Hybrid Harris hawks optimization with cuckoo search for drug design and discovery in chemoinformatics

One of the major drawbacks of cheminformatics is a large amount of information present in the datasets. In the majority of cases, this information contains redundant instances that affect the analysis of similarity measurements with respect to drug design and discovery. Therefore, using classical methods such as the protein bank database and quantum mechanical calculations are insufficient owing to the dimensionality of search spaces. In this paper, we introduce a hybrid metaheuristic algorithm called CHHO–CS, which combines Harris hawks optimizer (HHO) with two operators: cuckoo search (CS) and chaotic maps. The role of CS is to control the main position vectors of the HHO algorithm to maintain the balance between exploitation and exploration phases, while the chaotic maps are used to update the control energy parameters to avoid falling into local optimum and premature convergence. Feature selection (FS) is a tool that permits to reduce the dimensionality of the dataset by removing redundant and non desired information, then FS is very helpful in cheminformatics. FS methods employ a classifier that permits to identify the best subset of features. The support vector machines (SVMs) are then used by the proposed CHHO–CS as an objective function for the classification process in FS. The CHHO–CS-SVM is tested in the selection of appropriate chemical descriptors and compound activities. Various datasets are used to validate the efficiency of the proposed CHHO–CS-SVM approach including ten from the UCI machine learning repository. Additionally, two chemical datasets (i.e., quantitative structure-activity relation biodegradation and monoamine oxidase) were utilized for selecting the most significant chemical descriptors and chemical compounds activities. The extensive experimental and statistical analyses exhibit that the suggested CHHO–CS method accomplished much-preferred trade-off solutions over the competitor algorithms including the HHO, CS, particle swarm optimization, moth-flame optimization, grey wolf optimizer, Salp swarm algorithm, and sine–cosine algorithm surfaced in the literature. The experimental results proved that the complexity associated with cheminformatics can be handled using chaotic maps and hybridizing the meta-heuristic methods.


Related work
A previously conducted study has investigated drug design and discovery, exhibiting differences in efficiency 31 . The available tools used to identify chemical compounds which are known as computer-aided drug design (CADD) allows the reduction of different risks associated with the subsequent rejection of lead compounds. CADD has an important role and exhibits high success rates for the identification of the hit compounds 32 .
The CADD methodology has two related concepts: ligand/hit optimization and ligand/hit identification. Methods hitting identification/optimization are based on the efficiency of the virtual screening techniques used to achieve the target binding sites. They are known to dock huge libraries for small molecules including chemical information or ZINC database, to identify the compounds based on the pharmacophore modeling tools (docking) to predict the optimal medicines and proteins obtained using the information from the ligand. The Pymol software 33 is useful in selecting the optimal ligand as the optimal drug, and the AutoDock software is employed to calculate the energy 5 . Thus, genetic algorithms (GAs) are applied in the AutoDock software and AutoDock Vina 34 . Also, in 35 , fuzzy systems have been introduced to address the optimization of the chemical product design. Another important method for drug design called QSAR is derived from CADD to extract the description of the correlation among different structures from a set of molecules and the response to the target 36 .
Drug design and discovery are the main aspects of cheminformatics 37 . Cheminformatics can be divided into two sub-processes. The first process considers three-dimensional information; this process is called encoding. The second process, which is called mapping, comprises building a model using machine learning (ML) techniques 38 . In the encoding process, the molecular structure is transformed based on the calculation of the descriptors 36 . Moreover, the mapping process aims to discover different mappings created between the feature vectors and their properties. In cheminformatics and drug discovery, the mapping can be performed using various machine learning 2,39 .
Chaotic maps are random-like deterministic methods that constitute dynamic systems. They have nonlinear distributions indicating that chaos is a simple deterministic dynamic system and a source of randomness. Chaos has random variables instead of chaotic variables and absolute searches can be performed with higher speeds when compared with stochastic search methods mainly based on probabilities. In a previous study 40 , chaotic maps have been considered to improve the performance of the whale optimization algorithm and balance the exploration and exploitation phases. Also, a grey wolf optimizer and flower pollination algorithm have been enhanced using ten chaotic maps to extract the parameters of the bio-impedance models 41 . Meanwhile, in 42 , the grasshopper optimization algorithm with chaos theory is employed to accelerate its global convergence and avoid local optimal. In 43 the schema of the CS algorithm based on a chaotic map variable value is introduced.
