key: cord-0732275-izqa1d0t authors: Dalcali, Adem; Özbay, Harun; Duman, Serhat title: Prediction of electricity energy consumption including COVID‐19 precautions using the hybrid MLR‐FFANN optimized with the stochastic fractal search with fitness distance balance algorithm date: 2022-03-22 journal: Concurr Comput DOI: 10.1002/cpe.6947 sha: 883c8bc471805d4b16293024c7ef6d8fe2225658 doc_id: 732275 cord_uid: izqa1d0t The increase in energy consumption is affected by the developments in technology as well as the global population growth. Increasing energy consumption makes it difficult to ensure electrical energy supply security. Meeting the energy demand can be achieved with the right planning. Proper planning is critical for both economical use of resources and low cost for the end consumer. On the other hand, erroneous estimation of demand may cause waste of resources and energy crisis. Accurate estimation is possible by accurately modeling the factors affecting electricity consumption. Apart from known factors such as seasonal conditions, days of the week and hours, modeling in extreme events such as pandemics that affect all our behaviors increases the success in modeling the future projection. This ensures that the security of electrical energy supply is carried out effectively with limited resources. For this purpose, in this study, a hybrid multiple linear regression‐feedforward artificial neural network (MLR‐FFANN) based algorithm model was proposed, taking into account the estimated impact of the COVID‐19 pandemic on the energy consumption values of Bursa, an industrial city in Turkey. The aim of the hybrid MLR‐FFANN approach was to simultaneously optimize the β polynomial for multiple linear regression and the weight and bias coefficients for the forward propagation neural network using the adaptive guided differential evolution, equilibrium optimizer, slime mold algorithm, and stochastic fractal search with fitness distance balance (SFSFDB) optimization algorithms. The success of the model whose parameters were optimized using the optimization algorithms was determined according to mean absolute error, mean absolute percentage error, and root mean square error evaluation criteria and statistical analysis of these results. According to the results of the analysis, the MLR‐FFANN approach whose parameters were optimized with the SFSFDB algorithm was more successful in the training of the dataset containing the COVID‐19 precautions. Today, meeting electrical energy demands is a very difficult problem considering the increasing population, industrialization, depletion of fossil resources, and increasing environmental concerns. In addition to fossil fuels, there is a need to meet increasing energy demands with low-cost and environmentally friendly renewable resources. However, as renewable energy sources are dependent on nature and exhibit seasonal characteristics, such energy production requires planning. Therefore, today, diversifying energy and ensuring supply security play a critical role for countries. Successful planning of resources means efficient use of energy and preventing waste of resources. By using estimation methods, short-, medium-, and long-term electricity consumption amounts can be determined and necessary measures can be taken to ensure a secure energy supply. The consumption of electric energy is affected by human activities and seasonal factors such as air temperature and humidity. However, the presence of unexpected circumstances also affects the success of the plans. The COVID-19 pandemic has affected the activities of the global community and as a result, has been reflected in the impact on the electricity consumption sector. The demand for electric energy is affected by human activities and mobility. Therefore, the restrictions brought about by countries during pandemic periods will affect their electricity consumption. 1,2 The rest of the study article is organized as follows: • The progress of the pandemic in Turkey and its effect on energy consumption is discussed in Section 2. • In Section 3, MLR-FFANN, SFS, and SFSFDB algorithms are explained. • Section 4 provides detailed information on the application of the SFSFDB optimization algorithm to the hybrid MLR-FFANN model. • Section 5 focuses on the analysis of the experimental results under different operational scenarios. • Finally, Section 6 provides the conclusions drawn from this study and ideas for future works. In this section, Turkey's energy outlook and Bursa's electric energy production and consumption are detailed. The course of the pandemic in Turkey and the measures taken by the government against the pandemic are examined. According to the 2020 data, the population of Bursa is 3,101,832, making it the fourth largest city in Turkey in terms of population. For a clearer understanding of Bursa's position in Turkey, data on industry and electricity consumption are given in Table 1 . 