1. Introduction
Since the subject of reservoir operation has been studied, no algorithm is capable of satisfying all the requirements of a reservoir. Each algorithm has been able to perform to an extent resulting in the formulation of several algorithms (Hosseini-Moghari et al., 2015). The nonlinear and nonconvex of reservoir operation problems has made linear programming unsuitable for its solution. However, linear programming and dynamic programming have been used by some researchers who can adopt full stochastic approach. Multi-reservoir operation comes with a large number of decision variables especially when the operation is a long-term one. This has made linear programming and dynamic programming difficult to use. Yeh (1985) notes that 3 major models are usually used for multi-reservoir optimization which are linear programming (LP), non-linear programming (NLP) and dynamic programming (DP). Yeh (1985) gives full review of these models. According to the author, LP has been used widely for multi-reservoir operations as researchers normally find a way to linearise the problem. NLP is slow and is less suitable for reservoir operation because it cannot handle non-convex problems common to reservoir operations. However, some researchers still adapt NLP for reservoir operation problems. Nonlinearity and nonconvexity can be conveniently handled by DP making it widely used by researchers. DP also suffers setbacks in memory and exponential increase in computational requirements making it applicable to a system with few reservoirs. Other algorithms also seek to linearise the nonlinear water resources problems before solving them as linear problems. A mixed integer programming technique is used to model hydropower, water supply and other reservoir uses. However, hydropower, which is dependent on head and water flow which is presented as nonlinear, is linearized with two-dimensional function (Zhou et al., 2014). Consequently, more desirable algorithms are needed to model reservoir operation for efficient management (Gowda and Mayya, 2015).
2. Evolutionary algorithms
Evolutionary algorithms (EAs) offer alternatives to LP, NLP and DP. On the contrary, evolutionary algorithms (EAs) use constraint-handling methods to make them suitable to handle constraints in reservoir management and other water management problems. The most common constraint handling technique is penalty method. This method penalizes any solution that violates the constraints by making it infeasible. Most of the algorithms are comfortable with this constraint handling technique, as it is simple and efficient. There are many applications of EA to water resources management with success. Meanwhile, in a multi-objective optimization, it is not possible to find a single solution (as in single objective) that will optimize all the objectives simultaneously. However, we have a set of trade-offs between all the objectives known as Pareto optimal schemes. One objective cannot be improved without having a compromise on one or more of the other objectives (Adeyemo and Olofintoye, 2014).
Since the introduction of evolutionary algorithms, many applications to water resources have been successfully experimented (Ahmad et al., 2014). An algorithm called co-operative game theory for alternative framework for effective allocation was proposed by Madani and Hooshyar (2014). The algorithm provides fair and efficient utility shares of the beneficiaries. It was used to solve optimal reservoir operation for multi-objective and multi-reservoir system for fair and efficient water distribution. A hypothetical 3-agent three-reservoir system was used to test the model and results show that the algorithm can solve the problem efficiently. The objective of the model was to maximize the annual revenue of hydroelectricity generated from the reservoir, which was got from the monthly release. The constraints are the continuity equation, storage limits and release limits. Zhang et al. (2014) present a reservoir operation optimization with the objective of maximizing the benefit of water resource by finding an optimal solution to hydropower station within the operating period at the same time satisfying physical and operational constraints. The major objectives of the reservoir is hydropower and water supply which is similar to human demand objective (Chang et al., 2010). Evolutionary algorithms are efficient for reservoir operation; especially, in maximizing hydropower generation.
Multiobjective evolutionary algorithms are formulated based on the operation of evolutionary algorithms with some modifications; however, they are different from other multiobjective optimization techniques. Multi-objective evolutionary algorithms (MOEAs) are known to generate many non-dominated solutions in a single run unlike the classical techniques (Adeyemo and Olofintoye, 2014). MOEAs are also less sensitive to the continuity or shape of the Pareto surface. Several researchers have extended DE, an evolutionary algorithm, for solving multi-objective optimization. Abbass and Sarker (2002)presented Pareto differential evolution (PDE) algorithm. This algorithm has a wide application in many multi-objective optimization problems (Madavan, 2002). Pareto-based multi-objective differential evolution (PMODE) was proposed by Xue et al. (2003). Differential evolution multi-objective (DEMO) was demonstrated and suggested (Robic and Filipic, 2005). Also, adaptive differential evolutionary algorithm, ADEA, was presented and applied (Pan et al., 2009). In the same year, Multi-objective evolutionary algorithm, MDEA, was presented and applied in many water resources problems (Adeyemo and Otieno, 2010, Adeyemo and Otieno, 2009a, Adeyemo and Otieno, 2009b). More recently, combined Pareto multi-objective differential evolution, CPMDE, was proposed and applied to engineering problems (Adeyemo and Olofintoye, 2014, Enitan et al., 2014, Olofintoye et al., 2014, Olofintoye et al., 2016).
