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In this study, the capability of the recently introduced moth swarm algorithm (MSA) was compared with two robust metaheuristic algorithms: the harmony search (HS) algorithm and the imperialist competitive algorithm (ICA). First, the performance of these algorithms was assessed by seven benchmark functions having 2–30 dimensions. Next, they were compared for optimization of the complex problem of four-reservoir and 10-reservoir systems operation. Furthermore, the results of these algorithms were compared with nine other metaheuristic algorithms. Sensitivity analysis was performed to determine the appropriate values of the algorithms’ parameters. The statistical indices coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), mean square error (MSE), normalized MSE (NMSE), mean absolute percentage error (MAPE), and Willmott’s index of agreement (d) were used to compare the algorithms’ performance. The results showed that MSA was the superior algorithm for solving all benchmark functions in terms of obtaining the optimal value and saving CPU usage. ICA and HS were ranked next. When the dimensions of the problem were increased, the performance of ICA and HS dropped but MSA has still performed extremely well. In addition, the minimum CPU usage and the best solutions for the optimal operation of the four-reservoir system were obtained by MSA, with values of 269.7 seconds and 308.83, which are very close to the global optimum solution. Corresponding values for ICA were 486.73 seconds and 306.47 and for HS were 638.61 seconds and 264.61, which ranked them next. Similar results were observed for the 10-reservoir system; the CPU time and optimal value obtained by MSA were 722.5 seconds and 1,195.58 while for ICA they were 1,421.62 seconds and 1,136.22 and for HS they were 1,963.41 seconds and 1,060.76. The R2 and RMSE values achieved by MSA were 0.951 and 0.528 for the four-reservoir system and 0.985 and 0.521 for the 10-reservoir system, which demonstrated the outstanding performance of this algorithm in the optimal operation of multi-reservoir systems. In a general comparison, it was concluded that among the 12 algorithms investigated, MSA was the best, and it is recommended as a robust and promising tool in the optimal operation of multi-reservoir systems. HIGHLIGHTS This is the first application of robust MSA in the optimization of water resources.; The capability of 11 metaheuristic algorithms in optimization of multi-reservoir systems was compared.; MSA was the superior model in terms of CPU time and obtaining the optimal solution.

Optimal operation of cascade hydropower reservoirs is a complex high-dimensional engineering problem. Developing an appropriate model to solve such problems requires an efficient search method proportional to the dimensions of the problem. Accordingly, this research employed the new fitness-distance-balance (FDB) selection method in the moth swarm algorithm (MSA) to achieve promoted FDB-MSA with a high performance in solving complex large-scale problems. To ensure the efficiency of the developed algorithm, five benchmark functions of Shekel, Six-Hump Camel, McCormick, Goldstein-Price and Rosenbrock were used. Then, the FDB-MSA was used for optimization of hydropower generation of a real five-reservoir system along Karun River at Iran. This is the largest cascade reservoir system in Iran, which supplies more than 90% of the country’s hydropower demand. The results of the developed algorithm were compared with those of genetic algorithm (GA) and particle swarm optimization (PSO) algorithm. It was found that the FDB-MSA could successfully increase the hydropower generation by 59.5% (6724 GW) compared to the actual generation of energy over a 180-months operational period. The corresponding values for PSO and GA algorithms were 54.3% and 9.2% respectively. In addition, the results revealed the superiority of FDB-MSA to GA and PSO, so that, it demonstrated the smallest difference (3.41%) between nominal and optimal power generation compared to the PSO (6.58%) and GA (33.89%).

Accurate estimation of solute transport has significant importance in water resources and environmental engineering. Among the various types of mathematical formulation for modeling of solute transport, the transient storage model has been widely applied by different researchers as an appropriate model. In this study, an improved version of symbiotic organism search (SOS) algorithm was used to estimate the parameters of transient storage model. A large set of data from natural rivers of USA was collected from the literature and used for derivation and validation of the algorithm. The performance of the algorithm was evaluated by standard statistical indices. Accordingly, the values of R and RMSE for transient storage model parameters (Kf, T and e) were obtained 0.922 and 30.62 (for Kf), 0.596 and 5645 (for T) and, 0.643 and 0.019 (for e) for whole dataset. In addition, the results of this study were compared with those obtained by different reserachers via other models. The results indicate the higher capability of improved SOS algorithim compared to the others in estimating the transient storage model parameters.