34 The total electricity consumption value per person in Bursa is above the national average. Similarly, industrial electricity consumption per person for Bursa is high in all of the years mentioned. The number of enterprises, as an important parameter of the industry indicator, realized in Bursa corresponds to approximately 3.88% of the number of enterprises realized in Turkey. In addition, an average of 6.29% of the exports produced in Turkey for the specified years originated from Bursa. Considering all these indicators, Bursa is seen as an important industrial city. Turkey has a growing population and strong economic growth. This is also reflected in the energy requirements. In the last 10 years, the Turkish economy has grown around 5% on average. This growth also increases energy consumption and makes it difficult to ensure energy supply security. Consequently, in order to ensure energy supply security, installed power has been continuously increasing, especially after Between 2000 and 2009, oil prices increased by 76% and natural gas prices by 114%. According to the projections made for the years 2015-2040, an increase of 186.3% in oil prices and 85.7% in natural gas prices is expected. 36 Considering the price instability in fossil fuels and the depletion of resources, renewable energy sources come to the fore as an alternative. Figure 1 shows that 50.05% of Turkey's installed power consists of renewable resources. Among renewable resources, hydraulic resources take the first place, with 31,177.9 MW. With the licensed power plant investments that were temporarily accepted in 2020, the amount of additional installed power is 5430.31 MW. Only 60.80 MW of this additional power amount is from fossil fuel. 37 The investments made can be evaluated as an indicator of the importance given to renewable energy in Turkey. In addition, with these investments, the energy supply will not be secured with imported resources, but with clean and renewable resources without fuel costs. According to the market development report published by the Energy Market Regulatory Authority, the total licensed electricity genera- Considering the consumption amounts for Bursa, the highest was realized in the industrial section, followed by the commercial establishments. Considering its share in total consumption and the amounts by type of consumer, Bursa is seen as a robust industrial city. The measures taken caused difficulties for people and countries both socially and economically. There were significant changes in the work, education, shopping, and entertainment habits during the pandemic period. Societies were forced to carry out many activities remotely or in accordance with social distancing rules. It was important to provide uninterrupted health services during these critical measures. In order for all these services to be carried out safely, electric energy had to be provided without any problems. Gradual restrictions were introduced in Turkey with the occurrence of cases in March 2020. Due to these restrictions, periodic closures or capacity reductions were experienced in the manufacturing sector. These restrictions and slowdowns in activities were also reflected in the electricity consumption. 40 Figure 2 presents the change in consumption for the years 2019 and 2020. 37 Especially in April and May, a significant decrease was observed in consumption amounts, followed by a recovery. In August, as a continuation of this recovery, 2020 consumption increased compared to the same time period of the previous year, and this trend continued until the end of the year. F I G U R E 2 Electricity consumption amounts COVID-19 has caused a decrease in electricity demand in many countries and an increase in the share of renewable energy sources in electricity production. In a study carried out in Germany, energy production from renewable sources increased by 8% in the first quarter of 2020, taking the same period of 2019 as a reference. 41 Similarly, in a study conducted in Italy, the effect of COVID-19 on electricity consumption was examined by taking into account its environmental dimensions. It was determined that the significantly reduced electricity consumption was supported by wind-based generation, resulting in a 30% decrease in wholesale energy prices. This has also had a positive impact on reducing carbon dioxide emissions. In addition, the researchers observed that the decrease in consumption affected the amount of energy supplied from traditional (thermal) sources. 42 In order to reduce and control the impact of the pandemic, governments have applied different restrictions. These policies can cause disadvantageous situations in many sectors. The detection of these situations is important, especially in the later stages of the pandemic or similar pandemics that may occur later, in terms of precautions to be taken. The first case in Turkey was seen on March 11, 2020, after which, various measures were taken to control the pandemic. The steps taken during the pandemic process are summarized in Table 3 . Regression analysis is a statistical technique used to investigate and model the relationship between variables in order to obtain an approximate function between the relevant response (output) and independent variables (inputs). 