Similarly, other multiobjective evolutionary algorithms are presented. Multi-objective cultured differential evolution (MOCDE) was presented to solve reservoir flood control problem (Qin et al., 2010). It was applied to three Gorges reservoir with success. MOCDE provides decision makers with many alternative non-dominated schemes with convergence to true Pareto optimal solutions and uniform coverage. It was suggested that MOCDE can also be useful in other water resources management problems. In the same vein, chaotic algorithm was combined with GA and DE which are population based search algorithms to solve hydropower maximization model of reservoir operation (Jothiprakash and Arunkumar, 2013). It was found that chaotic algorithm performed better than other algorithms tested. Also, flood control ability of a river-type reservoir was evaluated for discharge process and accurate simulation method for the flood storage by Zhang et al. (2017). The data was gathered from 394 river cross sections and digital elevation model data of the three Gorges reservoir area. The analysis showed that static capacity of the reservoir, dynamic flood control capacity and the maximum flood water flow regulated by the dynamic capacity. These parameters are useful for the reservoir operation in real time.
Many hybrid algorithms are tested on many water resources problems. They perform better than using one algorithm for single and multiobjective optimization. Hybrid algorithm applications to reservoir operations; namely, hydropower, flood control, ecological base flow, and water distribution systems (WDS), are important.
3. Reservoir operation and EA models
The objectives of estimating different water demands downstream of a dam and optimizing the dam to ensure deficits are minimized while economic benefits of the dam are maximized are presented by Wu and Chen (2013). In achieving these objectives, the hydrological simulation by the soil and water assessment tool (SWAT) was employed to estimate the demands. The optimization tool used was SCE algorithm, an evolutionary algorithm. The data utilized are observed weather data which are outflows from the dam, inflow into the dam, reservoir water levels and hydropower generation (Wu and Chen, 2013). The data available was 22 years of data. Irrigation demand was estimated by estimating crop water demand and modified using SWAT model simulation results. SWAT is used to estimate effective rainfall.
This same model was used for irrigation management using SWAT model. SWAT model was developed by the United States department of agriculture (USDA) agricultural research service. It is used to evaluate the effect of different cultural land management patterns and climate on water, sediment yield and agricultural chemical yields (Wu and Chen, 2013). Neitsch et al. (2005) give the description of the hydrological part of the model. This is applied to water balance equation in the soil profile with surface runoff, evaporation, lateral flow, infiltration, precipitation, percolation, and groundwater flow. SWAT may be set up for the whole river basin by discretizing them into sub basins and hydrological response units (HRUs). The discretization is done by using shuttle radar topographic mission (SRTM) digital elevation model (DEM) data, land cover data from Chinese academy of science and soil attributes dataset from Guangdong soil survey (Wu and Chen, 2013). Another constrained gravitational search algorithm was presented by Moeini et al. (2017) for large scale reservoir problem were satisfied and also led to great reduction in search space size. They proposed two formulations for each proposed algorithms with consideration for water release at operation periods which are decision variables of the problem. The ability of the algorithm was demonstrated by using it to solve “Dez” reservoir in Iran with success.
The soils are categorized into different types based on the soil survey dataset. Thereafter, divisions of where different soil types are found are done on the entire catchment. The daily, weekly or monthly meteorological centres are formed. The data is thus fed into the SWAT hydrological part. Wu and Chen (2013) used this method to derive simulated monthly inflow to the reservoir. Though SWAT was used to simulate daily time step, it was aggregated to monthly data to suit the model. The monthly-simulated inflow was checked against the recorded inflow data for the reservoir and found that they match with R2 of 0.85. In the study, SWAT simulation of surface runoff, lateral flow and seepage was used for the estimation of irrigation water demand in the catchment. This model was used eventually to improve hydropower generation of the reservoir. SWAT aids in reservoir operation by aiding in optimizing irrigation release and ensuring more water is available for hydropower in the reservoir.
