BinCOA: An Efficient Binary Crayfish Optimization Algorithm for Feature Selection

The increased utilization of digital instruments like smartphones, Internet of Things (IoT) sensors, cameras, and microphones has resulted in extensive amounts of big data. Inherent challenges associated with big data include significant data dimensionality, redundancy, and irrelevant information. The main objective of feature selection is eliminating unnecessary features, thereby minimizing time and space requirements. This paper proposes a new Binary Crayfish Optimization Algorithm (BinCOA) for feature selection. The Crayfish Optimization Algorithm (COA) is a new metaheuristic algorithm inspired by the simulation of Crayfish search for food, summer resorts, and competitive habits. The original COA has been augmented with two primary enhancements to improve its performance. The refracted opposition-based learning strategy is a novel enhancement incorporated into the initialization step of the COA algorithm to strengthen the algorithm’s capability for exploitation. The crisscross strategy is added to the original COA, increasing the COA’s convergence accuracy. The algorithm’s performance is assessed by evaluating a set of 30 benchmark datasets. The proposed BinCOA is evaluated in comparison to seven contemporary wrapper feature selection methods. The experimental finding indicates that BinCOA consistently outperforms existing algorithms in classification accuracy, average fitness value, and the number of selected features. Furthermore, the statistical significance of the results is verified by calculating the Wilcoxon rank-sum test.


I. INTRODUCTION
Due to the swift adoption of the internet and computer technologies, vast amounts of data, each comprising hundreds of features, are generated.In data mining, the task is to extract valuable information from this extensive dataset to make informed decisions.Meticulously choosing pertinent and beneficial features can significantly influence various applications such as data mining [1], the Internet of Things [2], machine learning [3], and image processing [4].For instance, within machine learning, redundant, irrelevant, and chaotic records in high-dimensional datasets diminish classification accuracy and escalate computational costs [5].Keeping and The associate editor coordinating the review of this manuscript and approving it for publication was Sawyer Duane Campbell .
processing the enormous amounts of data sensors collect is a common problem with IoT techniques.The additional challenge pertains to the existence of irrelevant and redundant features.Consequently, Preprocessing, such as feature selection, is required to handle high-dimensional data and remove redundant or duplicate features.[6].Feature selection is a crucial aspect of data preparation, playing a significant role in building robust models.It entails identifying and finding the most significant features from the given dataset.
A feature selection framework comprises three primary components: (i) Classification methods like support vector machines (SVMs) [7], k nearest neighbour (kNN) [8], etc., (ii) evaluation criteria, and (iii) the search algorithm employed to identify the most optimal features.Feature selection methods can be classified into two primary categories: wrapper strategies and filter strategies.Wrapper methods judge feature subsets based on how well they work with the classification algorithm.A wrapper employs the classification algorithm independently, allowing for the assessment of the selected subset's quality depending on its classification effectiveness [9].A filter approach operates without dependence on any learning model; evaluating subsets of features solely depends on the data, independent of the specific model in use.It's crucial to highlight that filter approaches may not always identify the optimal subset of features.Nonetheless, there's a general observation that wrapper approaches often yield the most optimal feature subset in terms of performance for a predetermined classifier [10].A feature selection technique aims to pinpoint the optimal subset of features from the entire set of possible subsets.Accurate search methods and metaheuristics are two main types of search algorithms [11].Accurate search methods explore the entirety of the search space, which, for example, in a feature set with k features, has a magnitude directly related to 2k, requiring substantial computational resources.Metaheuristic algorithms, on the other hand, exhibit a stochastic nature by initiating their optimization process with randomly generated solutions, effectively exploring the search space.The effectiveness of metaheuristics in addressing feature selection problems relies on their potential to provide solutions approaching optimality within a reasonable timeframe [12].Due to their simplicity and ease of implementation, metaheuristics display significant adaptability when applied to specific problem domains.A notable feature of these algorithms is their remarkable ability to prevent premature convergence, maintaining a delicate balance between exploration and exploitation, two critical facets.
The Crayfish optimization algorithm (COA) [13] is a newly devised metaheuristic algorithm inspired by the simulation of Crayfish searching for food, summer resort, and competitive habits.The searching for food stage and competitive habits stage represent the exploitation phase of COA, while the summer resort stage constitutes the exploration phase of COA.COA introduces several variables to govern the algorithm's exploration and exploitation, enhancing randomness and optimizing its effectiveness.As a result, we have been prompted to utilize a binary version of COA.As mentioned earlier, metaheuristic algorithms have significantly impacted feature selection issues in the last few years.Despite the extensive research in this field, many metaheuristic algorithms still encounter challenges that require attention.Continued development of optimization techniques is necessary to achieve further improvements in results.So, two primary enhancements have been incorporated into the original Crayfish optimization algorithm (COA) to strengthen its performance.These enhancements reinforce opposition-based learning and cross-cross strategy.The refracted opposition-based learning strategy is implemented to enhance the diversity of the population and minimize the risk of the method becoming stuck in a suboptimal local state.The crisscross strategy is implemented to Strengthen the accuracy of convergence.Our contributions can be summarized in the following points: •Combining the refracted opposition-based learning strategy with COA, which has the potential to augment the diversity and traversal of the initial population.
•The crisscross strategy is implemented to improve the COA's convergence accuracy.
•BinCOA: A binary modification version of the COA algorithm is proposed to address challenges associated with feature selection.
•The algorithm's effectiveness is assessed through experiments conducted on a collection of 30 well-established benchmark datasets.
The remaining manuscript is structured as follows: Section II presents the literature review, and Section III briefly reviews the Crayfish Optimization Algorithm (COA).The proposed BinCOA algorithm is introduced in Section IV, The Experiments and Analysis are introduced in detail in Section V, and finally, the conclusions are detailed in Section VI.

