Reservoir operation based on evolutionary algorithms and multi-criteria decision-making under climate change and uncertainty

Water scarcity and climate change pose serious challenges for decision-makers with regard to water supply during critical and drought periods (Gohari et al. 2017). Increased greenhouse gases and growing population complicate resources allocation and management (Kamperman & Biesbroek 2017). Reservoir operation, runoff simulation, and water allocation are important in water resource management. Climate change is triggering temperature increase and is impacting the quality and quantity of water available in reservoirs, runoff, and sediment load (Intergovernmental Panel on Climate Change (IPCC) 2014). Industrial countries with their large gas emissions and countries with emerging economies combine to cause climate change which then is being alleged to be causing sea level rise, tropical storms, and floods and droughts. Thus, prediction of weather extremes and their impact on available resources is necessary (Beermann 2017).

In recent years, mathematical models and climate change scenarios have been combined in order to achieve better management of water supply (Santos et al. 2017). These mathematical models are used for prediction of demand, water supply, runoff, and flood control for the future and base periods. Buchtele (1993) applied different climate change scenarios and models for the prediction of runoff from a basin. Investigating the uncertainty of different climate change models, the Had-CM3 model was found to be having the lowest uncertainty and then the HEC-HMS model was used for the prediction of runoff in the base and future periods. High correlation index and low mean absolute error showed that the model was accurate and the runoff volume would decrease for the period of 2000–2020.

Burn & Simonovic (1996) investigated the change in water release under climate change and different scenarios of inflow to the reservoir. The runoff volume for the period of 2000–2020 was predicted as inflow to the reservoir and with the computed inflow or runoff the volume of water release was computed using Lingo software. The water release curve and comparison with demand values showed that the reliability index of the reservoir for water supply decreased for the future period as compared to the base period (1980–2000).

Xu (1999) used general circulation models (GCMs) for the prediction of temperature and precipitation and then these values were used for runoff prediction using hydrological models. One of the important issues was related to the large scale of computational cells in the GCMs which were introduced by different downscaling methods.

A conceptual monthly water balance model, based on 15 climate change scenarios, was used for flow prediction in the central basin in Sweden (Xu 2000), and results showed decreasing snow and flow volume for the period of 2000–2025.

In another study, an artificial neural network (ANN) was used for flow prediction under climate change. First, temperature and precipitation were computed for the period of 1980–2000 and then these values were used as inflow for runoff prediction in the future period. The ANN was found to perform well under climate change (Agarwal & Singh 2004).

Alfieri et al. (2006) computed the change in power production of a powerhouse for the water released from an upstream dam for the period 2000–2025 under climate change. Nonlinear programming was used for minimizing an objective function with the aim of decreasing the hydropower shortage downstream. Results showed that the power supply under climate change was in accordance with higher vulnerability index for the future periods.

Water allocation under climate change and uncertainty of climate change models were investigated in another case study (Wang et al. 2008). A weighting method based on a probability density function (PDF) was used for the determination of uncertainty and the selection of the best model. The Had-CM3 model was used and for temperature and precipitation values and using the predicted runoff, water allocation was then done for the future period 1990–2010.

Kisi (2011) applied a wavelet regression model (WRM) for runoff prediction under climate change for a future period. The A2 scenario and five climate change models were used for temperature and precipitation. Runoff was predicted using WRM and ANN where WRM was more accurate for runoff prediction for the base period.

The LARS-WG model was used in another study for downscaling of GCMs with high accuracy and then with predicted temperature and precipitation, irrigation water demands were predicted (Hassan et al. 2014).

A multi-objective problem of reservoir operation with the aim of increasing the reliability index and decreasing the vulnerability index under climate change was investigated for the prediction of water to be released from a multi-reservoir system. A hybrid framework of multi-objective genetic algorithm and climate change model was used for the computation of rule curves and the computed curves showed decreasing reliability index and increasing vulnerability index for the period 2046–2065 (Ahmadi et al. 2014).

Ashofteh et al. (2017a) applied a dynamic system (WEAP model) for water resources management in a basin in Iran for a future period (2046–2065) under climate change. Results showed the inflow to the reservoir in the basin decreased and the demand for irrigation increased compared to the base period. A dynamic model (ZRW-MSM 2.0) was used in another study to investigate the effect of climate change on water resources management of a basin in Iran. Results reported population and drought growth for the future period with the increase of demands (Gohari et al. 2017).

Ashofteh et al. (2017b) applied the logic genetic programming method for reservoir operation under climate change and found that logic genetic programming had a smaller value for the objective function, the reliability index for water supply for the future period decreased, and the vulnerability index increased for the future period compared to the base period.