In another instance, a different methodology was adopted to reservoir operation. The hydrological components of precipitation, evapotranspiration and inflow are stochastically formulated using simulation models (Tsoukalas and Makropoulos, 2015). Afterwards, long synthetic time-series are produced. After this, parameterization of operating rules of the reservoir is done. Hydrosystem is simulated using the stochastically generated time series to determine the management policy. The desired performance metric is done using defining appropriate objective functions. Thereafter, optimization of the two objective functions is done using five different algorithms (3 multi-objective surrogate based optimization (MOSBO) and 2 multi-objective evolutionary algorithm (MOEA)). Finally, benchmarking of all the algorithms is done using performance indicators and methods. It was found that the algorithms performed very well in the reservoir operation model presented.
Accordingly, progressive optimality algorithm – dynamic programming successive approximation (POA-DPSA) was used to solve a developed multi-objective reservoir model (Bai et al., 2015). The gains of the reservoirs were estimated over a long series data. It was concluded that joint operation of two reservoirs considered could improve hydropower generation than operating the reservoirs independently. Another study on the three Gorges reservoir was conducted to optimize the spillways operation. Historical flood hydrograph and design flood hydrograph were calculated using progressive optimality algorithm to find optimal spillways operation in real time (Liu et al., 2017). Li et al. (2014) also optimized joint operation of a multi-reservoir system with a multi-dimensional DP model. There are many constraints for individual reservoirs and many more for the entire reservoir system, which could be solved by the two algorithms without any complication.
In addition, the function presented by Hakimi-Asiabar et al. (2010) were solved previously using SOM-based multi-objective GA (SBMOGA) which outperformed the existing multi-objective optimization techniques (NSGA-II) (Hakimi-Asiabar et al., 2009). The efficiency of SBMOGA is limited by SOM neuron number. There are tangible improvements in convergence rate, solution diversity, solution quality and running time using SLGA. It was demonstrated that SLGA is capable of solving large scale multi-reservoir and multi-purpose reservoir operation optimization problems (Hakimi-Asiabar et al., 2010).
Furthermore, in another study by Tsoukalas and Makropoulos (2015), there are a lot of decision variables to be solved with optimization of long term operating rules for multi-reservoir systems. This makes the procedure complicated. The objective functions are also nonlinear and subject to hydrological uncertainty. The solution is usually coupling simulation model to optimization model to solve the stochasticity of the parameters. Their study uses multi-objective surrogate based optimization (MOSBO) to make computational effort reduced. They compared the three MOSBO algorithms with two multi-objective evolutionary algorithms (EAs). It was found that MOSBO are more efficient resulting in robust and uncertainty-aware operating rules that are faster. PSO model the hydrological uncertainty through stochastic simulation to develop uncertainty-aware reservoir operating rules (Tsoukalas and Makropoulos, 2015). The multi-objective model was able to handle conflicting multiple objectives. The results have a negotiation tool for making decisions between competing water users depending on the reservoir.
In the same way, cuckoo optimization algorithm (COA) can solve nonlinear optimization as a recent evolutionary algorithm presented by Rajabioun (2011). It was inspired by a bird (cuckoo) lifestyle. Also, imperialist competitive algorithm (ICA) was also presented in 2007 and has population-by-population technique common to all other EAs (Atashpaz-Gargari and Lucas, 2007). Both algorithms, COA and ICA, were used in the optimization of reservoir operation (Hosseini-Moghari et al., 2015). These algorithms are relatively new. They were tested on several benchmarked problems with success. In the reservoir operation, they produced results that are highly competitive when compared with NLP and GA. COA generated results that are robust and more superior to ICA. ICA shows ability to converge to global optimum. The EA parameters were chosen by trial and error method. For GA, roulette wheel was used for better performance. Summarily, both algorithms performed excellently in reservoir operation model presented which has objectives of maximizing net benefit from the reservoir (Hosseini-Moghari et al., 2015). Following the same trend, Al-jawad and Tanyimboh (2017) presents an improved results using real-world reservoir system. The total annual supply and demand imbalances were greatly reduced with their state-of-the-art evolutionary algorithm namely Borg MOEA. Drawdown constraint was introduced to the reservoir operation where near-optimal solutions were found reliably and speedily.