In fact, the methodology of hybridizing MAs is widely used in different domains of optimization other than feature selection 44 . In this vein, combinations of different ML techniques and MAs (e.g., search strategies) have been applied in many fields with modifications and hybridization to benefit from one technique in uplifting search efficiency. For instance, the salp swarm algorithm combined with k-NN based on QSAR is an interesting alternative, which provides competitive solutions 45 . Also, Houssein et al. 37 introduced a novel hybridization approach for drug design and discovery-based hybrid HHO and SVM. However, in this study, we applied hybridization to select the chemical descriptor and compound activities in cheminformatics. Particularly, this study proposes an alternative classification approach with respect to cheminformatics, termed as CHHO-CSbased SVM classifier, for selecting the chemical descriptor and chemical compound activities; the hybrid HHO and CS were enhanced based on the chaos (C) theory.

Materials and methods
In this section, we briefly discus the QSAR model, the basics of SVM, the original HHO, the original CS, and the chaotic map theory.
Quantitative structure-activity relationship. QSAR provides information based on the relation between the mathematical models associated with the biological activity and the chemical structures. QSAR is widely used because it can detect major characteristics of the chemical compounds. Therefore, it is not necessary to test and synthesize compounds. The inclusion of ML methods to study QSAR helps to predict whether the compound activity is similar to a drug-like activity in case of a specific disease or a chemical test. The compounds possess complex molecular structures, containing many attributes for their description. Some of the features include characterization and topological indices. Therefore, molecular descriptors are highly important in pharmaceutical sciences and chemistry 4 . Support vector machine. SVM is an important supervised learning algorithm commonly used for classification 46 . SVM extracts different points from the data and maps them in a high-dimensional space using a nonlinear kernel function. SVM works by searching for the optimal solution for class splitting. The solution can be used to maximize the distance with respect to the nearest points defined as support vectors, and the result of SVM is a hyperplane. For obtaining optimal results, SVM has some parameters that have to be tuned. The C controls the interaction between smooth decision boundaries and the accurate classification of the training points. If the C has a significant value, more training points will be accurately obtained, indicating that more complex decision curves will be generated by attempting to fit in all the points. The different values of C for a dataset can be used to obtain a perfectly balanced curve and prevent over-fitting. Ŵ is utilized to characterize the impact of single training. Low gamma implies that each point will have a considerable reach, whereas high gamma implies that each point has a close reach. The implementation of SVM has been extended to cheminformatics. In this work, steps of SVM are presented in Algorithm 1, and its graphical description is presented in Fig. 1 This species possesses a mechanism that allows them to catch prey even when they are escaping. This process is modeled in the form of a mathematical expression, allowing its computational implementation. HHO is a stochastic algorithm that can explore complex search spaces to find optimal solutions. The basic steps of HHO can be obtained with respect to various states of energy. The exploration phase simulates the mechanism when Harris's hawk cannot accurately track the prey. In such a case, the hawks take a break to track and locate new prey. Candidate solutions are the hawks in the HHO method, and the best solution in every step is prey. The hawks randomly perch at different positions and wait for their prey using two operators, which are selected on the basis of probability q as given by Eq. (1), where q < 0.5 indicates that the hawks perch at the location of other population members and the prey (e.g., rabbit). If q ≥ 0.5 , the hawks are at random positions around the population range. For facilitating the understanding of HHO, a list of symbols used in this algorithm is defined as follows: 1. Vector of hawks position (search agents) X i 2. Position of Rabbit (best agent) X rabbit 3. Position of a random Hawk X rand 4. Hawks average position X m 5. Maximum number of iterations, swarm size, iteration counter T, N, t 6. Random numbers between (0, 1) r 1 , r 2 , r 3 , r 4 , r 5 , q 7. Dimension, lower and upper bounds of variables D, LB, UB 8. Initial state of energy, escaping energy E 0 , E The exploration step is defined as: The average location of the Hawks X m is represented by: (1) X(t + 1) = X rand (t) − r 1 |X rand (t) − 2r 2 X(t)| q ≥ 0.5 (X rabbit (t) − X m (t)) − r 3 (LB + r 4 (UB − LB)) q < 0.5 The average position can be obtained by using different methods, but this is the simplest rule. A good transition from exploration to exploitation is required, here a shift is expected between the different simulated exploitative behaviors based on the escaping energy