metaheuristic algorithms

Step spillways are an example of these massive hydraulic structures that, in addition to passing the excess water of the dams, also cause the consumption of flow energy downstream of the dams. Considering the complex hydraulics of the flow on these spillways and the presence of nonlinear limitations, their optimal design is a very difficult problem. In this study, a new framework based on Metaheuristic algorithms, including Harris's hawk Optimization (HHO), gray wolf Optimizer (GWO), invasive weeds Optimization (IWO) and water cycle Algorithm (WCA), considering the minimization of the amount of concrete used in spillway and the maximization of energy dissipation in Spillway toe were developed as objective functions to design these spillways. Algorithms' performance was first checked and validated on basic functions. Then, to achieve the objectives of the study, the spillway of the Siah Bisheh dam was selected as the study dam and the efficiency of the developed models based on the four mentioned algorithms was evaluated on it. The results showed that, in addition to improving the current spillway design in terms of construction costs and dissipation energy, the HHO-based model has good accuracy and convergence compared to other Metaheuristic algorithms. As the comparison of the design obtained from HHO with the current spillway design showed, in addition to a 35% reduction in the volume of concrete consumed, the amount of energy dissipation increased by 15%, which indicates the success of the design model developed in a multi-objective manner using HHO.

In recent decades, metaheuristic algorithms have been successfully applied in various aspects of water resource engineering and management issues, especially in reservoirs' optimal operation. In this paper, a new method based on Symbiotic Organisms Search using the Fitness-Distance-Balance (FDB-SOS) algorithm has been developed for modeling optimal operation of complex multi reservoir system Baft, Safarood, and Jiroft reservoirs of Halilrood basin situated at latitude 56◦51ʹ-61◦30ʹ N and longitude 26◦18ʹ-29◦30ʹ E. The system consists of 3 different agricultural irrigation demands allocation with environmental prioritize in the long-term (from 2000 to 2019) approach. The developed model was used to solve the complex multi-reservoir system operating Halilrood basin. The new FDB-SOS algorithm results were compared with other developed evolutionary algorithms, including Harmony Search Algorithm (HS) and Imperialist competitive algorithm (ICA). Results showed the new FDB-SOS algorithm’s sustainability index was obtained 87.23, 74.34, and 96.03 percent of downstream demands for Baft, Safarood, and Jiroft reservoirs. The finding revealed that the new FDB-SOS algorithm was the superior algorithm in optimal operation of the multi-reservoir system.

Concrete gravity dams secure their stability by the weight of the concrete used in their structure. Therefore, minimizing their weight (the volume of concrete consumed in their body) can reduce the costs significantly. This study aims to evaluate the performance of three metaheuristic optimization algorithms: harmony search, particle swarm optimization, and artificial bee colony, to find the optimal cross-section size of the gravity dam. In this way, the Koyna dam located in India is considered a case study. The programming is applied in Matlab software. Each algorithm under the constraints of this problem (the sliding, overturning, and vertical tension on the body of the dam) is run 6 times. Finally, the lowest value was chosen as the optimal result. The results revealed that however all the algorithms have the optimal outputs than their real one but the optimum one is for the harmony search algorithm. To investigate the role of available uncertainties of dam cross-section, Monte Carlo simulation is engaged. The achieved results based on reliability show more safety of dam design.

The occurrence of successive droughts, along with increasing water needs and lack of proper management of water resources has caused a water crisis that has various environmental and economic consequences. In addition to the drought, the change in the cropping pattern towards water crops has also made the water crisis the first critical phenomenon in recent years in the community, which has a direct impact on the agricultural sector as the largest consumer of water. Therefore, optimizing the cropping pattern is one of the most important factors in managing water resources and coping with water shortages. In this study, to determine the optimal cropping pattern of major crops in Silakhor plain in the next three years using two approaches using Linear Programming and Meta-Heuristic Algorithms.

In the first step, in order to determine the optimal cropping pattern with the aim of maximizing farmers' incomes in the next three years and the limited water and land available, the amount of rainfall recharge is used as a criterion to determine the water exploitation interval and determine the minimum and maximum exploitation each year. In order to forecast rainfall, SARIMA time series models and Genetic Programming were used considering the data of the last 10 years in both seasonal and monthly modes, and according to RMSE and D.C. criteria, a better model was selected. Then, for each crop year, 100 exploitation scenarios were determined according to the amount of groundwater recharge caused by rainfall and the amount of exploitation in previous years. In the second step, Linear Programming was used to determine the optimal cropping pattern with the aim of maximizing farmers' incomes and limitations of exploitable water in each scenario and arable land. The price of each product is projected according to the average long-term inflation of the country, i.e., 20%, and the profit from the cultivation of each product was calculated as a proportion of the price of the product in each year by examining the previous years. Finally, the performance of three types of Static, Dynamic, and Classified Dynamics Penalty Functions into two algorithms, Differential Evolution and PSO was investigated to achieve the results obtained from Linear Programming. Static penalty functions use a constant value during the optimization process, whereas in dynamic penalty functions, the fines are modified during the process and depend on the number of generations. In the classified dynamics penalty, groups of violations are also determined, and the penalty of each response is determined according to the amount of violation of the restrictions and the generation number.