Many evolutionary algorithms presented for reservoir operation are efficient and produced competitive results. Evolutionary algorithms are suitable for solving complex reservoir operation problems whether single reservoir or multi-reservoirs. They are well adapted for various reservoir arrangements in series or parallel. Evolutionary algorithms have ability to produce many solutions in one single simulation run which is a great advantage over classical algorithms. Therefore, the algorithms are recommended for solving many difficult water resources problems.
4. Hybrid models in hydropower
The inability of many evolutionary models to achieve perfect success in all water resources problems that are prevalent is a problem. One algorithm will perform perfectly in an area but deficient in another. This is evident because of so many uncertainties presented by water resources models. Combination of algorithms to solve one problem is thus necessary. One algorithm is used to solve a part of the problem, which is complemented by the other algorithm. Delegation of different algorithms is achieved with the algorithm best suited for a particular problem is assigned. The hybrid algorithm helps to overcome deficiency in individual algorithms. Hybrid algorithms have been tested with success on many hydropower and flood control models.
When reservoir inflows are forecasted accurately with good optimization techniques, more balanced and efficient solutions for a multipurpose system of reservoir can be achieved. Hydropower generation is enhanced and improved. In forecasting inflow in reservoir operation, especially long and short term forecast, there are uncertainties. The use of combined long and short term forecast of stream flow can be improved for decision making (Zhao and Zhao, 2014). The joint effect of these forecast uncertainties, especially in the process of decision-making, was investigated by Zhao and Zhao (2014). The study suggested a reliable long term forecast as the only viable way for reservoir operation. In demonstrating this, Olofintoye et al. (2016) proposed the use of a data driven ANN model combined with their recent algorithm, combined Pareto multi-objective differential evolution (CPMDE) (Olofintoye et al., 2014) to solve hydropower problem of Vanderkloof dam in South Africa. Their model was formulated for real time operation. Daily reservoir inflow was forecasted using ANN and CPMDE was used to propose daily reservoir operation in real time. A multiple input single output (MISO) ANN and a single hidden layer were adopted in the study. The two objective functions are maximizing hydropower production within a short period of forecast – a short-term objective- and minimizing deviation from the optimized storage control curve. These objectives are conflicting. Inflow obtained for the three previous days are used to update the model. Thus, the present day inflow is forecasted and used for real time reservoir operation. A year data was used for the simulation (Olofintoye et al., 2014). The model presented was efficient because inflow was accurately calculated and two algorithms are used simultaneously to achieve success.
Another hybrid algorithm called clonal selection algorithm (CSA) was also demonstrated by Swain et al. (2011) and performed excellently. The hydrogenating units have no fuel cost; however, scheduling of hydrothermal involves minimizing total thermal production cost and also making use of hydro-resource as much as possible. The objective function of their model was to minimize the total fuel cost for running the thermal system. The constraints were the power balance reservoir volume and total water discharge. They considered another system where the objective function is to minimize total fuel cost responsible for running the thermal system in meeting load demand. The constraints are demand, thermal generator, hydro generator, reservoir capacity, water discharge, hydraulic continuity and hydropower generation. The methodology processes adopted are initialization, affinity evaluation (objective function), clonal proliferation, mutation and selection. The constrained hydrothermal generation scheduling problem was successfully solved using clonal selection. The optimization of short-term hydrothermal system presents non-linear form of objectives and constraints. CSA based algorithm was found to be effective in finding near-global solutions using lesser computational effort (Swain et al., 2011).