factor E of the prey, which diminishes dramatically during the escaping behavior. The energy of the prey is computed by Eq. (3). where E, E 0 , and T represent the initial escape energy, the escape energy and the maximum number of iterations, respectively. The soft besiege is an important step in HHO, it is shown if r ≥ 0.5 and |E| ≥ 0.5 . In this scenario, the rabbit has all sufficient energy. When it occurs, the rabbit performs random misleading shifts to escape, but in the metaphor, it cannot. The besiege step is defined by the following rules: where �X(t) is the difference locations vector for all rabbits and for presently positions in the iteration t, and J = 2(1 − r 5 ) Is the rabbit's spontaneous jumping ability throughout the escaping phase. The J value varies randomly in each iteration to represent the rabbit's behavior. In the extreme siege stage when r ≥ 0.5 and |E| < 0.5 , The prey is exhausted and has no escaping strength. The Harris hawks are hardly circling the trained prey, and they can make an assault of surprise. For this case, the current position is changed using: Consider the behavior of hawks in real life, they will gradually choose the best dive for the prey if they want to capture specific prey in competitive situations. This is simulated by: The soft besiege presented in the previous Eq. (7) is performed in progressive rapid dives only if |E| ≥ 0.5 but r < 0.5 . In this case, the rabbit has sufficient energy to escape and is applied for a soft siege before the attack comes as a surprise. The HHO models have different patterns of escape for a leap frog and prey movements. The Lévy flights (LF) are launched here to emulate the various movements of the Hawk and rabbit dives. Eq. (8) computes such patterns.
where S represents the random vector for size 1 × D and LF is for the levy flight function, using this Eq. (9): Here u, v are random values between (0, 1), β is the default constant set to 1.5.
The final step in the process is to update positions of the hawks using: where Y and Z are obtained using Eqs. (7) and (8).
During progressive fast dives, HHO is also hard-pressed, where it may happen if |E| < 0.5 and r < 0.5 . Here the strength of the rabbit to escape is not sufficient and the hard siege is suggested before the numerous surprise attacks are made to catch and kill the prey. In this step, Hawks seek to reduce the various distances between their prey and the average position. This operator is explained as follows: The values of Y and Z are proposed by using new rules in Eqs. (12) and (13), where X m (t) is obtained using Eq.
(2).  19 . The cuckoo quest hypothesis is inspired by a bird known as the cuckoo. Cuckoos are interesting creatures not only because they can make beautiful sounds but also for their aggressive strategy of reproduction. In the nests of other host birds or animals, adult cuckoos lay their eggs. Cuckoo search is based on three main rules: 1. Growing cuckoo lays one egg at a time and dumps the egg in a nest selected randomly. 2. The best nest with high-quality eggs will be delivered to the next generation.
3. The number of host nests available is set and the host bird finds the egg laid by a cuckoo with a probability ρ a ∈ [0, 1].
The probability is based on these three rules such that the host bird can either throw away the egg or leave the nest and build a completely new nest. This statement may be approximated by a fraction ρ a of n nests that are replaced by new nests (with new random solutions). The pseudo-code of CS is shown in Algorithm 2.
chaotic maps. The majority of MAs have been established based on stochastic rules. These rules primarily rely on certain randomness obtained using certain distributions of probabilities, which are often uniform or Gaussian. In principle, the replacement of this randomness with chaotic maps can be beneficial because of the significant dynamic properties associated with the behavior of chaos. This dynamic mixing is important to ensure that the solutions obtained using the algorithm are sufficiently diverse to enter any mode in the objective multimodal landscape. These approaches, which use chaotic maps, are called chaotic optimization instead of random distributions. The mixing properties of chaos will perform the search process at higher speeds than traditional searches based on the standard probability distributions 47 . One-dimensional non-invertible maps will be used to produce a set of variants of chaotic optimization algorithms to achieve this ability. Table 1 presents some of the prominent chaotic maps used in this study. In addition, chaotic maps are obliged to result in 0/1 based on the normalization concept. The main task of chaotic maps is to avoid the local optima and speed up the convergence. Here, it is important to mention that the nature of chaotic maps could also increase the exploration due to the intrinsic randomness. It is necessary to properly select the best map that helps each algorithm for a specific problem. Another important point to be considered is that chaotic maps do not take decision about the exploration and exploitation of the algorithms. However, along with the iterations, the chaotic values generated by the maps permit to change the degree of exploration or exploitation of the search space.