Ashofteh et al. (2017c) applied multi-objective genetic programming for reservoir operation with the aim of increasing reliability and decreasing vulnerability. The rule curve for irrigation demand obtained from this programming showed less shortage index for the period of 2026–2039.

Applying two-dimensional dynamic programming for reservoir operation under climate change, Zhang et al. (2017) showed that the fixed rule curve could not respond to the demand for the future period and hence used adaptive rule curves for the future period.

Using multi-objective genetic algorithm for reservoir operation for power and water supply considering climate change, Yang et al. (2017b) showed that it was capable of supplying 300 million m³/year of water for the future period.

Neural network and support vector machine were used for prediction of inflow to a reservoir under climate change by Yang et al. (2017a), who found that runoff decreased for the future period compared to the base period and there was uncertainty in different climate change models for runoff volume.

Previous studies have investigated water resources management under climate change. In this study, a new hybrid framework, based on an artificial intelligence method and climate change models, is used for the operation of a reservoir in Iran. First, temperature and precipitation based on climate change methods are computed for the base period (1981–2000) and the future period (2011–2030) and then the IHACERS software as a hydrological model is used for the prediction of runoff. The predicted runoff is used as inflow to the reservoir and the bat algorithm as an artificial intelligence method is used for the minimization of irrigation deficit downstream because meta-heuristic algorithms have been successfully applied to reservoir operation (Fallah-Mehdipour et al. 2011, 2013). For example, Wang et al. (2011) applied an interactive genetic algorithm for reservoir operation and results showed this method was accurate and its solution was closer to the global solution compared to a nonlinear programming method. Ostadrahimi et al. (2012) applied a particle swarm optimization algorithm (PSOA) for the operation of a multi-reservoir system with the aim to supply demands and the algorithm exhibited faster convergence. Asgari et al. (2015) used a weed algorithm for reservoir optimization with the aim to decrease irrigation shortage and the algorithm yielded solutions closer to the global solution. The bat algorithm is one the newest algorithms to be used in engineering optimization. In this study, this algorithm was used for optimization of reservoir operation.

The reason for applying the bat algorithm to reservoir operation is its high potential for optimization. Niknam et al. (2013) applied this algorithm with the aim to increase energy production. Results showed that the algorithm converges in less time than did the genetic algorithm and particle swarm algorithm. Bozorg-Haddad et al. (2014) used the bat algorithm for reservoir operation with the aim to decrease hydropower shortage and results showed that the algorithm had a higher ability to find the global solution than the other evolutionary algorithms or traditional methods, such as nonlinear programming method or dynamic programming method.

When demand and water resources are to be predicted for future periods, the methods with higher reliability should be employed. The hydrological method and artificial intelligence methods can be combined as a hybrid framework for water resources management. The difference between the current study and previous studies is the combination of climate change with the bat algorithm for reservoir operation optimization and hydrological model, while the previous studies, such as Bozorg-Haddad et al. (2014) and Ahmadianfar et al. (2015) investigated reservoir operation based on the bat algorithm without the consideration of climate change and its effect on reservoir operation. In this study, one can use the hybrid framework for other reservoir operation problems. Figure 1 shows the flowchart of the model procedure including the major stages at different levels of this study. In addition, the other key point is the computation of uncertainty of climate change models based on the Bayesian statistical method which determines the more reliable climate model for the next application, such as runoff simulation. Furthermore, the genetic algorithm and the particle swarm algorithm were used for comparison with the bat algorithm and a multi-criteria decision-making was used to select the best method for reservoir operation in the base and future periods. The proposed model has been developed for Dez dam in Iran.

First, the IHACRES module for the basin should be calibrated. Thus, observed temperature, discharge, and precipitation for the base period are used. Then, runoff volume of the basin for the period 2011–2030, based on temperature and precipitation input, is computed.

There are different sources of uncertainty which are divided into the following groups:

• 1.

  uncertainty in AOGCM models for the simulation of climate change variables;

• 2.

  uncertainty in different downscaling methods;

• 3.

  uncertainty in runoff simulation methods.

In this study, the first kind of uncertainty was determined based on Bayesian strategy. The following levels were considered for the computation of uncertainty (Katz 2002):

• 1.

  A prior probability distribution was generated for statistical parameters.

• 2.

  The likelihood distribution of the observed data was determined as a function of parameters.

• 3.

  The posterior probability distribution was determined, based on the computed distribution of input data and the likelihood function.

