An Improved Ant Colony Algorithm for Optimized Band Selection of Hyperspectral Remotely Sensed Imagery

The ant colony algorithm (ACA) has been widely used for reducing the dimensionality of hyperspectral remote sensing imagery. However, the ACA suffers from problems of slow convergence and of local optima (caused by loss of population diversity). This paper proposes an improved ant colony algorithm (IMACA) based band selection algorithm (IMACA-BS), to overcome the two shortcomings of the standard ACA. For the former problem, a pre-filter is applied to improve the heuristic desirability of the ant colony system; the Pearson’s similarity measurement of the degree of redundancy among the selected bands is taken as one of the terms in the heuristic function, and this further accelerates the convergence of the IMACA-BS. For the latter problem, a pseudo-random rule and an adaptive information update strategy are, respectively, introduced to increase the population diversity of the ant colony system. The effectiveness of the proposed algorithm was evaluated on three public datasets (Indian Pines, Pavia University and Botswana datasets), and compared with a series of benchmarks. Experimental results demonstrated that the IMACA-BS consistently achieved the highest overall classification accuracies and significantly outperformed other benchmarks over all of the three experiments. The proposed IMACA-BS is, therefore, recommended as an effective alternative for band selection of hyperspectral imagery.


I. INTRODUCTION
Hyperspectral image (HSI) containing hundreds of spectral bands provides abundant spectral information about on-ground objects. HSI has broad application prospects in a wide range of fields, among, inter alia, agriculture, forestry, environment and ecology. However, the massive bands of HSI pose a great challenge to data processing and analysis [1], The associate editor coordinating the review of this manuscript and approving it for publication was Weiping Ding . leading to the curse of dimensionality phenomena [2]. It is, therefore, essential to reduce data dimensions to facilitate the analysis of hyperspectral data. Feature extraction and feature selection are two kinds of typical data reduction techniques [3]. Feature extraction techniques (e.g., principal components analysis), are developed to compress data by using complex mathematical transformations. Though these methods may extract useful features from the HSI data sets, the interpretable primitive physical significance of the data is often lost in the data transformation process. VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/ In recent years, feature selection methods have received increasing attention in light of their reliable performance in preserving the primitive physical interpretability of the original data [4]. These methods aim to select a feature subset with low redundancy and high relevance to the specific task (e.g., classification) [5]. In general, feature selection methods can be categorized into three types: unsupervised, semisupervised, and supervised [6]. Unsupervised methods select feature subsets without the assistance of labeled classes. However, it is very hard for them to achieve promising results since they may neglect the possible correlation between different features. Semi-supervised methods utilize labeled and unlabeled samples to maximize the margin between data points of different classes, but they rely heavily on the number of labeled samples [7]. In contrast, supervised methods that select bands with powerful classification capacity under the supervision of class labels always achieve promising band selection results [8]. In this paper, we focus on supervised feature selection methods.
Generally, supervised feature selection consists of three types of searching strategies. These are exhaustive searches, sequential searches, and random searches [9]. Exhaustive searches (such as branch and bound [10]) enumerate all the possible combinations of features, which always leads to an unacceptable high time complexity [11]. Sequential searches, such as sequential forward selection (SFS), sequential backward selection (SBS), and sequential floating forward selection (SFFS) [12], are also computationally intensive as well as increasing the number of selected features. In comparison, random searches select features randomly and always deliver promising results with relatively high efficiency. Recently, nature-inspired random search algorithms have been widely used for feature selection from HSI data [13], [14], due to their powerful searching capacity in a high-dimensional space. These include genetic algorithms (GA) [15], clone selection algorithms (CSA) [16], particle swarm optimization (PSO) [17], and ant lion optimizer (ALO) [18].
The ant colony algorithm (ACA) is a typical heuristic search algorithm inspired by natural biological systems. It simulates the behaviors of real ants in the process of seeking food. Through the cooperation between individual ants, ACA has the capacity to solve complicated optimization problems, such as finding the optimal route to food [19]. The positive feedback mechanism of ACA may help an ant colony find the optimal solutions in a short time. ACA has been used in the field of image processing, pattern recognition, and feature selection [20]- [22]. These efforts have demonstrated the ACA as a potentially effective algorithm to solve complex optimization problems. Recently, ACA was also applied in feature selection from HSI data [20], [23]. Nonetheless, some studies illustrated that the standard ACA was incapable of solving the NP-hard feature selection problem due to its two intrinsic flaws [24]. First, the ACA is often slow to converge on optimal solutions owing to its random initialization strategy. Second, the population diversity of the ant colony may decrease significantly during the searching process because of the strong positive feedback via pheromone trails. These two issues easily trap the standard ACA on local optima in the process of feature selection.
In this paper, an improved ant colony algorithm (IMACA) based band selection algorithm (IMACA-BS) is proposed to select the optimal band subset from the HSI data sets. In order to accelerate the convergence of the ant colony system, a pre-filter is introduced to optimize pheromone initialization of the ant colony system. Pearson's similarity, measuring the degree of redundancy among the selected bands, is employed in the heuristic function. To maintain the population diversity of the ant colony, a pseudo-random rule and an adaptive information update strategy are both employed in the IMACA-BS. The effectiveness of the proposed IMACA-BS was tested on three types of public HSI datasets and compared with a series of benchmarks, including the ACA based band selection algorithm (ACA-BS), the genetic algorithm-based band selection algorithm (GA-BS), the particle swarm optimization-based band selection algorithm (PSO-BS), the hybridization of GA and PSO based band selection algorithms (GAPSO-BS), the sequential forward floating selection-based band selection algorithm (SFFS-BS), and the newly proposed ant lion optimizer-based band selection method (ALO-BS) [25].
The key innovations of the proposed method can be summarized as: 1) a novel pre-filter is designed and applied for the first time to accelerate the convergence of the standard ACA-BS, and 2) an adaptive information update strategy is introduced to avoid the ant colony being trapped on local optima. The paper is organized as follows. Section 2 introduces the proposed IMACA-BS in detail. Section 3 presents the HSI datasets. The experimental results are provided in Section 4, followed by a discussion in Section 5. The conclusions are drawn in Section 6.