Also, the nonlinear, nonconvex and multi-modal objective functions of multi-reservoir operation were optimized by self-learning genetic algorithm (GA) (Hakimi-Asiabar et al., 2010). Self-learning GA is an improved form of the SOM-Based multi-objective GA which was presented by Hakimi-Asiabar et al. (2009). The monthly reservoir operation of 3 reservoirs namely Karoon, Dez and Gotvand were investigated. The model considers the conflicting objectives of hydropower generation, water supply demand downstream and river water quality control. Meanwhile, the first objective function of minimizing unsatisfied water demand is a quadratic function. Also, the hydropower generation is maximized which has average water head as one of its components. However, the hydropower generation function is nonlinear and nonconvex. Meanwhile, to control the river water quality, the function minimizes the summation of diverted return flows volume and also wastewaters to control the salinity of the river. The constraints are continuity equations, reservoir capacity, spillways capacity, reservoir releases, water balance at the irrigation nodes, mass balance for calculating downstream river salinity, wastewaters and return flows discharge, acceptable level of water salinity in rivers and effective water head for each reservoir. To sum this up, there are 12 constraints and 3 objective functions, which were successful optimized.
Furthermore, evolutionary algorithm was improved using principal component analysis and crowding distance operator (MOSPD) (Yang et al., 2015). The resulting algorithm is titled multi-objective complex evolution global optimization method. This algorithm was applied to Oroville-Thermatito Complex (OTC) for hydropower reservoir operation. OTC is a crucial head-water resource for the California State Water Project (SWP). This hydropower operation comes with joint management resulting in usual nonlinearity in reservoir height to storage relationship. This is formulated as polynomial function. Also, the algorithm improves the convergence and diversity of the solutions along the Pareto front. Consequently, comparative analysis of this new algorithm with other popular algorithms like multi-objective differential evolution (MODE), multi-objective genetic algorithm (MOGA), multi-objective particle swarm optimization scheme (MOPSO) and multi-objective simulated annealing approach (MOSA) was conducted. Surprisingly, MOSPD produced results that are better and highly competitive with the other algorithms. Also, MOSPD produced better alternatives for operating and managing the OTC reservoir more efficiently and effectively especially under different climate (Yang et al., 2015). The objective functions adopted by Yang et al. (2015) for their model are to maximize storage volume and hydropower generation which are conflicting. These are subject to nine different constraints. MOSPD generated non-dominated solution towards higher objective function values and also solutions, which are uniformly and diversely distributed along Pareto front. Therefore, MOSPD is a good algorithm for hydropower optimization especially for modelling OTC reservoir.
No doubt, hydropower operation presents a large, stochastic, time-coupled, space coupled and non-linear optimization models and usually multi-objective. In addition, there are several objectives and constraints to be solved. Recently, Rampazzo et al. (2015) presented two approaches to solve hydropower reservoir operation problem. The two techniques are genetic algorithm and differential evolution, which are evolutionary metaheuristics algorithms. They perform exploitation and exploration of the search space. Incidentally, the hydropower model resulted in two multi-objective optimization algorithms, which are hydroelectric nondominated sorting genetic algorithm, HNSGA and hydroelectric nondominated sorting differential evolution, HNSDE. Both algorithms are based on NSGA-II mechanism (Deb et al., 2002). They are both applied to solve the hydropower-planning problem presented. The model presents four objective functions. The objectives of the model are minimizing the thermal complementation cost, maximizing the reservoir final volume, maximizing the power generation and maximizing the monthly minimum power generated. In conclusion, both algorithms performed excellently in finding nondominated solutions to hydropower problem presented.
Hydropower generation has improved with the use of hybrid evolutionary algorithms. The advantages of one algorithm over the other are explored in one aspect of the problem while the other algorithm complements. In this way, better solutions are achieved that are superior to using one algorithm. Apart from hydropower use of reservoir, hybrid algorithms can also be adapted to flood control to achieve similar success.
5. Hybrid models in flood control
Flood control is an integral part of reservoir operation. Flood is a disaster that is frequent, serious and extended over a wide area. One way to mitigate against flood is the use of reservoir as a storage for excess water which otherwise could cause flood. Furthermore, reservoir helps during flood season by diminishing flood peaks, reducing flood damage, and also preserve flood (Hlavinek, 2009). Reservoir operation includes flood management, which is an important water resources management research. There are conflicting objectives of maintaining dam safety at the same time minimizing downstream flood. This results in multi-objective optimization with many objectives, constraints and decision variables (Luo et al., 2015b). Flood can be managed with reservoir using hybrid multiobjective evolutionary optimization techniques.