43 If there is more than one independent variable in the regression analysis, it is called MLR. In most MLR problems, it is not known how the independent variables relate to the dependent variables. Therefore, the first step and the main problem are to find an approximation method to relate them. 44 Generally, first-order and second-order polynomial models are used, as given in Equations (1) and (2). where denotes the polynomial coefficients and x the independent variables, y is defined as the dependent variable, and identifies other forms of variation, such as errors or lack of numerical convergence. The k index represents the total number of variables. The i and j indices represent a certain variable between 1 and k. If Equations (1) and (2) are written in a matrix form, Equation (3) is obtained. TA B L E 3 Milestones of COVID-19 and the steps taken in Turkey Date February 3, 2020 Turkey suspends all flights from China. March 11, 2020 The first coronavirus case was announced in Turkey. March 14, 2020 Passenger transportation banned with 16 countries, 9 of which were European countries. March 18, 2020 The first death due to coronavirus occurred. March 20, 2020 With the Presidential circular, all scientific, cultural, artistic, and similar meetings and activities were stopped until the end of April. March 21, 2020 Curfew restrictions were imposed on citizens aged 65 and over. March 22, 2020 With the Presidential circular, flexible and remote working was allowed in public institutions and organizations. March 23, 2020 Formal education was interrupted and distance education programs were started. International flights were completely suspended. Intercity transportation was subject to the permission of the Governorship. Entrance to places such as picnic areas, forests, and historical sites was prohibited at the weekend. April 3, 2020 30 metropolitan areas and 1 province were closed to entry and exit of vehicles with some exceptions. Curfews were imposed on those under 20 years old throughout the whole country. The curfew for 65 years and older has been lifted between 12:00 and 18:00. The curfew for children aged 0-14 has been lifted between 11:00 and 15:00. The curfew for young people between the ages of 15 and 20 has been lifted between 11:00 and 15:00. May 23-26, 2020 A curfew was imposed during the Ramadan Holiday (4 days). The curfew for 65 years and older has been lifted between 12:00 and 18:00. June 1, 2020 The intercity travel restriction has been lifted. Flexible and remote working in the public sector has come to an end. The curfew imposed on people over the age of 65 has been lifted. June 20, 2020 A curfew was imposed during the university entrance exam (first step). June 27-28, 2020 A curfew was imposed during the university entrance exam (second step). Flexible and remote working in public institutions and organizations was allowed. November 17, 2020 A curfew will be imposed on weekends outside of 10.00-20.00. Restaurants will only provide takeaway service, shopping malls and markets will be closed at 20 The South African and Brazilian variants were also seen in Turkey. As of March 2, 2021, pre-school education institutions, primary school, secondary school 8th and 12th grades will start education in all cities and will start at other levels, including secondary and high schools, in low and medium risk provinces. The scope of the curfews has been changed according to the provinces with the new Controlled Normalization Process announced on March 1, 2021. The provinces have been divided into four different risk groups (low, medium, high, and very high) and the level of precaution has been determined according to the risk group. March 2, 2021 BURSA: In the medium risk group. According to this: • A curfew will be applied between 21.00 and 05.00 on weekdays. • A curfew will be applied between 21.00 and 05.00 on weekends. • For our citizens aged 65 and over and under the age of 20, the curfew will be lifted outside the hours stated above. • The food and beverage sector, which will operate between 07:00 and 19:00, will serve with a 50% capacity limitation. The related matrices and vectors can be elaborated as in Equation (4). To estimate the coefficients of MLR models, the least squares method given for the vector sample in Equation (5) ANNs are a distributed computing technology, inspired by the information processing technique of the human brain that can record the experimental information of systems. The ANN topology is divided into two types: feedforward (FF) and back propagation neural networks (BPNN). 46 The FFANN is used more widely because it requires less memory in the implementation phase. The FFANN allows a one-way signal flow. In addition, feedforward neural networks are organized in multiple layers: the input layer, the hidden layer, and an output layer. The neurons of each layer are interconnected by the weights and bias terms of the other neurons in the previous layers. 47 This system is represented by the mathematical expression given in Equation (6) . where n is the number of input nodes and ij is the connection weight of the jth node in the hidden layer from the ith node in the input layer; denotes the jth hidden node bias and x i denotes the ith input. Accordingly, Equation (7) is used to calculate the output of each hidden node. The final outputs are defined as given in Equations (8) and (9). where jk is the connection weight from the jth hidden node to the kth output node and k represents the bias value of the kth output node. As can be understood from the equations, the most important parts of these structures are the weight and bias values because they determine the final value of the output. In order to find these values at the optimum value, the training of the neural network is very important. 