A. CRITERION FUNCTION
The criterion function evaluating the contribution of each band to classification accuracy is critical to band selection algorithms. Due to the possible appearance of singular covariance, some statistical-based criterion functions (e.g., Bhattacharya distance, Jeffreys-Matusita distance, and Divergence) are not suitable for band selection. In practice, the overall classification accuracy (OA) is therefore employed as the criterion function in band selection algorithms [26], where the band subsets are selected to maximize the OA. In this research, the support vector machine (SVM) that always achieves accurate classification results with a limited number of training samples, was employed and served as the criterion function for band selection [27].  represents the selected band subset (m < n). The major steps of the ACA for band selection are illustrated in Figure 1. First, initialize the control parameters and pheromone of the ant colony system. Second, release a total of Ps (population size of the ant colony) ants and randomly allocate them to the graph nodes; each ant selects a band subset independently by exploring the nodes in sequence using a transition rule. Third, when selecting m nodes for each ant, calculate the OA of the band subsets and select or update the optimal one (with the best OA). Finally, update the pheromone concentration on the paths, and continue the iterations until the stopping criterion is met. Two major operations of the ACA-BS, the transition rule and the update of pheromone, are elaborated in detail hereafter.

1) TRANSITION RULE
In the ACA-BS, each ant selects the next node by means of a roulette wheel selection with the probability pb ij (Equation (1)), which is directly proportional to the pheromone concentration on the edge (b i , b j ) and the heuristic desirability η ij (t) of the next selected node.
where α denotes the rate of information accumulation during the movement of the ants, and β is the heuristic coefficient; tabu k represents the tabu list of nodes that have been visited by the ant k; τ ij (t) and η ij (t) denote the pheromone concentration and heuristic desirability on the edge (b i , b j ) at time t, respectively. The heuristic desirability can be calculated as: where O ij is the overall classification accuracy achieved by SVM with bands i and j.

2) UPDATE OF PHEROMONE
In this study, an ant-quantity system proposed by Dorigo et al. (1999) was adopted to simulate ants' secretion behavior in which the amount Q of pheromone secreted by each ant is a constant [28]. The pheromone concentration τ ij on the edge (b i , b j ) will change with the time as follows: where ρ is a volatility coefficient that controls the volatilization rate of the pheromone, and τ k ij is the newly dropped pheromone by the ant k on the the edge (b i , b j ) which can be calculated as: where O max denotes the maximum OA provided by the SVM with band i and one of the other n − 1 bands; Q is a constant.