First, the PDF of climate change scenarios and monthly precipitation and temperature was computed and then the Monte Carlo method was used for the simulation of large data.

The bat algorithm, genetic algorithm, and particle algorithms as powerful methods are considered for optimizing of reservoir operation with consideration of climate change condition. Thus, these methods are defined here based on the equation and mathematical models so that the process for each algorithm is defined in the following sections.

Also, the following assumptions were considered for the bat algorithm:

• 1.

  All bats applied the echolocation ability for finding of food and this ability allowed the bats to separate an obstacle from the food.

• 2.

  Each bat can search prey by a sound with the velocity at location (y_l) with frequency (f), wavelength and loudness (A₀).

• 3.

  The loudness can change from A₀ as a large constant value to a minimum value (A_min).

In addition, the frequency is in the domain of f_min and f_max. Also, the wavelength domain is between and ⁠. The emission rate of sound for each bat is r and it is between 0 and 1. Figure 2 shows the bat algorithm.

The bat algorithm occupies the following levels:

• 1.

  Start.

• 2.

  The initial values of random parameters (y_l, v_l, f_l,….) should be determined.

• 3.

  The objective function for each bat position should be evaluated and the situation should be updated.

• 4.

  Then, the number of iterations should be compared with the maximum iterations and if it is equal or more than the maximum iterations, results should be reported or else the next level should be done.

• 5.

  The situation should be updated.

• 6.

  The rnd as a random number should be compared with r_l and if it is more than r_l, the random fly should be considered or else the situations should be evaluated.

• 7.

  If rnd <A_l and f(y_l) < f(Y_*) are satisfied, evaluate the situation and determine the best solution.

• 8.

  Or else, the algorithm returns to the third level (Figure 2).

First, the initial velocity and position are generated. Then, the objective function is computed for each particle. The p best and g best as a local solution and global solution are computed in the next level. Then, the velocity and position are updated based on the previous formula.

The weighted aggregates sum product assessment (WASPAS) acts, based on the weighted sum model and the weighted product model. This module is useful when there are some methods and some indexes. For example, the reservoir operation is considered based on the bat algorithm, genetic algorithm, and particle swarm algorithm; and there are some indexes, such as reliability index, vulnerability index, resiliency index, and one objective function for each method. The best method can be selected when a multi-criteria decision is used by the user. If the f indexes are considered for the evaluation of each method and the value of each method for each index is considered based on the x_i value, the following levels are considered (Zavadskas et al. 2012):

• 1.
  Compute the normalized x for beneficial criteria and non-beneficial criteria. The indexes where a high percentage of them are suitable are named beneficial criteria and vice versa for non-beneficial criteria (Bozorg-Haddad et al. 2014).

  

  (22)

  

  (23)
• 2.
  and are computed based on weights assigned to each index (Bozorg-Haddad et al. 2014):

  

  (24)

  

  (25)

  In order to evaluate the proposed model, four indexes are considered, resiliency index, vulnerability index, reliability index, and objective function. In fact, these four indexes have the same priority and thus, the assigned weight (w_f) is equal to 0.25 for each index.

• 3.
  Finally, the total is computed as:

  

  (26)

⁠

The Dez dam is known as the 50th highest dam in the world. This dam is located in the Andimeshk in south Iran (Figure 3). This is an arch dam and was constructed between 1953 and 1963. It is a multi-purpose dam and is used for flood control, irrigation water supply, and power generation; however, in this research, the focus is on the water supply for irrigation demand purposes because it has greater priority for decision-makers.

The decision variable is the water release and the state variable is the dam storage.

The penalty function was added to the objective function.

There are four main agriculture crops including forage, wheat, barley, and feed corn in the basin. Annual water requirement at a particular time (WR_t) for each crop in the base period is measured. For example, the water requirement for forage, wheat, barley, and feed corn is 1,555.12, 424.23, 769, and 1,234 mm, respectively. Subsequently, the future demand for each crop could be computed based on Equation (39). Usually, the WR_t is computed based on crop reference evapotranspiration. If the reference evapotranspiration is unavailable, this parameter will be computed based on a regression equation between temperature and evapotranspiration. On the other hand, parameter should be computed in the next stage. Therefore, the relative humidity, wind speed, and the length of germination periods should be computed first. Sequentially, is computed and then, ET_C is computed based on Equation (36), where V is the demand volume and A is the area under cultivation.

Also, the following indexes were used for evaluation of different methods.

• 1.

  Reliability index:

• 2.

  Vulnerability index:

• 3.