48 The aim is to obtain the minimum error value at the end of both the training process and the testing process of the neural network. Based on calculating the difference between the actual and predicted values, the mean square error (MSE) is used to evaluate the forward propagation neural network. This mathematical expression is given in Equation (10). where e i represents the error value of the ith data, x i and o i are defined as the actual and estimated value of the ith data, respectively, and n is the total number of data. The FFANN model with the structure of 4-5-1 is illustrated in Figure 3 . The stochastic fractal search (SFS) algorithm was developed because there was no information exchange between fractals and the many parameters that needed to be determined according to the problem to be optimized by the fractal search algorithm. 49 The SFS algorithm is constituted of two basic processes: the propagation and update processes. The update process also consists of two parts: the first and second update processes. The propagation process performs the local search feature in the algorithm, and the update processes perform the global search functions. 50 The two functions given in Equations (11) and (12) are proposed for the propagation process of fractals. In Equation (12), BP represents the position of the fractal that gives the best fitness value found up to that generation, BP is the fractal that gives the best fitness value, and P i denotes the propagating fractal; the expression defines randomly generated numbers in the range of [0, 1]. In addition, P in Equation (12) represents the position of the spreading fractal. The value is the standard deviation value that expresses the step length of the Gaussian walking function. The standard deviation expression is calculated as given in Equation (13) . Equation (13) shows that the difference between the fractal with the best fitness value and the spreading fractal is obtained by multiplying the expression log(g)/g. The g in the log(g)/g expression added to Equation (13) represents the generation value and creates a damping effect in the standard deviation function, that is, the value of the standard deviation decreases as the number of generations progresses. Although this causes a more local search, it increases the probability of finding a solution with an even better fitness value in the immediate vicinity of the found solution point. After the propagation process is performed, the first and second update processes are run. For these operations, first of all, a probabilistic value is given to each fractal by taking into account the order of the fitness values, using the expression given in Equation (14). where N is the number of fractals in the generation and the expression rank(P i ) expresses the rank of the fractal in the generation according to its fitness value. The first update process starts after the probabilistic value is calculated. Depending on whether the randomly generated expression is smaller or larger than the probabilistic value, the relevant dimension of the relevant fractal is updated. This process is as given in Equation (15) . The r and t subindices given in Equation (15) represent randomly selected fractals from within the generation. After the first update process, Equation (14) is reordered and the fractals are assigned probabilistic values. For fractals entering the second update process, the position of the fractal is changed according to whether a randomly generated number between 0 and 1 is smaller or larger than 0.5. The second update process is performed with the expression given in Equation (16). The algorithm continues to generate a new generation and generate new solution points until it meets the termination criterion. The purpose of the fitness distance balance (FDB) method is to effectively guide meta-heuristic search (MHS) algorithms in the search process. 50 The feature that distinguishes the FDB method from other selection methods is the calculation of the score values of the solution candidates and the selection process according to the score values. In the calculation of the score, the fitness values of the solution candidates and their distance from the best solution candidate in the population are taken into account. This ensures that the solution candidate with a high fitness value is selected. On the other hand, this prevents the selection of a solution candidate that is very close to the best solution in the population. This selection strategy of the FDB method contributes to the solution of the early convergence problem frequently encountered in the MHS process. [51] [52] [53] The steps to implement the FDB method are as follows: i. The score values of the solution candidates in the P population should be calculated. If Xbest is assumed to be the best solution in population P, the scores of the solution candidates in population P are expressed by the vector S given in Equation (17). ii. While calculating the score of each solution candidate, the values of fitness and distance are taken into