C. IMPROVED ANT COLONY ALGORITHM-BASED BAND SELECTION ALGORITHM (IMACA-BS)
In the IMACA-BS, the pheromone on each path is initialized according to the heuristic desirability between each pair of nodes by means of a pre-filter. During the searching process, the information between the potential node and all the selected nodes is applied to guide a search ant to make a state transition with the pseudo-random rule. As well, an adaptive information strategy is introduced to avoid leaving pheromone only in certain (rather than all) optimal paths by the searching ants. before presenting the flowchart of the proposed IMACA-BS, we first elaborate below the pre-filter and the searching process of the ant colony.

1) PRE-FILTER
The pheromone on the edge (b i , b j ) is initialized according to the heuristic desirability O ij . The overall accuracies with band i and one of the other n − 1 bands are calculated, and the p (a user defined number) bands that produce the highest OAs with band i are selected and denoted as C ( Figure 2). Note that the value of p can be determined according to statistical result [29], and it is set as n/2 in this research. The pheromone on the edges between node (band)i and other n − 1(j) bands can be calculated as follows: where O ij is the OA of SVM with band i and band j, O max and O min represent the maximum and minimum OA provided by SVM with band i and one of the other n − 1 bands. VOLUME 8, 2020

2) SEARCH PROCESS OF ANT COLONY
When the search ant k arrives at band i, it will make a state transition according to a pseudo-random rule as follows: where q is a random number uniformly distributed in [0, 1], and q 0 = 1 − e −1 / t (t = 1, 2, . . . , T , T denotes the number of maximum iterations); p k ij (t) denotes the probability for the k-th ant to select the node j, which can be calculated as follows: To minimize the redundancy of the selected band subset so as to improve the global search capacity of the proposed algorithm, the η ij (t) adopted in the proposed IMACA-BS is determined according to Pearson's correlation as follows: where V k is the band subset visited by the ant k; r(s, j) is the Pearson's correlation between the s-th and j-th bands calculated as: where R b s and R b j denote the reflectance value of bands s and j, respectively;R b s andR b j are the mean value of bands s and j, respectively; n p is the total number of pixels of the hyperspectral imagery. After all ants (with a number of Ps in total) have selected m bands, update the pheromone on edges as follows: where τ k ij denotes the pheromone increment on the edges from the ant k for population diversity maintenance, which can be dynamically calculated as follows:

3) STEPS OF THE IMACA-BS
The flowchart of the proposed IMACA-BS algorithm is demonstrated in Figure 3, with the major steps being detailed as follows: Step 1: Initialize the control parameters of the IMACA-BS, including Q, ρ, α, β, m, Ps, and the number of maximum iterations T .
Step 2: For each band i, a pre-filter is employed to initialize the pheromone according to Eq. (5), and set the evolution generation t as 0.
Step 3: Place Ps search ants on the nodes and let each ant randomly select an initial position which is subsequently added into the corresponding tabu list.
Step 4: Transfer the state of the ant k (k = 1, . . . , Ps) from node i to j with the transition probability, until that the number of elements contained in a solution reaches m.
Step 5: Calculate the OA with the band subsets and memorize the current optimal band subset.
Step 6: Update the pheromone on the paths using the adaptive pheromone update strategy defined by Eq. (10). Continue the iterations by repeating step 3-6 until t is equal to T .
Step 7: Output the band subset with the best OA.

