuff et al. (2006) used the SFLA for discrete groundwater and water distribution network problems. Upon comparing the results with GA, it was discerned that SFLA is a reliable tool for solving optimization problems. Sun et al. (2016) altered the SFLA by mixing the cloud model algorithm for the optimization of reservoir operation. The model has been discovered to have better search capabilities and quicker convergence, and parallel calculation can efficiently cut down the time required. Fang et al. (2018) studied MODE combined with chaos SFLA for the optimization of water allocation problems. The findings show that MODECSFLA is more efficient than NSGAII and MOPSO. Li et al. (2018a) improved the SFLA through the chaos catfish effect and used it to operate a cascade reservoir. Improved SFLA has been discovered to be better than SFLA, PSO, immune SFLA and cloud SFLA. Yang et al. (2019) used an improved chaotic normal cloud shuffling frog leaping algorithm (CNSFLA) for an ecological planning model with multiple objectives. Finally, CNSFLA's performance analysis checks its efficient search capability for high quality and stability. Table 8(b) provides the summary of the application of SFLA to water resource planning and management.
NEW ALGORITHMS USED IN THE OPTIMIZATION OF WATER RESOURCES ENGINEERING
The complexity of the problems has escalated owing to increased demands, climatic conditions, global warming, and depleting resources. Hence, researchers have developed various new and advanced techniques to optimize the problems related to the planning and management of water resources. Asgari et al. (2016) applied a weed optimization algorithm (WOA) for the optimization of multireservoir system problems. WOA is a metaheuristic optimization technique inspired by the weed's life cycle. The result suggests a faster convergence rate and a solution quite close to the global optimum. Ehteram et al. (2017) used the shark algorithm (SA) for the optimization of reservoir operation and inferred that the results were superior to those of GA and PSO. Karami et al. (2018) proposed the improved krill algorithm (IKA) for the optimization of reservoir operation by augmenting the speed of convergence and decreasing the possibility of a local trap. The results obtained from IKA were promising. Ehteram et al. (2018a) used a new metaheuristic algorithm known as the spider monkey algorithm (SMA) to reduce the irrigation deficiencies in Iran's multireservoir system. It was found that SMA is an appropriate method for reservoir operation policies. BozorgHaddad et al. (2018) used an anarchic society algorithm (ASO) for the optimization of the water distribution network and identified that ASO outperformed. Li et al. (2018b) used a moth flame optimization algorithm (MFOA) for the multireservoir system and observed it to be superior to NSGAII, MOPSO, MODE, and MOBA in terms of improved uniformity and diversity distribution. Bahrami et al. (2018) used cat swarm optimization (CSO) for the reservoir operation. It was found that CSO was efficient in finding the global solution. Feng et al. (2018) used an orthogonal progressive optimality algorithm (OPOA) to optimize hydropower generation, and the results indicated its feasibility for the multireservoir system. Yan et al. (2018) employed an ameliorative whale optimization algorithm (AWOA) for the multiobjective water allocation problem. Kumar & Yadav (2018) used teaching learningbased optimization (TLBO) and Jaya algorithms (JA) for the multireservoir operation. It was found that JA performed better than TLBO and other algorithms available in the literature. Ehteram et al. (2018b) used a kidney algorithm (KA) to generate an optimal solution for reservoir operation and discerned that it performed better than GA, BA, WOA, SA, and PSO.
DISCUSSIONS AND CONCLUSIONS
The literature review has revealed that with the advancements in computing power, researchers have developed various methods to solve realworld problems. Metaheuristic and heuristic are emerging study areas for handling a variety of water resources problems, as seen by the vast range of applications listed above. The main advantage of the heuristic and metaheuristic algorithms is the use of search populations that are simultaneously exploring in the search space for the possible solutions, sharing information among the systems, to obtain a better solution. Different evolutionary algorithms such as GA, GP and DE, and swarm intelligencebased algorithms such as ACO, PSO, ABC, HBMO, HS, FA, CS, BA, and SFLA were covered in the review. Future management approaches will have to deal with a variety of challenges that may occur as a result of high nonlinearities, a larger range of uncertainties, reallife challenges, continuous, discrete, complex, stochastic, multireservoir, multiobjective problems and the integration of huge system components. For better decision making in water resource management, metaheuristicsbased optimization frameworks are becoming increasingly important. The main question arises about which algorithm to use. EAs have a wide range of applications since they may be used to solve any problem that can be represented as a function optimization problem. For realworld challenges involving multimodal functions, EAs provide significant benefits. Any form of objectives and constraints can be directly incorporated into EAs. Each of the algorithms of metaheuristics has its advantages and limitations. GA is one of the oldest and most common techniques in the field of water management, with many applications. The major advantages occur in its ability to manage nonlinear, nonconvex, and diversity positions as well as in its multimodal strategies and ability to solve the given problems to optimal or nearoptimal solutions. However, it also requires the right tuning of the algorithmspecific parameters, such as mutation, crossover and reproduction. GP is a comprehensive, continuous, highly scalable, and efficient algorithm that needs less time to compute and provides good performance. However, it necessitates internal parameters such as crossover and mutation probability. Likewise, DE had advantages similar to that of the GA, but the selection of algorithmspecific parameters is needed; for instance, the scaling factor and crossover rate.
SI techniques are based on the swarm's cooperative group intelligence principles and have proven to be other classes of alternative metaheuristic methodologies for handling various types of water resource optimization problems. SI algorithms, like EA populationbased random search techniques, with heuristic guidance that can cover a variety of problem complexities such as nonlinear, nonconvex, multimodal solutions, and so on. SI applicability and convergence properties, however, may differ from one problem to the next. For example, to solve nonuniform, complex and nonlinear problems, the ACO is powerful enough, and it is capable of accomplishing rapid convergence. But, tuning parameters such as the relative pheromone trail, heuristic information, and evaporation are required. Similarly, PSO needs tuning of parameters such as inertia weight, social, and cognitive parameters are required. If the parameters are set correctly, the algorithm can achieve a global solution. Other SI algorithms like ABC, HS, FA, CS, BA, SFLA, and HBMO also have similar comparable capabilities and weaknesses, like ACO and PSO. Table 9 compares the strengths and weaknesses of different algorithms. It should be noted that numerous studies have proposed different algorithms for different water resources problems and suggested that certain algorithms are comparatively better than others. However, the results may be applied to those problems that may not be generalized into one or not covered by either of the various types of problems, as each problem may have different complexities according to the problem dimension and existing interactions for the problem. Consequently, the right algorithm option and use for this problem must be based on the form and characteristics of the problem. There are various studies wherein hybridizations of one or more algorithms have been performed. Similarly, modifications of existing algorithms have been done by incorporating elitist, selfadoptive, binary, nondominated, and chaotic concepts, to get more acceptable results. Finally, no single optimization algorithm is universally declared as a winner that can successfully address all types of problems. Besides, an algorithm is neither extraordinary nor completely inferior; it depends on the problem type. One might be good at solving a particular type of problem but not others. Hence, before judging, many algorithms and their variants need to be compared.
Algorithms .  Strengths .  Weaknesses . 