account. In population P, the distance between the ith solution candidate and Xbest (the best solution in P) is calculated using the Euclidean metric as given in Equation (18) . iii. The distance vector D of the solution candidates in the population P can be represented as given in Equation (19) . iv. Another parameter used in calculating the scores of the solution candidates is the fitness value. The fitness values of the solution candidates in the population P are represented by the vector p. The p and D vectors are normalized so that the two parameters do not dominate each other in the score calculation. The score calculation of the ith solution candidate is given in Equation (20). The parameter given in Equation (20) is used to weight the effects of p and D parameters. The parameter can have an infinite number of values in the range [0, 1]. A larger value of the parameter increases the effect of the fitness value on the score. In this case, the effect of the distance value on the score decreases. When = 1, the score value of the solution candidate depends only on the fitness value. When = 0, the solution candidate's score depends only on the distance value. This ensures that the solution candidate farthest from P best is selected in the population. Therefore, the variation in the population increases as the parameter is close to zero. This provides discovery capability for MHS algorithms. This parameter gives the FDB the ability to adapt. The parameter has the important function of switching and balancing between operating and reconnaissance tasks. A step-by-step explanation can be given for improving the search performance of MHS algorithms using the FDB method. Before applying the FDB method to an MHS algorithm, the search process lifecycle of the MHS algorithm should be analyzed and the process in which the algorithm provides diversity should be determined. Therefore, the SFS algorithm needs to be rearranged based on the general steps of the MHS process. 54 The purpose of rearranging the algorithm is to reveal the exploration and exploration processes, and the step in which the FDB method is applied. After the exploration process, the diffusion process is carried out, and the tasks of searching for a neighborhood and providing diversity in the update process are fulfilled. In the next step, reference positions that guide the search process lifecycle in the SFS algorithm are examined. Thus, reference positions and the methods used to select them are determined. In this process, three reference positions are selected, one using the turn-based method and the other two randomly. According to the information obtained here, the FDB selection method was applied. Thus, the process of ensuring diversity in the population was realized. Equations (17)- (20) are taken into account in the FDB selection method. The SFSFDB flowchart is given in Figure 4 . In the training of ANNs, a large number of uncertainties occur with the relationship between different datasets and the combination of many solutions. This uncertainty and different relationship status make their training process difficult. Moreover, ANNs have a nonlinear structure, which affects the behavior of the network in the learning process. Therefore, the importance is increasing of determining the most appropriate values of the weight and bias coefficients used in the training of the network and the activation functions used in the neurons. Considering this situation, the weight and bias coefficients of FFANN and the polynomial coefficients of MLR in the proposed MLR-FFANN model were determined simultaneously by optimization algorithms. In this study, the application of the SFSFDB algorithm described in Section 3.3 to the training of the proposed MLR-FFANN model is explained step by step as follows. Step 1: In this step, the prepared dataset is read from the relevant file and the values of the dataset are normalized between 0 and 1 using Equation (21) . The maximum number of iterations of the SFSFDB algorithm, the size of the population and the number of dimensions are entered into the system by the user. In addition to this step, the initial population is created within the minimum and maximum values determined for the parameters (weight, bias, and polynomial coefficients) of the proposed MLR-FFANN model to be optimized. Step 2: The fitness function values of the initial population are calculated and the position value with the best fitness value is determined. Step 3: The algorithm checks whether the current iteration number has reached the determined maximum number of iterations. If not, the natural process of the algorithm continues. If reached, the best value and best position values of the fitness function are displayed. Step 4: Depending on the structure of the algorithm, the maximum diffusion number is determined. Depending on the maximum diffusion number, the steps of the diffusion process in Figure 4 are applied. Step 5: According to Step 4, after the condition in the diffusion process is met and the necessary operations are performed, the algorithm performs the first updating process step in the flow diagram. The algorithm checks whether each ordered P i value is less than the randomly generated number. Depending on this condition, the