the proposed cHHo-cS
In this section, the proposed CHHO-CS is explained in detail, which is used to improve the search-efficiency of basic HHO. Typically, HHO has the characteristics of acceptable convergence speed and a simple structure. However, for some complex optimization problems, HHO may fail to maintain the balance between exploration and exploitation and fall into a local optimum. Especially in the face of high dimension functions and multimodal problems, the shortcomings of HHO are more obvious. The optimization power of the basic HHO depends on the optimal solution 57 . In this paper, we introduced two strategies (Chaotic maps, and CS) to enhance the performance of the basic HHO.
The following points are worthwhile: • Chaotic maps influence: applying chaos theory to the random search process of MAs significantly enhances the effect of random search. Based on the randomness of chaotic local search, MAs can avoid falling into local optimum and premature convergence. In the basic HHO algorithm, the transition from global exploration to local exploitation is realized according to Eq. (3). As a result, the algorithm will easily fall into a local opti-Scientific RepoRtS | (2020) 10:14439 | https://doi.org/10.1038/s41598-020-71502-z www.nature.com/scientificreports/ mum. Hence, in the CHHO-CS algorithm, a new formulation of initial escape energy E 0 and escaping energy factor E with chaotic maps are employed as demonstrated in Algorithm 3. Figure 2 shows the influence of a chaotic map on the energy parameter E obtained by the proposed method versus the basic HHO. Notably, the curve in the left-side linearly decreasing versus the proposed non-linear energy parameter defined by the new formulation of E, which clearly focuses on providing the search direction towards the middle of the search process to infuse enough diversity in population during the exploitation phase. • CS method influence: in the basic HHO, the position vectors X rand and X rabbit are responsible for the exploration step defined by Eq. (1), which plays a vital role in balancing the exploitation and exploration. More significant values of position vectors expedite global exploration, while a smaller value expedites exploitation. Hence, an appropriate selection of X rand and X rabbit should be made, so that a stable balance between global exploration and local exploitation can be established 58 . Accordingly, in the CHHO-CS algorithm, we borrow the merits CS method to control the position vectors of HHO. At the end of each iteration T, CS trying to find the better solution (if better solution found then update X rabbit and X rand ; otherwise left obtained values by HHO unchanged). Consequently, CS will determine the fitness value of the new solution, if it is better than the fitness value of the obtained from HHO, then the new solutions will be set; otherwise the old remains unchanged.
To be specific, the steps of the CHHO-CS algorithm are executed as; chaotic maps are employed to avoid falling into local optimum and premature convergence. Moreover, a balancing between exploration and exploitation is performed by CS. Then, SVM is used for classification purposes. The flowchart of the proposed CHHO-CS method is represented in Fig. 3. The pseudo-code of the proposed CHHO-CS method is illustrated in Algorithm 3. Here is important to mention that for SVM and feature selection, in the CHHO-CS each solution of the µ is a parameter between 0.9 and 1.08 The control parameter P ∈ (0, 0.5) and x ∈ (0, 1) and P = 0 www.nature.com/scientificreports/ population is encoded as a set of indexes that correspond to the rows of the dataset. For example, if a dataset has 100 rows a possible candidate solution in the population for five dimensions could be [10,20,25,50,80], such values are rows with the features to be evaluated in the SVM. The location vector in the soft and hard besiege with progressive rapid dives in HHO is updated as follows: www.nature.com/scientificreports/ feature selection. FS is a data pre-processing step, which is used in combination with the ML techniques.
FS permits the selection of a subset without redundancies and desired data. FS can effectively increase the learning accuracy and classification performance. Therefore, the prediction accuracy and data understanding in ML techniques can be improved by selecting the features that are highly correlated with other features. Two features show perfect correlation; however, only one feature is introduced to sufficiently describe the data. Therefore, classification is considered to be a major task in the ML techniques; in classification, data are classified into groups depending on the information obtained with respect to different features. Large search spaces are a major challenge associated with FS; therefore, different MAs are used to perform this task.
fitness function. Each candidate solution is evaluated along with the number of iterations to verify the performance of the proposed algorithm. Meanwhile, in classification, the dataset needs to be divided into training and test sets. The fitness function of the proposed CHHO-CS method is defined by the following equation: and where R refers to the classification error and C is the total number features for a given dataset D. β refer to the subset length and α represents the classification performance defined in the range [0, 1]. T is a necessary condition and G is a group column for the specific classifier. Each step in the algorithm is compared with T, where the obtained fitness value must be greater than in order to maximize the solution. It is important to remark that the fitness (or objective) function in Eq. (15) is also used by the CS to compute the the positions of X rand and X rabbit .

