firefly algorithm

Estimation and forecasting of qualitative parameters along with quantitative parameters of water alongside the river to make correct managerial decisions is one of the objectives of managers and planners of the water industry should be accurately simulated. Most of the models for qualitative parameter estimations require very large input parameters that are either difficult to access or require much time and money to determine. Therefore, the use of data-driven models in this field has been developed to save time and money.

In this paper, the application of artificial neural networks and its combination with the firefly algorithm to predict the amount of Total dissolved solids (TDS) of water in the Gavehrood River located in Iran, Kermanshah has been trained and validated. with this purpose, water quality data of hydrometric station upstream of the Gavoshan reservoir dam are used for the statistical period (1991-2010). Based on different inputs, the multilayer perceptron (MLP) artificial neural network and its combination with the firefly algorithm are tested. The best algorithm of the inputs, the number of hidden layers and the number of neurons in each layer in the artificial neural network are determined. The input data imported to the models include the flow rate (Q), Sodium (Na), Magnesium (Mg), Calcium (Ca), Sulfate (So4), Chloride (Cl), Bicarbonate (Ho3), Electrical conductivity (EC) and Total Dissolved Solides of the river in the previous period (TDSt-1) and the output data of TDS. The number of hidden layers is obtained to be 1 and the number of hidden layer neurons is achieved to be 9. Also, the neural network function in this study is considered as a waterfall type and the results are compared by combining artificial neural networks with the firefly algorithm. The model outputs are compared with measurement data using the error measurement criteria.

In this regard, the values of the used error evaluation indices including the observed standard deviation (RSR), Nash Sutcliffe coefficient (NSC), correlation coefficient (R) and root mean square error (MSE) for artificial neural network are yielded 0.154, 0.976, 0.989 and 25.27, respectively and in the case of the neural network combination with the firefly algorithm, are achieved to be 0.129, 0.983, 0.992 and 17.8, respectively.

Therefore, the performance of the hybrid method of artificial neural networks by using the firefly algorithm in predicting TDS is more appropriate than artificial neural networks.

In this study, a hybrid model was developed in order to approximate the discharge coefficient of side weirs located on converging channels for first time. In other words, the ANFIS network was optimized by means of the Firefly Algorithm (FA). After that, six ANFIS and ANFIS-FA models were defined by input parameters. In addition, in this study, the Monte Carlo simulation was employed to study the modeling accuracy. Furthermore, the k-fold cross validation approach was implemented for validating the modeling results. By analyzing the modeling results, it was concluded that hybrid models are more accurate than ANFIS models. The superior model simulated the discharge coefficient values with reasonable accuracy. For example, the values of R2, MAE and RMSE for the superior model were calculated 0.003, 0.011 and 0.015, respectively. Also, about 98% of the superior model results have an error less than 12%. According to the uncertainty analysis results, the superior model had an overestimated performance. A sensitivity analysis indicated that the flow Froude number at the side weir downstream is the most effective input parameter.

Piano-Key weirs are a new type of overflow that are designed to increase the drainage capacity of dams and canals. If the keys forming this overflow model are placed on an arc of a circle, it is called curved piano-key weir. In this research, the performance of three models of Intelligent Support Vector Regression (SVR), Support Vector Regression- Firefly (SVR-FA) and Support Vector Regression- Grasshopper (SVR-GOA) to predict curved piano-key weir flow rate were evaluated. Determination Coefficient (R2), Mean Squared Error (MAE), Root Mean Squared Error (RMSE), and Scattering Index (SI) are four statistical indicators that are used to determine the accuracy of intelligent models. The result of these evaluation criteria during the test period is that the SVR-GOA model with values ​​of 0.99275, 0.01220, 0.00026 and 0.00046 compared to the SVR-FA model with values ​​of  0.95666, 0.03844, 0.00200 and 0.00342 and SVR with values ​​of 0.94249, 0.04013, 0.06027 and 0.00410 for R2, MAE, RMSE and SI indicators, are more accurate in predicting curved piano-key weir flow rate