necessary processing is carried out. Step 6: When the condition step in Step 5 is completed, the second updating process is started. In this step, all solution candidates in the population are ranked. Depending on the specified condition, either the selection method of the SFS algorithm is applied or the FDB selection method is applied, depending on Equations (17)- (20) . After the selection steps are performed depending on the specified conditions, the position of the P i solution candidate in the population is updated. Step 7: The current iteration number of the algorithm is increased and the algorithm goes to Step 3 and checks whether the condition there is met. In this study, a multiple linear regression and feedforward neural network-based hybrid algorithm was proposed to predict the electric energy consumption of the city of Bursa during the COVID-19 pandemic, and the design of this algorithm was carried out using AGDE, EO, SMA, and SFSFDB optimization algorithms. Although the optimization algorithms used minimized the mean squared error, they aimed to find the most appropriate weight and bias coefficients of the FFANN model and the polynomial coefficients of the multiple linear regression algorithm. Furthermore, the success of the following design structures in training of the FFANN model was examined in the optimization process. The case studies of the FFANN structural designs were carried out as follows. • Case 1: Using the hyperbolic tangent function in the hidden and output layers for the FFANN model. Table 5 . Depending on these results, all working cases and the ranking of the network structures are shown in Table 6 in order to identify which working condition among the network structures used in the different working cases was more successful in the FFANN training process of the AGDE algorithm. The comparative analysis and ranking of FFANN structures in simulation cases for all optimization algorithms are given in Table 13 . These rankings are shown depending on the sum of the ranking results, mean values of these results, and standard deviation values given in Tables 6 and 10-12. According to these ranking results, the FFANN structure that completed the training and testing process the most successfully was determined among the simulation cases for each optimization algorithm. The identified FFANN structures are denoted in Table 13 in different colors for each optimization algorithm. In (Table 14) are shown in detail in the bar graphs in Figure 7 . The results of the evaluation criteria of the best cases in each optimization algorithm (Figure 7 and Table 14 ) are shown in bar graph form in Figure 8 for both training and test data so that the results can be better interpreted. After determining the best cases used in the training process of FFANN for each optimization algorithm (Table 14) , the results of the evaluation criteria of the best FFANN structures in the cases, the ranking of these results for both training and test data, and the sum of these ranking results, mean value, and standard deviation values are shown in Table 15 . In other words, the final ranking in Table 15 clearly shows that the EO algorithm was the first in the training of the dataset, followed by the SFSFDB and SMA algorithms. The FFANN structures determined for all optimization algorithms were adapted to the proposed hybrid MLR-FFANN algorithm. By using MLR-FFANN algorithms, where the most appropriate weight, bias, and polynomial coefficients were determined by the optimization algorithms, the electric energy consumption of the Bursa Metropolitan Province was predicted during the COVID-19 pandemic period until September 2020. As a result of the prediction process, the evaluation criteria, the ranking of these criteria, and the final ranking of the algorithms are shown in Table 16 . According to the final ranking of the algorithms, the MLR-FFANN method trained with the SFSFDB algorithm was more successful than other algorithms in estimating the electric energy consumption values of Bursa during the COVID-19 pandemic. When Tables 15 and 16 were evaluated together for the final rankings of the optimization algorithms, the MLR-FFANN, whose training process was completed with the SFSFDB algorithm, was more successful than the MLR-FFANN trained with the other (EO, SMA, and AGDE) algorithms. Figure 9B shows the difference between the actual and estimated electric energy consumption values. Actual and predicted electricity energy consumption data are detailed in Figure 9C . Outlier detection is critical in the development of appropriate models for recognizing individual data that may differ from the data chunk contained in a dataset. 55 In the literature, the methods consisting of both numerical and graphical algorithms have been proposed for this purpose. 56 where X is a (n × k) matrix consisting of n data (rows) and k parameters ( In this study, the statistical hat matrix, Williams plot, and leverage approach, which enables outliers to be recognized in the model results, were used to check the reliability of the proposed model. 