III. DATA SOURCE
In our experiment, three public hyperspectral datasets were employed to test the performance of the proposed algorithm (IMACA-BS), including the indian pines, pavia university, and botswana datasets. Indian Pines Dataset (INDIAN DATASET): The indian dataset is gathered by airborne visible/infrared imaging spectrometer (AVIRIS) sensor. It has a spatial extent of 145 × 145 pixels with a spatial resolution of 20 m. the dataset consists of 224 original bands over a spectrum range of 0.4-2.5µm. a total of 200 bands were reserved after discarding the bands that were adversely influenced by moisture absorption. there were 16 land use/cover types in the ground truth (Table 1). the number of training, validation and testing samples for each of the 16 classes collected from the ground truth map are shown in Table 1.
Pavia University Dataset (Pavia Dataset): The original pavia dataset, acquired by the reflective optics system imaging spectrometer (ROSIS) sensor, consists of 115 bands in the spectral region of 0.43-0.86 µm. the dataset has a spatial resolution of 1.3 m with a spatial extent of 610 × 340 pixels. the bands influenced by water absorption were removed, and there were 103 bands remaining in the dataset. in total nine land use/cover types were identified (Table 2). the number of training, validation and testing samples of each class are shown in Table 2.
Botswana Dataset: The original botswana dataset, collected by the hyperion sensor on EO-1 at a 30m pixel resolution, contains 242 bands covering a spectral range of 0.4-2.5 µm. after the elimination of the uncalibrated and noisy bands that were seriously influenced by water absorption, 145 bands were remained. The ground truth of the dataset contained 14 identified classes (Table 3). the number of training, validation and testing samples are shown in Table 3.

IV. EXPERIMENTAL RESULTS AND ANALYSIS A. EXPERIMENT SETUP
In this experiment, the effectiveness of the proposed algorithm (IMACA-BS) and benchmark comparators including ACA-BS, GA-BS, PSO-BS, GAPSO-BS, ALO-BS, and SFFS-BS, were investigated on the indian pines, pavia university, and botswana datasets. With the training and validation samples, the SVM classifier was used for the evaluation of the land-cover/use discrimination ability of the band subsets. The parameters of SVM were optimized using a 5-fold cross-validation. the band selection algorithms were coded and executed under the MATLAB environment on a pc (i.e. an intel (r) core (TM) CPU i5-4460 processor (3.20 GHz) and 8 GB RAM). Each algorithm was repeatedly run 10 times on each dataset, and the average OAs of the band subsets were calculated for different numbers of bands (5, 10, 15, 20, 25, 30, 35, and 40). The McNemar test was employed to compare and investigate the difference between the results of the proposed IMACA-BS and of the benchmarks.
Generally, the parameters of the aca-based band selection algorithm were set according to previous experience [30], [31]. The parameters of ACA-BS and IMACA-BS, including the population size ps, the information heuristic factor α, the desired heuristic factor β, and the pheromone evaporation factor ρ, exert a strong effect on the band selection results [32]. Here α and β are two adjustable parameters controlling the relative influence of pheromone τ ij and heuristic desirability η ij , and ρ determines the pheromone evaporation rate [33].
The parameters of the ACA-BS and IMACA-BS were optimized by repeating the experiments 10 times, and the parameter combinations leading to the highest average OAS were used for band selection. In the process of parameter VOLUME 8, 2020   Table 4. For a more detailed comparison of the algorithms, the average OA AND per-class accuracy in the case of m = 40 are reported in Table 5, with the best OAs for each class highlighted in boldface. As illustrated in the table, the IMACA-BS outperforms other band selection algorithms in discriminating complex classes. For instance, the most difficult to distinguish classes, Corn-mintill (class 5) and Soybean-clean (class 11) that were often misidentified as Corn (class 3), were better identified with the band subset selected by the IMACA-BS.
The mcNemar test was further adopted to analyze whether there is a significant difference in classification accuracy between the proposed method and benchmarks. The significance testing was carried out between the trials of the IMACA-BS and that of one benchmark with the same order, for example, the first trial of the IMACA-BS and GA-BS. the results (i.e. average p-values) of the significance testing are presented in Table 5. It can be seen from the table that all of the average p-values were lower than 0.05, demonstrating that the IMACA-BS achieved significantly better classification results in comparison with benchmark comparators.   Table 1.

TABLE 6.
The overall accuracy (%), per-class accuracy (%), Kappa coefficients (K ), and the significance testing results (p-value) between the proposed method and other algorithms in terms of classification accuracy with the Pavia university dataset (m = 40); class names are in Table 2.
To further investigate the effectiveness of the band selection algorithms, the average per-class classification accuracy and the corresponding standard deviation with the pavia dataset are presented in Table 6. As shown by the table, the IMACA-BS outperforms the benchmarks in terms of land use/cover class discrimination, especially for the complex classes. For example, the complicated bare soil (class 2) and meadows (class 5) were better identified by the IMACA-BS algorithm. the mcnemar test results were summarized and shown in Table 6. It can be seen that all of the average pvalues were lower than 0.05, indicating that the IMACA-BS performed significantly better than other algorithms in terms of classification accuracy.