Results
To  Table 2.
A common machine learning classifier has been used in experiments including called SVM also was combined with the proposed CHHO-CS method for the classification purpose.
Performance analysis using UCI datasets. Description and pre-processing of the datasets, results, and comparison of the proposed CHHO-CS is described in the following subsections.
UCI Data description. The proposed algorithm is examined on ten benchmark datasets obtained from the UCI machine learning repository 59 illustrated in Fig. 3 and it is available at "https ://www.openm l.org/searc h".
Statistical results. SVM is used for the classification task. Following the previous methodology, in this experiment, iterations are set to 1,000 for each of the 30 runs. The experimental results are reported in Tables 4 and 5. In this experiment, the CHHO-CS-Piece based on SVM achieves the best mean and Std.
Classification results. Since SVM is one of the most promising methods of classification, its performance needs to be analyzed. In this experiment, the number of iterations are set to 1,000, also the obtained results are reported in Tables 6 and 7. Notably, the CHHO-CS-Piece based on SVM obtains the best classification accuracy, sensitivity, specificity, recall, precision, and F-measure. performance analysis using chemical datasets. Description of chemical datasets. In this study, two different datasets are used to experimentally evaluate the performance of the proposed method. (1) The MAO dataset comprises 68 molecules and is divided into two classes: 38 molecules that inhibit MAO (antidepressants) and 30 molecules that do not. MAO is available at http://iapr-tc15.greyc .fr/links .html. Each molecule should have a mean size of 18.4 atoms, and the mean degree of the atoms is 2.1 edges. In addition, the smallest molecule contains 11 atoms, whereas the largest one contains 27 atoms; each molecule has 1,665 descriptors.
(2) The QSAR biodegradation dataset comprises 1,055 chemical compounds, 41 molecular descriptors, and one class; it is available at http://archi ve.ics.uci.edu/ml/datas ets/QSAR+biode grada tion. These chemical compounds are obtained from the National Institute of Technology and Evaluation of Japan (NITE). The MAO dataset is transformed into a line notation form to describe the structure of the simplified molecular-input line-entry system (SMILES) using the open babel software 60 ; E-dragon 61 is subsequently applied to obtain the molecular descriptor. Information obtained with respect to the second QSAR biodegradation dataset was preprocessed by the Milano Chemometrics and QSAR Research Group, University of Milano-Bicocca and is available at http:// www.miche m.unimi b.it/ www.nature.com/scientificreports/ Data preprocessing. Here, the required steps to preprocess the data set information are presented. The information obtained from the molecules is transferred to the features representing chemical compounds 36,39 . The data obtained from the proteins are stored in a special chemical format. Further, the software should be used to transfer the information into the isomeric SMILES. The data set contains different instances with specific multidimensional attributes (commonly two-dimensional 2D and 3D according to the QSAR model. The E-dragon software is used to compute the descriptors from this dataset. The descriptors contain physicochemical or structural information as solvation properties, molecular weight, aromaticity, volume, rotatable bonds, molecular walk counts, atom distribution, distances, interatomic, electronegativity, and atom types. They are used for determining values of generations and instances which belong to a class as shown in Fig. 4.
Statistical results. Here, the SVM is used for the classification task. Following the previous methodology, in the first experiment, iterations are set to 100 for each of the 30 runs. The experimental results are reported in Tables 8. In this experiment, the CHHO-CS-Piece based on SVM obtains the best mean and Std. The same rank is obtained for maximizing the classification accuracy solution, Sensitivity, Specificity, Recall, Precision, and F measure. In this case, the HHO-CS with SVM is the second-ranked in mean value, Std, and maximizing the classification accuracy solution, sensitivity, specificity, recall, precision, and F-measure. The iterations are configured to 1,000; the idea is to obtain the best solutions. In this case, the results are presented in Table 9, where the CHHO-CS-Piece combined with the SVM is the fist ranked approach for the mean value, and Std, the same occurs for maximizing the classification accuracy solution, sensitivity, specificity, recall, precision, and Table 2. Parameters setting of competitor algorithms used in the comparison and evaluation. Step length = 0.01

CHHO-CS Both HHO and CS parameters
x 0 = rand default for maps Classification results. Since SVM is one of the most promising methods of classification, its performance needs to be analyzed. In the first experiment, iterations are set to 100; the experimental results are reported in Table 10.
