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Simultaneous optimization of several competing objectives requires increasing the capability of optimization algorithms. This paper proposes the multi-objective moth swarm algorithm, for the first time, to solve various multi-objective problems. In the proposed algorithm, a new definition for pathfinder moths and moonlight was proposed to enhance the synchronization capability as well as to maintain a good spread of non-dominated solutions. In addition, the crowding-distance mechanism was employed to select the most efficient solutions within the population. This mechanism indicates the distribution of non-dominated solutions around a particular non-dominated solution. Accordingly, a set of non-dominated solutions obtained by the proposed multi-objective algorithm is kept in an archive to be used later for improving its exploratory capability. The capability of the proposed MOMSA was investigated by a set of multi-objective benchmark problems having 7 to 30 dimensions. The results were compared with three well-known meta-heuristics of multi-objective evolutionary algorithm based on decomposition (MOEA/D), Pareto envelope-based selection algorithm II (PESA-II), and multi-objective ant lion optimizer (MOALO). Four metrics of generational distance (GD), spacing (S), spread (Δ), and maximum spread (MS) were employed for comparison purposes. The qualitative and quantitative results indicated the superior performance and the higher capability of the proposed MOMSA algorithm over the other algorithms. The MOMSA algorithm with the average values of CPU time = 2771 s, GD = 0.138, S = 0.063, Δ = 1.053, and MS = 0.878 proved to be a robust and reliable model for multi-objective optimization.

Deriving optimal operation policies for multi-reservoir systems is a complex engineering problem. It is necessary to employ a reliable technique to efficiently solving such complex problems. In this study, five recently-introduced robust evolutionary algorithms (EAs) of Harris hawks optimization algorithm (HHO), seagull optimization algorithm (SOA), sooty tern optimization algorithm (STOA), tunicate swarm algorithm (TSA) and moth swarm algorithm (MSA) were employed, for the first time, to optimal operation of Halilrood multi-reservoir system. This system includes three dams with parallel and series arrangements simultaneously. The results of mentioned algorithms were compared with two well-known methods of genetic algorithm (GA) and particle swarm optimization (PSO) algorithm. The objective function of the optimization model was defined as the minimization of total deficit over 223 months of reservoirs operation. Four performance criteria of reliability, resilience, vulnerability and sustainability were used to compare the algorithms’ efficiency in optimization of this multi-reservoir operation. It was observed that the MSA algorithm with the best value of objective function (6.96), the shortest CPU run-time (6738 s) and the fastest convergence rate (

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%).

This paper comparatively investigates the capability of 10 solo and hybrid Data Driven Models (DDMs) in predicting the pier scour depth. These models include Support Vector Machine (SVM), Adaptive ...

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.

This is the first attempt to study the effect of debris on the scour at side by side pier and abutment. A large set of experimental tests was carried out at the hydraulic laboratory of Shahid Bahon...

The use of evolutionary algorithms (EAs) for solving complex engineering problems has been very promising, so the application of EAs for optimal operation of hydropower reservoirs can be of great help. Accordingly, this study investigates the capability of 14 recently-introduced robust EAs in optimization of energy generation from Karun-4 hydropower reservoir. The best algorithm is the one that produces the largest objective function (energy generation) and has the minimum standard deviation (SD), the minimum coefficient of variations (CV), and the shortest time of CPU usage. It was found that the best solution was achieved by the moth swarm algorithm (MSA), with the optimized energy generation of 19,311,535 MW which was 65.088% more than the actual energy generation (11,697,757). The values of objective function, SD and CV for MSA were 0.147, 0.0029 and 0.0192, respectively. The next ranks were devoted to search group algorithm (SGA), water cycle algorithm (WCA), symbiotic organism search algorithm (SOS), and coyote optimization algorithm (COA), respectively, which have increased the energy generation by more than 65%. Some of the utilized EAs, including grasshopper optimization algorithm (GOA), dragonfly algorithm (DA), antlion optimization algorithm (ALO), and whale optimization algorithm (WOA), failed to produce reasonable results. The overall results indicate the promising capability of some EAs for optimal operation of hydropower reservoirs.

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.

Transient storage model (TSM) is the most popular model for simulating solutes transport in natural streams. Accurate estimate of TSM parameters is essential in many hydraulic and environmental problems. In this study, an improved version of high-level Moth-Swarm Algorithm (IMSA) was used to predict the TSM parameters. First, the performance of the improved model was successfully assessed through several benchmark functions. Next, a series of 58 measured hydraulic and geometric datasets was used to validate the model. The data were divided into two series randomly, 38 datasets were selected for derivation and the remaining 20 datasets were used to verification. Then the results of IMSA were compared with other algorithms proposed by previous researchers. Two statistical indices of root mean square error (RMSE) and coefficient of correlation (CC) were employed to evaluate the performance of the model. The results showed that despite the high complexity and uncertainty associated with the dispersion processes, the IMSA algorithm could accurately predict the TSM parameters.

This paper is intended to investigate the effect of Narmab storage dam on downstream inundated area for three reservoir operation scenarios. ArcView GIS was coupled with HEC-RAS to produce a flood map for flood discharge of different return periods. Google-Earth software was applied to depict the extent of floodplain in actual landscape. The inflow hydrographs for 4 return periods (50-, 100-, 500- and 1,000-year) were routed through Puls method in order to obtain the outflow hydrographs passing through dam spillway. Results show that, through the operation of reservoir, the downstream inundated area can be reduced up to 75.1 % as a function of reservoir available storage. Furthermore, calculations showed that the reduction rate of inundated area for 50-year floods is largely more than 1,000-year floods, implies the high ability of Narmab dam on flood control especially for floods with shorter return period.

In this study the effect of upstream face slope of a trapezoidal broad-crested weir on discharge coefficient and water surface profile was investigated using the laboratory models. The velocity and pressure distribution profile were determined. The location of the critical section above the weir was specified. The dimensions of flow separation zone were also measured for different upstream face slopes. The results showed that decreasing the upstream face slope prevents development of separation zone. In this case, the flow was passed through the weir more regularly and the water surface and pressure drop were decreased. Decreasing the upstream face slope to 21°, increased the discharge coefficient up to 10% and reduced the separation relative length and height up to 80% and 95% respectively.

Undular flow above the broad-crested weirs is an open channel flow phenomenon which occurs under certain hydraulic conditions. The flow surface on the weir transforms to sinusoidal waves and the number of waves may vary from one to over 10. Hence weir cannot be utilized to measure the flow discharge due to the formation of surface undulations above its crest. Propagated waves can be disturbed remarkably to the channel downstream. In this study, effects of upstream face slope of rectangular broad-crested weirs on the undular weir flow were investigated. The results obtained indicated when the weir upstream slope reduced from standard angle 90° to 40°, the relative wave height decreased up to 78% and the relative wave length increased up to 55%. The experimental results showed that wave was not generated above the weir with 21° upstream face. Furthermore, effects of the radius of curvature of weir upstream corner on the undular wave characteristics were studied. This study established that curvature and slope has similar effects on the wave elimination.