56 followed step by step according to the procedure mentioned above. Thus, the Williams plot for the results from the SFSFDB model is plotted in Figure 10 . The cyan color line in Figure 10 is the critical H* value or the leverage constraint which is computed as 0.1317 in this study. Moreover, the red line of R = ±3 is defined as the suspected limits. It can be seen that the majority of data points lie in the range 0 ≤ H ≤ H* and −3 ≤ R ≤ 3. As a result, the points corresponding to 96.3068% of the total number of data in the data set fall into the domain, while the remaining 3.6932% can be expressed as points outside the domain. These results show that the applied model is statistically acceptable and valid. The cumulative frequency graph can be consulted for further comparison of the accuracy of the proposed models. [55] [56] [57] [58] [59] [61] [62] [63] [64] [65] [66] This statistical methodology gives an idea of the average absolute percent relative error or absolute percent relative error models below a certain value. Equation (26) is explained as a relative percent error: where E i is identified as the relative deviation of a represented/predicted value from an experimental value. x i and o i are defined as the actual and estimated/predicted value of the ith data, respectively, and n is the total number of data. The mean absolute percentage relative errors given in Equation (27) are used to calculate the absolute deviation of the experimental data. In this study, the cumulative frequency curve given in Figure 11 , in which absolute percent relative error values are plotted against the cumulative frequency values, provides further comparisons regarding the accuracy of the proposed models. As can be seen from Figure 11 , The robust predictions can be made as a result of the proposed algorithm being a sufficiently successful model. Therefore, it is necessary to determine whether it is a sufficiently successful model. The important thing here is that accuracy should not be evaluated alone when determining the adequacy of the model. Considering this situation, the degree of effectiveness of the independent variables affecting the model should be investigated by performing a sensitivity analysis. The cosine amplitude method (CAM), which is defined as one of the best sensitivity analyzes in the literature, was used in this study. 67 The variable (R ij ), which affects the electrical energy consumption the most, is used to measure the degree of sensitivity among the independent variables. The higher the R ij , the more the independent variables affect the electrical energy consumption. If the relationship between the independent variables and electrical energy consumption is positive, the R ij value is positive, and if the relationship between them is negative, the R ij value is also negative. X array with n arguments is X = {x 1 , x 2 , x 3 , … , x n }, each element of this array as "x i " and if there are "m" of each argument, the elements of the data set are X i = {x i1 , x i2 , x i3 , … ,x im }. If the relationship between the dependent and independent variables in the data set is called x i and x j , the R ij value is calculated as in Equation (28) 68 ; Evaluation criteria for all optimization algorithms Figure 12 shows the results of the sensitivity analysis according to the CAM performed within the scope of this study. er(t − 1) is defined as the error value between the previous prediction and the true value, and er(t − 2) represents the error value between the two previous prediction and the true value. As can be seen from the results of the analysis, the factor that affects the electrical energy consumption estimation the most is the average humidity value with 0.9271. Average wind speed value follows the average humidity value with 0.9206. Average pressure with 0.8555 and average temperature with 0.8326, which are very close to these values, are seen as the most the other influencing factors. It is seen that the previous error value, er(t − 1) and the two previous error values, er(t − 2), also highly affect the estimation process. It is seen that the days of the week and COVID-19 precautions have a less effect than the others. In this study, the recently proposed SFSFDB algorithm was used for the first time as Moreover, the activation functions in the hidden and output layers used in these network structures were discussed in different study cases as com- • The validity of the suggested method was demonstrated by outlier analysis, which shows that all data points are within an acceptable range. • Environmental factors had a more pronounced effect on the estimation of electrical energy consumption than days of the week, error values, and COVID-19 precautions, according to the results of the sensitivity analysis. • As a result, COVID-19 pandemic precautions were used as input data in the dataset for the estimation of electric energy consumption, and the hybrid MLR-FFANN approach, whose parameters were optimized with the SFSFDB algorithm, successfully carried out the training and learning processes. 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They are also grateful to the Bandirma Onyedi Eylul University Coordinatorship of Scientific Research Projects for the support provided under application number BANU-BAP-19-1003-004. The authors declare that they have no conflict of interest. The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions. https://orcid.org/0000-0002-1091-125X