The results show that with increasing groundwater exploitation, farmers' incomes also increase; However, in the exploitation of more than 223.5, 222.2, and 225.1 million cubic meters for the cropping years 2020-2021, 2021-2022, and 2022-2023, respectively, the limitation of the total arable land has prevented the increase of the area under cultivation, and by increasing exploitation, farmers' incomes remain stable. Also, in order to cultivate four crops of wheat, barley, rice, and corn with the current area under cultivation in Silakhor plain, 142 million cubic meters of water is harvested annually from underground sources. By optimizing the cropping pattern for the four crops studied, with the current water exploitation, the income of farmers in the region will increase by 18%. In general, the PSO algorithm answers this problem much faster. The average number of iterations of the PSO algorithm to solve each scenario in this problem is 38% of the number of iterations of the Differential Evolution algorithm. Overall, in solving this problem, the PSO algorithm has performed better in 84% of the scenarios. In penalty functions, the best performance in both algorithms belongs to the classified dynamics, dynamic, and static penalty functions, respectively. By changing the penalty function from static to classified dynamics penalty function, the number of iterations of the Differential Evolution algorithm to achieve the Linear Programming solution is reduced by an average of 11%; In contrast, the PSO algorithm did not react significantly to the change in the penalty function, and its repetitions decreased by an average of only 3%.

The results show that the cropping pattern of the region is not optimal, and with the increase of water exploitation, it will move towards the cultivation of water products. Also, by optimizing the cultivation pattern of the region, farmers' incomes can be increased. Examination of Differential Evolution and PSO algorithms with three types of penalty functions also show that using the classified dynamics penalty function in the PSO algorithm can have good results.

One of the main challenges hindering optimal water resources management is the problem of optimal exploitation of dam reservoirs. Different methods have been used for optimization problems, but since conventional optimization methods are unable to solve complicated optimization problems, the metaheuristic algorithms are increasingly focused on. As such, the present study uses a genetic metaheuristic algorithm for optimizing Chah-Nimeh water wells of the Sistan region. The main objective is to optimally allocate the water of Chah-Nimeh reserves to users in the Sistan region using a genetic algorithm in the context of managerial scenarios with an emphasis on the scenario of dust stabilization. The results of the genetic algorithm show that in the first year, the optimal discharge rate is 20.3531 million m3 and the demand is 98.3121 million m3, so 77.959 million m3 of the demand is unsatisfied. The results reveal that the genetic algorithm could give a proper optimal answer. Furthermore, it is found that in dust stabilization scenario, shortly after the implementation of the scenario, the discharge will not be possible for the agricultural sector anymore (by 2010).

Estimation of sediment concentration in rivers is very important for water resource projects planning and managements. Various models have been developed so far to identify the relation between discharge and sediment load. One of the most common methods for estimating sediment of rivers is sediment rating curve. For better estimation of the amount of sediment based on the sediment curve rating equation¡ it is possible to optimize its coefficients. One of the methods used for optimizing the coefficients of the sediment curve rating equation is taking advantage of meta-heuristic algorithms. Nowadays¡ optimization algorithms are used regularly for solving complex and non-linear problem. The main objective of this research is the use of genetic algorithms and particle swarm to optimize the relationship between discharge and sediment discharge in Kohak station on the Sistan River and comparison the results of these models with sediment rating curve. For the calculation of sediment discharge by the models initially necessary statistics and information including flow discharge and sediment concentrations have been measured since 1981-2011 in the stations are collected. Genetic Algorithm(GA) and Particle Swarm Algorithm(PSO) models were coded in MATLAB. After the models were trained with 70% to 30% of the data at both stations were tested. Evaluation parameters efficiency such as coefficient of determination (R2)¡ root mean square error (RMSE) and Nash-Sutcliffe coefficients (CE) are used in evaluating the models. The results showed that the genetic algorithm with 33484.47 values at Kohak station has lowest root mean square error in all models. After genetic algorithm¡ Particle swarm algorithm with 34754.31 values has lowest values of the objective function.