II. LITERATURE REVIEW
Metaheuristic approaches are commonly categorized into four distinct groups according to the sources that inspire them: human-based methods [14], swarm intelligence [15], evolutionary algorithms [16], and physics-based methods [17].Human-based methods draw inspiration from how people interact and connect in society.Agrawal [18] introduced a binary variant of the knowledge-based gaining sharing method (GSK) to address feature selection issues, known as FSNBGSK.This approach utilized the k-nearest neighbors (kNN) classifier to assess its performance across 23 benchmark datasets.The proposed method exhibited superior classification accuracy and a minimal number of selected characteristics compared to other algorithms.Examples of algorithms based on human approaches include imperial competition algorithms (ICA) [19], the cultural evolution algorithm (CEA) [20], the volleyball premier league (VPL) [21], and teaching-learning-based optimization (TLBO) [14].Hybridizing multiple algorithms has become a popular approach in feature selection, enabling researchers to leverage the unique strengths of various algorithms [17].Swarm intelligence approaches draw inspiration from the collective behaviour of animals in swarms, offering valuable contributions to solving feature selection (FS) problems.Notable algorithms in this category include Binary Horse Herd Optimization (BinHOA) [22], Binary Cuckoo Search (BCS) [23], Binary Dragonfly algorithm (BDA) [24], and Binary Flower Pollination Algorithm (BFPA) [25].Xue et al. introduced a new approach for Particle Swarm Optimization (PSO) to reduce computational time, minimize the number of features, and maximize the accuracy of classification [26].Additionally, Al-Tashi et al. [27] presented a binary version of hybridization modes based on WOA.The SA algorithm is integrated into the WOA framework in the first model.In contrast, the SA algorithm enhances the optimal solution obtained after each iteration in the subsequent model.The results indicate that the methods described in this research are better than existing binary algorithms in terms of accuracy and computational time, with experiments conducted on 18 UCI benchmark datasets.
Evolutionary algorithms emulate the principles of natural evolution, drawing inspiration from the Darwinian theory of evolution.Among these is the genetic algorithm (GA), a type of evolutionary approach for its exceptional ability to effectively address challenges associated with feature selection [28].The results from implementing nested GA have shown a notable enhancement in classification accuracy.For instance, using the Genetic Algorithm (GA) algorithm in conjunction with chaotic optimization has demonstrated effectiveness in text categorization [29].Other types of evolutionary methods include differential evolution algorithms (DE) [30], geography-based optimizers [31], and stochastic fractal search [32].
Physics-based methods are formulated from the fundamental principles and rules of natural physics, and metaheuristic algorithms of this nature have significantly contributed to addressing challenges in feature selection.Notable algorithms in this category include the Lightning Search Algorithm (LSA) [33], Multi-verse Optimizer (MVO) [34], Electromagnetic Field Optimization (EFO) [35], Henry Gas Solubility Optimization (HGSO) [36], and Gravitational Search Algorithm (GSA) [37].Additionally, Simulated Annealing (SA) [38], inspired by metallurgical processes involving controlled heating and subsequent cooling of materials, is considered.The Equilibrium Optimizer (EO) algorithm has emerged as a prominent addition to physics-based approaches in recent years [39].Ahmed et al. [40] developed an upgraded version of the Equilibrium Optimizer to address feature selection problems.The method was tested on 18 kNN datasets and compared to 8 established approaches, encompassing classical and mixed metaheuristic algorithms.Another development is the binary version of the Equilibrium Optimizer, denoted as BinEO, introduced by D. A. Elmanakhly et al. [3].This variant incorporates an opposition-based learning method and a local search algorithm [3].The k-nearest neighbour and SVM classifiers were widely employed as wrapper techniques.A comparative analysis using various established algorithms demonstrated the Binary Equilibrium Optimizer's (BinEO) effectiveness.
The Crayfish Optimization Algorithm (COA) is a novel meta-heuristic algorithm that belongs to the swarm intelligence meta-heuristics algorithms.It mimics crayfish behaviour in competition, summer resorts, and foraging.COA has demonstrated superior performance compared to other widely recognized metaheuristics, showcasing its robust exploration and exploitation capabilities and effectiveness.In our proposed paper, we present utilizing a binary version of COA as a wrapper feature selection technique to enhance the efficacy of feature selection and classification tasks.To strengthen the performance of COA, the refracted opposition-based learning and crosscross strategy was combined with the original COA.The refracted opposition-based learning strategy is implemented to increase population diversity and lower the likelihood of the method being caught in an ideal local state.The crisscross technique is employed to improve the accuracy of convergence.