Genetic algorithm (GA) 


Genetic Programming (GP) 


Differential Evolution (DE) 


Ant Colony Optimization (ACO) 


Particle Swarm Optimization (PSO) 


Artificial Bee Colony (ABC) 


Harmony Search (HS) 


Firefly Algorithm (FA) 


Cuckoo Search (CS) 


Bat Algorithm (BA) 


Shuffled Frog Leaping Algorithm (SFLA) 


Honey Bee Mating Optimization (HBMO) 


Algorithms .  Strengths .  Weaknesses . 

Genetic algorithm (GA) 


Genetic Programming (GP) 


Differential Evolution (DE) 


Ant Colony Optimization (ACO) 


Particle Swarm Optimization (PSO) 


Artificial Bee Colony (ABC) 


Harmony Search (HS) 


Firefly Algorithm (FA) 


Cuckoo Search (CS) 


Bat Algorithm (BA) 


Shuffled Frog Leaping Algorithm (SFLA) 


Honey Bee Mating Optimization (HBMO) 


ACKNOWLEDGEMENTS
The authors acknowledge the helpful comments and suggestions made by anonymous reviewers to enhance the manuscript. The authors also like to acknowledge with a deep sense of gratitude the valuable help received from the authorities of Sardar Vallabhbhai National Institute of Technology (SVNIT) and the P.G. Section of Water Resources Engineering.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.