In this research, an evolutionary based Neuro-fuzzy technique was utilized to estimate the discharge coefficient of labyrinth weirs. In order to optimize the parameters of the adaptive Neuro-fuzzy inference system (ANFIS), the Firefly Algorithm (FFA) was implemented. In modeling the ANFIS-FFA and ANFIS methods, the Monte Carlo simulation was used to evaluate uncertainty of the model. Furthermore, several models with significant flexibility and generalizability were provided using the k-fold cross validation method. First, the input dimensionless parameters including the Froude number (Fr), ratio of the head above the weir to the weir height (HT/p < /em>), cycle sidewall angle (α), ratio of length of the weir crest to the channel width (Lc/W), ratio of length of the apex geometry to the width of a single cycle (A/w) and the ratio of width of a single cycle to weir height (w/p < /em>) were defined. After that, seven different models were introduced for ANFIS and ANFIS-FFA. Then, using a sensitivity analysis, the superior models (ANFIS-FFA 5 and ANFIS 5) and the most effective input parameter (Froude number) were identified. In addition, the error distribution results showed that about 70% of the superior model (ANFIS-FFA 5) results had an error less than 5%. In other words, the superior model had a high statistical significance. Ultimately, the uncertainty analysis for the superior models was carried out.

Firefly algorithm (FA) is an effective optimization technique based on swarm intelligence, which has been successfully applied to various practical engineering problems. In this paper a new dynamic firefly algorithm is applied for demand estimation of water of river Hirmand in Sistan area and comparative with different firefly algorithm for 2006-2017 years. The data from 2006 to 2014 are used for learning and teaching and finding the optimal weights of the model, and the rest of data (2015-2017) are applied to test the models. The results show that all five FA variants can achieve promising solutions. But NDFA obtains better performance than four other FA variants and its prediction accuracy is up to 97.98%. After ensuring the accuracy of the algorithm, water demand of river Hirmand from 2018-2020 is predicted. And risk assessment of the water shortage under three scenarios of high, average, and low inflow levels for this years.

Rainfall is the main motivator in the hydrologic cycle of the basin and it is an element of meteorological phenomena undergoing severe changes in time and place. The suitability of density and distribution of rain gauges in the rain gauge networks of each area is an effective step in the success of the water plans, regional projecting and effective use of the information (Karamouz et al., 2010). Many researchers have shown that the geostatistical prediction method provides better estimates of the regional rainfall than the traditional methods. Tanaka and Putthividhya (2013) used the geostatistical method to assess the quality of the rainfall estimation in the Basin of Chao Phraya. They tried to calculate the difference between the rainfall data and the results obtained from the above methods by plotting Thiessen Network and the co-ordinate lines by nverse Distance Weighting and Ordinary Kriging methods. They also examined the correlation between the height, humidity and temperature with the recorded rainfall values. The findings showed that height had a significant correlation with Monsoon rainfall, while humidity and temperature correlated with the monthly rainfalls. Yang and He (2013), using the super innovative firefly algorithm concluded that this algorithm is more  suitable than the optimal search strategy. Considering the problems of Urmia Lake located in the northwest of Iran, comprehensive studies with an inclusive approach to the problems in this basin are considered necessary. Indeed, it is necessary to concentrate more on the process used in the design of the rain gauge networks and begin to redesign the existing networks in order to refine and complete them.