In fulfilling its purposes of flood control, hydropower generation, industrial water supplies, irrigation, navigation and domestic water uses, a reservoir should be able to impound water and control streamflow. Reservoirs are operated based on their operating rules. These rules are determined by calculating the inflow and outflow of the reservoir without depleting the water in the reservoir and also performing its functions effectively throughout the year. These operating rules tend to minimize deficit in water supplies at the same time maximizing the benefits derived from the reservoir. Financial and operational risks are enormous when reservoir is operated in a competitive market. This analysis tools and techniques should be improved significantly to meet the challenge. Decision support system (DSS) can also provide a superior way to deal with this unstable inflow and instantaneous decision making (Jin and Wu, 2014, Zimmer et al., 2015). DSS has been demonstrated to be more stable and gives reliable decisions in the operation and optimization of hydro power plant (Sharma et al., 2015). Operating rules, DSS and other techniques play important role in reservoir operation especially flood control.
Flood control is usually taken as one of the key operation of a reservoir. It was stated in the introduction that reservoir operation system presents complicated procedures. So, usually, researchers consider only two most vital objectives of flood control and power generation. Irrigation and navigation are usually ignored and treated as constraints in many models. The reliability and safety are considered though the model is formulated to be cost effective (Zhang et al., 2014). During the flood season, the model is formulated to make inflow equal to outflow thereby maintaining constant volume. Of course, this is to ensure that flood control volume is preserved. Therefore, during non-flood period, reliable output from hydropower station and maximum power generation are considered. Ultimately, infeasible solutions are identified and discarded by the use of penalty values. The constraints identified in the model are water volume balance equation and other constraints like reservoir storage volume, storage level discharge and output capacity.
Moreover, flood control can be formulated in different ways. In formulating a multi-objective optimization for flood control, Luo et al. (2015b) presents two objectives for Ankang reservoir in China. The first objective was to minimize the highest upstream water level where the release volumes are variables. This is to ensure that the reservoir does not store large flood water thereby ensuring the safety of dam and decrease loss of upstream area. The second objective was to minimize the release volume during the period. This ensures the reservoir has floodwater volume to protect the downstream areas. The constraints are the upper and lower limit of water levels at upstream, release volume, which should be nonnegative and water balance equations.
On the other hand, model predictive control (MPC) has been applied to solve many water management problems especially real time applications. In the same way, automatic downstream water level control, a linear quadratic regulator, was solved by Wahlin and Clemmens (2006) using MPC. The algorithm helped in keeping the water level at set points. Similarly, a gate movement control by real time flood control operation of existing gate operation using MPC has also been documented (Delgoda et al., 2013, Barjas Blanco et al., 2010). However, the algorithm has limitation for handling nonlinear problems, which are common to complex systems in water resources modelling. Therefore, the combination of MPC with GA is thus necessary. By and large, GA is known for handling complex systems with ease. The hybrid of both algorithms thus presents advantages. While real time operations are handled by MPC, GA handles complex nonlinear, non-convex, constrained and non-differentiable problems with local minimum optimization problems. MPCGA performed better than the present operation in flood control in the reservoir operation problem presented. This is to further support the later study of Olofintoye et al. (2016) that real time operations have advantages over normal operations.
Therefore, real time flood control model was developed for 12 gated weirs. Consequently, the algorithm used was a hybrid of GA and model predictive control called MPCGA (Hsu et al., 2015). Also, the case study was Demer River in Belgium. The hybrid allows the coping with nonlinear behavioural system of the model. It also helps in escaping local optimum. The cost function was minimized and simultaneously avoided constraint violation. Finally, it was concluded that the current regulation strategies was improved with fixed regulation rules.
Also, multi-objective immune algorithm with preference-based selection (MOIA-PS) was presented to solve flood control problems in reservoir operation (Luo et al., 2015a). The reservoir operation presented has a preference for flood control and dam safety. Therefore, irrigation water demand should be met as a constraint. MOIA-PS offers a difference from conventional EAs. Conventional EAs try to find good approximations of the entire Pareto front. However, MOIA-PS obtains a set of preferred Pareto solutions located within a small part of the preferred area on the Pareto front. The demonstration of this was done on the Ankang reservoir with four typical floods. It was observed that a local area of Pareto front has the preferred non-dominated solutions. The proposed MOIA-PS obtains more non-dominated solutions which are densely and evenly distributed with the Pareto front preferred area than outstanding algorithms like NSGA-II and the immuned inspired multi-objective, NNIA. MOIA-PS is thus suggested to solve reservoir operation for flood control as it reduces flood risks and ensure dam safety while satisfying irrigation demands. The main constraints of the model are water balance equality limit, reservoir upstream water level limit, discharge volume limit and final reservoir level limit.