D. BOTSWANA EXPERIMENT
The classification accuracy with the full-bands and the differently sized (m varies over a range of 5-40) band subsets achieved by the six algorithms were illustrated in Figure 6.
As shown in the figure, the classification accuracy (OA = 85.26%) with the full-bands was lower than that of most band selection algorithms for the cases of m > 5. The average OA achieved by each band selection algorithm generally increased with the increase in band subset size. The proposed IMACA-BS always obtained the best accuracy, while the GAPSO-BS produced the second-best accuracy for most of the cases (5 < m ≤ 25). The average OAs of the GA-BS and PSO-BS were close to each other (except for the cases of m = 25, and m = 30). In contrast, the average OA of the ALO-BS was the lowest for the cases of m ≤ 35. In the case of m = 40, the IMACA-BS achieved the highest average OA (reaching up to 91.32%), whereas the ACA-BS obtained the lowest (only 89.05%).
The average per-class classification accuracy achieved by the algorithms is summarized in Table 7. The outperformance of the IMACA-BS is clearly demonstrated by the classification accuracy at class-level, especially for the Reeds1 VOLUME 8, 2020 TABLE 7. The overall accuracy (%), per-class accuracy (%), Kappa coefficients (K ), and the significance testing results (p-value) between the proposed method and other algorithms in terms of classification accuracy with the Botswana university dataset (m = 40); Class names are in Table 3. classification (class5) which was often misclassified as Floodplain grasses2 (class 4) and Riparian (class 6). With the bands selected by the IMACA-BS, the average classification accuracy of Reeds1 was improved to 76.58%, about a 3-5% increase compared with those of benchmarks.
Similar to previous experiments, the significance of the difference between the proposed IMACA-BS and other benchmarks was tested using the McNemar test at a significance level of 0.05. The testing results including average p-values and the standard deviations are presented in Table 7. It can be seen from the table that all of the average p-values were lower than the significance level. The classification results achieved by the IMACA-BS were, thus, statistically significantly better than those by other algorithms.