In this experiment, the CHHO-CS-Piece based on SVM obtains the best results. In this case, the HHO-CS with SVM is the second-ranked in most of the assessment criteria. A final experiment for SVM is performed by using 1,000 iterations and the reported values in Table 11 confirms that the CHHO-CS-Piece combined with the SVM the convergence analysis. This section aims to analyze the convergence of the proposed CHHO-CS based chaotic maps presented in this paper. Figures 5 and 6 shows the convergence curves for the competitor algorithms over the ten UCI Machine Learning Repository datasets along the iterative process 100, and 1,000 iterations respectively. Over the ten UCI datasets, the convergence curves plotted in Figs. 5 and 6 provides evidence that the proposed CHHO-CS method using SVM obtained the best results compared with the original On the other hand, the convergence curves plotted in Fig. 7a-d provide evidence that the proposed CHHO-CS method with SVM classifier obtained over the two datasets (MAO and QSAR biodegradation) the best results compared with the original HHO and CS algorithms and the other competitor algorithms along with the two-stop criteria (100 and 1,000 iterations).  www.nature.com/scientificreports/ In worthwhile, the convergence curve is presented because it is a graphical form to study the relationship between the number of iterations and the fitness function. It declares the best-performed algorithm by comparison between various approaches and when increasing the number of iterations, it represents a direct correlation. The convergence curves plotted in Fig. 5a-j revealed that the proposed CHHO-CS-Piece method achieved better results compared with the competitor algorithms. Also, in the same context, the convergence curves plotted in Fig. 6a-j revealed that the proposed CHHO-CS-Piece method achieved better results compared with the competitor algorithms.
To sum up, the experiments were conducted on MOA and QSAR biodegradation datasets and the obtained results are interesting and due to the lack of space, we have added the results of the best map only. For example, in the first MOA dataset with the SVM classification technique in different stop conditions 100, and 1,000 iterations as shown in Fig. 7a-d, respectively. Moreover, on the MAO dataset, with 100 and 1,000 iterations, it is interesting that CHHO-CS-Piece with SVM is better than the other competitor algorithms. Meanwhile, for the second QSAR biodegradation dataset, the optimal solutions with SVM are computed with 100, and 1,000 iterations as stop condition, it is interesting that the version CHHO-CS-Piece with SVM provides the optimal solutions in comparison with the other metaheuristic algorithms. www.nature.com/scientificreports/ conclusion metaheuristic algorithms and machine learning techniques are important tools that can solve complex tasks in the field of cheminformatics. The capabilities of MAs and ML to optimize and classify information are useful in drug design. However, these techniques should be highly accurate to obtain optimal compounds. In this paper, a hybrid metaheuristic method termed CHHO-CS which combined the Harris hawks optimizer (HHO) with operators of the cuckoo search (CS) and chaotic maps (C) in order to enhance the performance of the original HHO. Moreover, the proposed CHHO-CS method was combined with the support vector machine (SVM) as machine learning classifiers for conducting the chemical descriptor selection and chemical compound activities.  The main tasks of the proposed method are to select the most important features and classify the information in the cheminformatics datasets (e.g., MAO and QSAR biodegradation). The experimental results confirm that the use of chaotic maps enhances the optimization process of the hybrid proposal. It is important to mention that not all the chaotic maps are completely useful, and it is necessary to decide when to use one or another. As expected, this is dependent on the dataset and the objective function. Comparisons of the proposed CHHO-CS method with the standard algorithms revealed that the CHHO-CS yields superior results with respect to cheminformatics using different stop criteria. In the future, the proposed CHHO-CS method can be used as a multi-objective global optimization or feature selection paradigm for high-dimensional problems containing many instances to increase the classification rate and decrease the selection ratio of attributes.