Similarly, in another study, Chaleeraktrakoon and Chinsomboon (2015)presented dynamic flood control rule curves (DFCRCs) for a dam operation. The reservoir size is too small for managing the flood control uncertainties using the current practice of flood control rule curves (FCRCs). The model comprises of a flood prediction model combined with a storage routing method. The volume and peak properties for an arriving flood were calculated by a prediction model. The predicted flood's DRCRCs are calculated with storage routing method. Three stages of flood are considered which are prior to arrival of flood, prior to flood peak and after flood peak (Chou and Wu, 2015). Each stage has its own operating rules. An efficient optimization algorithm called BOBYAQ (The bounded optimization by quadratic approximation, (Powell, 2009)) is used as a calibration algorithm for optimal parameter rule to comply with the objectives and characteristics of different flood stages. However, the operator specifies these levels – with relative priority given to flood mitigation, water conservation and dam safety.
Another similar study considering the three flood stages was presented by Hsu et al. (2015). Different algorithms are used for solving the flood control management presented. Adaptive network-based fuzzy inference system (ANFIS) and a real-time recurrent learning neural network (RTRLNN) were used concurrently in this model. Also, the reservoir operation was optimized using mixed integer linear programming (MILP) and an intelligent real-time operation model of a reservoir for flood control was developed. Radar- and satellite meteorological techniques, meteorological image similarity analysis, forecasted typhoon tracks, ANFIS and RTRLNN were used to forecast total inflow into the reservoir. The algorithms are suitable for flood control with the simulated results generated and tested on the watershed.
Flood control is a complex water resources management problem, which is difficult to solve using a single algorithm. However, better results can be generated with hybrid algorithms. Meanwhile, the results generated in the algorithms presented show that evolutionary algorithms are capable to solve flood control problem and other water resources problems. Moreover, a modification to the algorithms, or combination of algorithms produces models that are competitive and efficient for reservoir operation for flood control.
6. Ecological base flow models
Water resources management should be improved to create a balance between flood and drought rampant in the watersheds. Effective management of reservoirs, which serve as a bank for excess water, is thus important. Reservoirs create stability to water resources because it absolves excess water during flood and releases the same in steady flow during drought. Water is supplied and made available for the ecosystem during low flows. Unfortunately, ecological flow has been receiving less attention than human demands by water resources researchers. Therefore, environmental impact should be given attention by water resources engineers in reservoir operation designs. There are many studies incorporating ecological base flow in the reservoir operation models.
Ecological base flow and human water demand requirements are very crucial. To optimize the ecological base flow and human water demand requirements, Chang et al. (2010) proposed constrained genetic algorithm (CGA) for a multi-use reservoir management. Also, in another study, Yin and Yang (2011)presented reservoir operation and environmental flow requirements in a model called couple reservoir operation and water diversion (CROWD). They integrate reservoir operation model and a water diversion model, which was adapted for the joint operation of Tanghe Reservoir and Liaoyang diversion in the Tang River Basin in China. Accordingly, ecological base flow requirements were used as constraints and the objective function is thus formulated to accommodate ecological base flow requirements with penalty function appropriate to form the fitness function. Also, the CGA techniques are used to search for feasible solutions for the reservoir (Chang et al., 2010).
In the same way, NSGA-II algorithm was used and the number of generation was 1000 to generate Pareto front of the study area (Yin and Yang, 2011). One model considered two compelling objectives of minimization of generalized shortage index (GSI) and degree of hydrological alteration, D (Yin and Yang, 2011). Ultimately, the algorithm by Yin and Yang (2011) achieved to global optimum at 600 generations when the average values of GSI and D were achieved. In another methodology, once the constraints are violated, the function is penalized therefore guiding the search away from infeasible region to feasible region within the search space (Chang et al., 2010). The formulated model was applied to a case study of Shih-Men reservoir that has 20 different yearly hydrological events. When considering reservoir operation in another model, the space was divided into three zones using different operating rules developed for allocating water in different water levels (Yin and Yang, 2011).