The use of clay blanket in reservoirs is one of the main methods of seepage reducing. In this study, with clay blanket modeling in a proposed reservoir by finite element method, 350 dataset was obtained using SEEP/W. Validation of SEEP/W was carried out by comparing seepage results obtained from a laboratory tests. For evaluation of suitable model for predicting seepage values (results of modeling), used from five artificial intelligence techniques comprising: multilayer perceptron neural network (MLP), radial base function (RBF), gene expression programming (GEP), support vector regression (SVR) and a novel hybrid model of the firefly algorithm (FFA) with the multilayer perceptron (MLP-FFA). All the techniques were trained with 70% of available dataset and tested using the remaining 30% dataset. Different combinations of input data that include the ratio of the permeability coefficient of foundation to the permeability coefficient of clay blanket (K_f/K_b ), the ratio of the length of blanket to upstream head (L_1/H), the ratio of thickness of foundation to thickness of blanket (h_f/t), the ratio of length of blanket to thickness of core (L_1/L_2 ) and the ratio of horizontal to vertical permeability coefficient of foundation (K_(f_x )/K_(f_y ) ) were used for evaluation of mentioned methods. The results were evaluated using four performance criteria metrics: root mean square error (RMSE), mean absolute error (MAE), Nash-Sutcliffe efficiency (NS), Willmott’s Index of agreement (WI) and Taylor diagram. The results of study showed that the MLP-FFA method provides better estimation results than the other models and therefore, could be applied an optimized for predictive model of earth fill dam seepage.

The high cost problem of urban water supply systems, along with the complexity of the design and unsuitable operation problems cause that optimization of the system before applying any changes, has become the basic needs of managers in this area. Due to the complexity of nonlinear and unique design of these networks, in recent years engineers using artificial intelligence and search algorithms to solve this problem. In the present study find solutions for the network in a town of Kerman with help of fast messy Genetic and firefly Algorithms and network simulation software intended WaterGEMS. First the water supply network in the study area simulated in WaterGEMS model and the properties required for optimization algorithms have been extract, then using the standard pressure and speed constraints, these algorithms create optimal choices. By entering these results in WaterGEMS model and re-running for limits check, the cost estimates are discussed and compared. The results show that the optimization of, fast messy Genetic algorithm with 37.7% is able to reduce the cost function of network compare to pre-optimized network. Also Firefly algorithm in the amount of 34.4%, is able to reduce costs. Finally, we can say that both optimization algorithms used in this study have been able to achieve a dramatic reduction in project costs.

As a crucial issue in aqua sciences, optimizing dam reservoirs exploitation has been studied with a variety of optimization techniques. One of these methods is using Meta-Heuristic algorithms such as Firefly and Ants Algorithms. Using the firefly algorithm, this study studies the exploitation optimization of Doroudzan reservoir in a 99-month period. The most sensitive parameter in sensitivity analysis of Firefly Algorithm, α, is known as the mutation rate. Selecting its appropriate value by Firefly worms leads to an appropriate solution and increases the efficiency of the Firefly Algorithm dramatically. To determine the efficiency of this algorithm in optimizing the utilization of the dam reservoir, the obtained results were compared with the results of Continuous Ant System and Ranking Ant System. The findings indicated that FACC algorithm with objective function rate of 4.196 had a satisfactory performance. ACOrCC and ACOrankCC algorithms with the values of 17.004 and 26.156 followed it respectively. In addition, FACC algorithm with a value of 0.959 had the highest reliability coefficient. The results indicated that regarding Chain constraints, all program performances led to feasible solutions; however, ignoring chain constraints, the Continuous Ant System algorithm was unable to find a feasible solution. Hence, applying these constraints in the main structure of this algorithm would enhance its efficiency significantly.

The largest amount of water in Iran is used in agricultural sector. Thus، efficient use of water in this sector will be significantly effective in maintaining water resources and optimum use of available water. In many regions، surface reservoirs are responsible for providing water to downstream agriculture. Optimal operation of reservoir is one of the major parts of surface water resource optimization. So far، several optimization approaches have been used، among them، the most popular methods are Evolutionary Algorithms. In this study، Firefly Algorithm (FA)، as a new method، was proposed for optimal operating of Bazoft reservoir. The operation modeling was carried out for a period of 120 months related to 1986 to 1995 years. The considered objective function was defined as minimizing the sum of squared differences between the demands and the release from the reservoir divided by maximum demand during operation. The model performance was examined compared to Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). These two mentioned algorithms are known as common and standard methods. The results indicated that firefly algorithm can better perform than other methods. The mean value of the objective function of this method was 0. 408، and the mean of the objective function for the GA and PSO were 0. 618 and 0. 913، respectively. In addition، FA has created less deficiency values and milder deficiency compares to GA and PSO.