V. DISCUSSION
Band selection is essential for the effective utilization of heavily redundant bands in hyperspectral images (HSI). However, band selection from HSI data sets is not a trivial task, considering the huge solution space. The proposed IMACA-BS method has proved to be superior to the meta-heuristic ACA-BS, GA-BS, PSO-BS, GAPSO-BS, and the traditional SFFS over all three experiments. In the GA-BS, the cross and mutation operations are randomly operated on candidate solutions, which leads to very slow convergence [34]. In contrast, the PSO-BS converges rapidly due to the use of the global optimal solution and personal optima in the process of population evolution [35]. However, such an evolving strategy may make the solutions resemble each other. The particle swarm, thus, cannot explore new promising areas, and suffers from premature convergence [35]. Similarly, the traditional SFFS also tends to become trapped on local optima because of a lack of global observation on selected feature subsets. Our experiments illustrate (Tables 5, 6 and 7) that it is difficult to achieve promising band selection results with these band selection methods.
Though the ACA possesses advantages over the above-mentioned algorithms in terms of searching mechanism (e.g., strong positive feedback), the ACA suffers from slow convergence and local optima problems (resulting from loss of population diversity). Improvements are, thus, necessary to make the ACA suitable to solve the NP-hard HSI datasets band selection issue. In this research, a novel improved ant colony algorithm (IMACA) was proposed for band selection of HSI data. In comparison with the standard ACA, the IMACA overcomes the two shortcomings (i.e. slow convergence and local optima problems) of the standard ACA in solving the complicated HSI band selection problem. For the former, a pre-filter is adopted to improve the heuristic desirability of the ant colony system by reducing the randomness of the search ants at the beginning of the search process. Besides, the similarity (i.e. the degree of redundancy) of the selected bands is measured and serves as the heuristic function in the IMACA-BS, which significantly reduces data redundancy. Such strategies markedly improve the searching efficiency of the ant colony, and thus significantly accelerate the convergence of the IMACA-BS. For the latter, a pseudo-random rule was applied to the IMACA-BS, which enables the paths with limited pheromone concentration to be selected as candidate solutions with a certain probability. At the same time, an adaptive information update strategy is employed to update the pheromone dynamically, which prevents pheromone on the potential optimal edges being volatilized. As demonstrated in our previous work, the computational complexity of the ACA-BS O(P s ×m × n × T × C 0 ) is lower than that of other benchmarks (i.e. GA-BS, GAPSO-BS, PSO-BS, and SFFS-BS) [36]. In comparison to the ACA-BS, the IMACA-BS further decreases the computational complexity since the number of candidate bands (n) is lowered by using a pre-filter. Therefore, the proposed method is effective and efficient for practical usage.
The above-mentioned advantages ensure the proposed IMACA-BS will always select better band subsets compared to ACA-BS as well as other benchmarks, including GA-BS, GAPSO-BS, PSO-BS, and SFFS-BS. As demonstrated in the three experiments, the IMACA-BS consistently acquired the band subsets with the highest capacity to separate land cover classes in most of cases, regardless of the size of band subsets. With the selected bands, high classification accuracies were achieved for most land cover types, especially for those complicated and confusing land cover classes with high between-class spectral heterogeneity and similarity, e.g., Corn and Corn-mintill in Indian Pines Experiment, Meadows and Bare soil in Pavia University Experiment, and Reeds1 and Riparian in Botswana Experiment. Our experimental results demonstrate that the proposed IMACA-BS is capable of getting rid of suboptimal solutions and eventually approaching or reaching the global optimal solution.
The proposed method involves three parameters, each of which exerts a huge impact on the band selection results. Herein, a ''grid search'' approach was employed to achieve the optimal parameter combinations. Such a strategy enables the IMACA-BS to achieve encouraging results, but it is tedious and time-consuming. In contrast, the signal to noise ratio method (S/N) that can indicate how a solution changes among experiments [37], might be an alternative to efficiently search for the optimal parameters [38]- [40], which deserves further investigations. Although the proposed method considers the degree of redundancy between candidate band and selected band subsets to accelerate convergence, this might affect the final classification accuracy in some cases. Future studies may further improve the IMACA-BS by directly measuring the contribution of a candidate band to classification accuracy in the band selection process. Finally, it is usually difficult to determine the optimal number of selected bands for band selection algorithms.
Fortunately, deep learning-based methods have become the new hot topic in a wide range of research fields (e.g. change detection [41] and transportation mode classification [42]), owing to their capacity to solve complex issues in an endto-end fashion. Deep learning-based band selection methods, thus, deserve further investigation.

VI. CONCLUSION
In this study, an improved ant colony algorithm (IMACA-BS) for band selection from a hyperspectral image (HSI) was proposed, which enables the ant colony to avoid being trapped on local optima by accelerating the convergence and maintaining the population diversity. The effectiveness of the proposed IMACA-BS was tested with three public HSI data sets (Indian Pines, Pavia University and Botswana datasets), and compared with benchmark comparators using the overall classification accuracy of the SVM. The experimental results demonstrated that the proposed IMACA-BS method consistently produced the most accurate classification results and significantly outperformed the ant colony algorithm (ACA-BS), the genetic algorithm (GA-BS), the particle swarm optimization (PSO-BS), the hybridization of GA and PSO (GAPSO-BS), and the traditional sequential forward floating selection (SFFS-BS). As well, the proposed method achieved the greatest classification accuracies for most of the classes in each experiment, especially for those complex classes with similar spectral characteristics. The proposed method is, therefore, suggested to be an alternative for band selection from HSI data sets.
PATRICIA DALE received the B.A. (Hons) degree in geography from Southampton University, U.K., in 1964, the M.Soc.Sc. degree in geography and the L.L.B. (laws) from The University of Queensland, Australia, in 1979, in 1993, respectively, and the Ph.D. in ecology degree from the Griffith University, Brisbane, and 1997. Since 1980, she has been researching land cover ecology at Griffith University, using a variety of remote sensing techniques to assess land cover characteristics and to monitor change. She is currently an Emeritus Professor with Griffith University with continued interest in remote sensing of environment. She has supervised postgraduate student's remote sensing research. He is currently a Professor and the Head of GIS Research Group, Northeast Institute of Geography and Agroecology, CAS, with a specific interest in GIS (3D/4D) modeling, landscape change analysis, and machine learning. He has authored over 30 peer-reviewed articles in international scientific journals. VOLUME 8, 2020