  Resiliency index:

Also, the following indexes were used for the evaluation of climate change models.

• 1.
  Correlation coefficient:

  

  (43)

  

  (44)

  

  (45)

  where r: the correlation coefficient, n: the number of data, ⁠: the simulated data, ⁠: the observed data, the simulated average, ⁠: the observed average, ⁠: the standard deviation for simulated data, RMSE: the root mean square error, and MAE: the mean absolute error.

First, daily temperature and rainfall based on climatology stations of Dez basin were completed for the AOGCM models for the temperature and precipitation simulation. Then, monthly temperature and precipitation data of AOGCM models were extracted from the IPCC base which included time series of climate variables of computational cells (IPCC-DDC 1999). Then, the monthly average of 20 years (1981–2000) was computed and these values were compared with observed values. In this study, the GCM-RDP program was used for the extraction of time series, because this program can obtain the time series after receiving the spatial coordinates of the location of a case study (Nezhad et al. 2013).

Figure 4 shows the performance of different climate change models and compares results with observed data. The HAD-CM3 model yielded the average temperature for the base period as 14.58°C which was close to the observed temperature of 14.75°C. Table 2 also shows this closeness based on statistical indexes. The correlation coefficient for HAD-CM3 model was 97% and MAE and RMSE had small values which showed the high performance of the HAD-CM3 model. Figure 4 shows simulated precipitation for the base period with different climate change models. The observed average precipitation for the base period was 93.75 mm and the simulated value based on HAD-CM3 model was 91.25 mm, again showing the HAD-CM3 model performed well for precipitation simulation. Table 2 shows small values of MAE and RMSE based on the HAD-CM3 model and the correlation coefficient (r) was high for the simulated precipitation.

First, monthly temperature and precipitation were downscaled under the A2 scenario. Then, the average monthly temperature and precipitation for a long period were simulated for the base and future periods. Simulated temperature for the future period in Figure 5 shows that the temperature is increasing from 1.16 to 2.5°C compared to the base period. The ECHAM4-OPY and GFLD-R30 model had predicted the least value of temperature increase for the future period and the HAD-CM3 model had predicted the greatest value of temperature increase for the future period. Also, Figure 6 shows the simulated precipitation for the future period and it had decreased from 3.33 mm compared to 9 mm for the base period. The ECHAM4-OPY3 and CSIRO-MK2 models had predicted the greatest value of precipitation decrease for the future period. Also, the HAD-CM3 model had predicted the least value of precipitation decrease for the future period. Figures 5 and 6 show the average monthly precipitation for the long term (20 years).

Figure 7 shows the computed weights for different climate change models. Each model based on the Bayesian equation (Equation (8)) had a weight and then the monthly PDFs of temperature and precipitation were computed. The HAD-CM3 model had the most weight for temperature and precipitation, whereas the CSRI-MK2 model had the least weight. Thus, the HAD-CM3 model had the most effect on temperature and precipitation in the region. The scenario of climate change of temperature and precipitation from each PDF was selected after determining the PDF of climate change scenario for the region based on Mont Carlo simulation.

Figure 8 shows runoff simulation for the base and future periods. The correlation coefficient for calibration data was 91% and 87% for verification data. Also, MAE and RMSE were 1.25 and 2.12 m³/s, respectively, for calibration and were 1.87 and 3.45 m³/s for verification, respectively. Figure 9 shows discharge for the base and future periods and runoff volume had decreased by 0.05 × 10⁶ m³ for the future period. The period between the years 1981 and 1992 is considered for the calibration model and the period between the years 1993 and 2000 is considered for model verification.

Computation of demand for the future period needed some information which was not available for the future period. First, a relationship between temperature and reference evapotranspiration based on the base period was extracted for use for the future period. This relationship was based on regression with a high correlation coefficient (R² = 0.90). Then, ET₀ was computed, based on the previous relationship after temperature was computed for the future period. Also, the K_C coefficient was computed based on each crop for the future period. Then, Equation (35) was used for evapotranspiration of crop. Finally, the demand volume was computed based on the previous equations. Table 3 shows the demand value for each crop. The increase of demand for different crops was from 0.55 to 1.63 × 10⁶m³ and Figure 10 shows the demand value for the base and future periods so that it is clear that the demand volume had increased for the future period. In fact, Figure 10 shows the computed water requirement for 20 years in future based on Equation (39) and it is compared with the observed value.