Accurate prediction of dew point temperature is very important in decision making in many fields of water resources planning and management, agricultural engineering and climatology. This study investigates the ability of some data-driven models (DDMs) in predicting daily dew point temperature. These models include traditional group method of data handling (GMDH), improved GMDH models (GMDH1, GMDH2), and two hybrid GMDH-based models (GMDH-HS and GMDH-SCE) which were developed by combination of GMDH with two optimization algorithms, harmony search (HS) and shuffled complex evolution (SCE). 11 years of daily recorded weather variables at Kerman synoptic station including mean temperature (Ta), sunshine hours (S), soil temperature (Ts), mean relative humidity (Rh), and wind speed (Ws) were used to evaluate the proficiency of developed models. Sensitivity analysis revealed that Rh is the most influential input variable in predicting dew point temperature. Seven quantitative standard statistical indices including coefficient of efficiency (CE), correlation coefficient (CC), root mean square error (RMSE), mean square relative error (MSRE), mean absolute percentage error (MAPE), relative bias (RB) and threshold statistic (TSx) were employed to examine the performance of applied models. The results indicated the superiority of combinatorial models (GMDH-HS and GMDH-SCE) to the other developed models in predicting the dew point temperature (Tdp). In terms of threshold statistic, GMDH2-HS had the highest values of TSx (the best model) and GMDH2-SCE, GMDH1-HS, GMDH1-SCE, GMDH2 and GMDH1 got the next ranks, respectively. It was observed that GMDH2-HS could predict the Tdp (with CE = 0.979 and RMSE = 0.745) better than the other models (with CE = 0.958 and RMSE = 0.932, in average), indicating its high efficiency.

An accurate estimation of Evapotranspiration (ET) is an important issue in hydrology, water resources management and irrigation scheduling. There are a wide range of methods for estimation of ET, among which, machine learning techniques and remote sensing-based approaches demonstrated more reasonable results. Accordingly, this study attempts to compare the capability of two developed models of Gene-Expression Programming (GEP) and Surface Energy Balance Algorithm for Land (SEBAL) in estimation of ET, at four different climate types of Temperate-Warm (T-W), Wet-Warm (W-W), Arid-Cold (A-C), and Arid-Warm (A-W). In this way, a-two year of daily records as weather variables (i.e., maximum and minimum temperature, dew-point temperature, vapor pressure, saturated vapor pressure, relative humidity, 24-h rainfall, sunshine hours, and wind speed) were considered as input variables, whereas ET values were computed as output variable (observed ET) by using FAO Penman–Monteith-56 method. After development of two predictive models, the statistical results were compared with well-known Hargreaves–Samani method. The results showed that while Hargreaves–Samani equation could not yield remarkable results in any of the climates, GEP and SEBAL demonstrated accurate predictions. In this way, GEP was the superior model in T-W (R2 = 0.902 and RMSE = 0.713 mm/day) and A-W (R2 = 0.951 and RMSE = 0.634 mm/day) climates but it dropped a bit in two other climates. However, SEBAL not only had the best performance in both climates of W-W (R2 = 0.967 and RMSE = 0.515 mm/day) and A-C (R2 = 0.990 and RMSE = 0.720 mm/day), but also demonstrated good predictions in T-W and A-W climates. Therefore, SEBAL is recommended as the best model for estimation of ET in all climate types.

Optimal operation of reservoirs is one of the most important issues in water resources management. In this study, a novel metaheuristic optimisation algorithm, called the water cycle algorithm (WCA), was used to derive operating policy for a multi-reservoir system. In the first step, the performance of the model was successfully assessed through several benchmark functions. The WCA was then used to derive the optimal operation of four- and ten-reservoir systems. It was then applied to the monthly operation of Golestan and Voshmgir consecutive dams located in Gorganrood basin in the north of Iran. In this way, the objective function was defined as minimising the total deficit for the study period. The WCA results were compared with the results of other developed evolutionary algorithms, including a genetic algorithm, harmony search algorithm, particle swarm optimisation and imperialist competitive algorithm. The results showed that, for cases of four- and ten-reservoir systems, the best solutions achieved by the WCA were 306·3918 and 1172·4197, which had differences of 0·5% and 1% compared with the global optimum solutions, respectively. In addition, it was found that the WCA was superior to other algorithms in calculating the annual deficit of the Golestan–Voshmgir multi-reservoir system.

Sediment flushing in many reservoirs of the world is accomplished with low efficiency. In this study, a new configuration was proposed for reservoir bottom outlet to increase the pressurized flushing efficiency. In the new configuration, a projecting semi-circular structure was connected to the upstream edge of bottom outlet. It was observed that by employing the projecting bottom outlet, the sediment removal efficiency increased significantly compared to the flushing via typical bottom outlet. In the case of new-configuration bottom outlet with L sc /D outlet = 5.26 and D sc /D outlet = 1.32, the dimensionless length, width and depth of flushing cone increased 280%, 45% and 14%, respectively, compared to the reference test. The proposed structure can ensure the sustainable use of reservoirs.

Due to the constricting and localization of flow by orifices, these hydraulic structures are commonly used in dams and water impoundment reservoirs to flush deposited sediments. They are also one of the most important flow measurement structures. In this study, the flow characteristics at upstream of a large circular orifice located at the wall of a water reservoir, in the case that the sediments were accumulated behind it, was investigated. The experiments were performed at the hydraulic laboratory of Shahid Bahonar university of Kerman, in a model of rectangular reservoir. The experiments were performed in two parts. First, the flow behavior during the scour development at upstream of the orifice and the extent of sediment erosion due to the orifice flow was investigated. Next, a semi-confined structure was located at the upstream of orifice to increase the sediment removal efficiency. The effect of the geometrical characteristics of structure on the dimensions of scour hole was determined. It was observed that the interactions of water, sediment and structure generated strong vortices upstream of the orifice, which caused the lifting and sweeping away of a large amount of sediment from the reservoir and let to formation of a semi-cone hole upstream of the orifice.