Table 4 shows the sensibility analysis for different evolutionary algorithms for the base and future period. The size population for the bat algorithm is 30 and 50 for the base and future period. Also, maximum loudness is 0.6 for the base and future period. The maximum frequency is 5 for the base and future period. In fact, the least value of objective function is searched in Table 4 and the corresponding parameter for this value of objective function is selected. Also, the other parameter for the other evolutionary algorithms can be seen in Table 4. In fact, the sensibility analysis shows the change of the objective function versus the change of different variables and then the suitable value for each variable is selected.

Table 5 shows ten random results for different algorithms and the following can be seen:

• 1.

  The average result for the bat algorithm was less than that for the genetic algorithm and particle swarm algorithm for the base and future periods.

• 2.

  The average solution for the genetic algorithm was worse than for the particle swarm algorithm and the bat algorithm for the base and future periods.

• 3.

  The coefficient of variation for the bat algorithm was smaller than for the genetic algorithm and particle swarm algorithm for the base and future periods.

• 4.

  Results for the base period for all algorithms were less than for the future period.

Figure 12 shows the water released for the base and future periods for different algorithms. The average water volume released for the base period for the bat algorithm was 16.5 (10⁶m³), while it was 15 (10⁶m³) for the future period. The water volume released for the base period for the particle swarm algorithm was 14.65 (10⁶m³) and was 13.1 (10⁶m³) for the future period. The water volume released for the base period for the genetic algorithm was 13.25 (10⁶m³) and it was 103.5 (10⁶m³) for the future period. Thus, there were two general results:

• 1.

  The water volume released for the future period for the all algorithms was more than for the base period.

• 2.

  The released water volume for the bat algorithm for the future and base periods was more than for the genetic and particle swarm algorithm.

Thus, the bat algorithm can meet demand for the future and base periods better than the other algorithms.

Table 6 shows the performance of different algorithms for reservoir operation. The reliability index for the base and future periods was more for the bat algorithm than for the particle swarm algorithm and genetic algorithm. Thus, the reservoir can meet demand based on the bat algorithm better than based on the other two algorithms. Also, the vulnerability index for the bat algorithm for the base and future periods is less than for the other two algorithms. The resiliency index for the particle swarm algorithm for the base and future periods was more than for the genetic algorithm and the bat algorithm and the objective function for the bat algorithm had a better value than for the genetic algorithm and particle swarm algorithm.

Table 7 shows the value of and ⁠. Also, Table 8 shows the value for different values of 2. It is clear that the bat algorithm had greater value for all intervals of than had the genetic algorithm and particle swarm algorithm. Also, the Copeland procedure was used to compare different methods among each other. Table 9 shows that the bat algorithm based on 11 intervals for had won compared to the genetic algorithm and particle swarm algorithm and, finally, Table 10 shows the superior status of the bat algorithm to the other methods.

In this study, reservoir operation for irrigation demand supply was considered and reservoir operation under climate change based on different climate change models was investigated. The study of climate change models showed that the temperature of Dez basin in Iran would increase for the period 2011–2030 and precipitation would decrease for this period. Also, the Bayesian method was used to determine the more reliable climate change model whose results showed the HAD-CM3 model had more weight than the other models for temperature and precipitation. Also, the IHACRES software based on A2 scenario and the HAD-CM3 model were used for runoff simulation and statistical results showed the high performance of the hydrological model. The results showed that the runoff volume would decrease by about 0.05 × 10⁶m³ for the future period compared to the base period and the predicted demand for the future period would be more than for the base period. The evolutionary algorithms for the future period yielded greater values than for the base period and the value of objective function for the bat algorithm for the future and base periods was less than for the other methods. The water volume released for all the evolutionary algorithms for the base period was more than for the future period and the bat algorithm for the future and base periods released more volume of water than did the particle swarm algorithm and genetic algorithm. Also, the WASPAS model showed that the bat algorithm was a better tool for reservoir operation than the genetic algorithm and particle swarm algorithm. In fact, the operation rule achieved by the bat algorithm could supply water demands better than the other algorithms based on different indexes such as reliability, vulnerability, and resiliency index. For example, the bat algorithm had the highest value of the reliability index compared to the other algorithms. Such observation reflects that the bat algorithm could introduce the highest stable operation rule with the best performance. The proposed model introduced in this article could be effective in the area of studying the influence of climate change on water resource management and planning. In fact, climate change is one of the major reasons for several real water scarcity occurrences around the world. Thus, the research contribution of this article could be of vital importance for developing water resource management concepts under climate change condition.

The authors are grateful for the financial support received from the University of Malaya Research Grant (UMRG) coded RP025A-18SUS University of Malaya, Malaysia.