III. CRAYFISH OPTIMIZATION ALGORITHM
The crayfish is an omnivorous creature that has the ability to consume a wide range of food sources [41].When crayfish are hunting, they use their claws to tear up big meat and then send it to their second and third feet to hold on to while they walk.Use your second and third walking feet to hold and nibble on small items.As depicted in Figure 3, crayfish commonly employ rapid hiding or utilize pincers as a defensive mechanism to safeguard themselves against potential theft by other crayfish.

A. INSPIRATION
COA draws inspiration from the foraging, summer vacation, and competitive behavior of crayfish.The foraging and competition stages might be considered the exploitation stage of the Cultural Evolutionary Approach (COA).In contrast, the summer resort stage can be seen as the exploration stage of COA.The initial part of the algorithm involves defining the crawfish colony Cr to accurately represent the characteristics of optimization by swarm intelligence.The variable Cr i represents the spatial location of the ith crayfish, serving as an indicator of a potential solution.The regulation of the exploration and exploitation of COA is contingent upon temperature, a stochastic variable that denotes the environmental temperature in which an organism resides.When the ambient temperature exceeds a certain threshold, the COA will transition into the summer resort or competition stage.COA will initiate the foraging stage when the temperature conditions are suitable.During the foraging stage, the most favorable position for food acquisition is referred to as the optimal solution.The present solution fitness i (the answer found by Cr i i ) and the optimal solution fitness food (the answer found by the optimal solution) both give the size of the food.Crayfish get new positions based on their place when the food is right.Cr i , food intake stayed the same p, and food placement was Updated on Cr foode .While eating, crabs tear up food with their claw foot if it's too big, then switch between their second and third walking feet to eat.
The sine and cosine formulas were employed to imitate the alternating eating habits of crayfish.

B. MATHEMATICAL FORMULA 1) INITIALIZATIO
The initial step in the process of the Cooperative Optimization Algorithm (COA) involves the generation of a set of Candidate solutions, denoted as Cr, within the given search space.This generation is done randomly.The Candidate solution, denoted a Cr, is formulated with consideration to the population of size N and the dimension (dim).The process of initializing the COA algorithm can be formulated as follows where Cr indicates the initial position of the population, N indicates the population's numbers, dim indicates the dimension of the population, Cr i,j is individual positions of i-th in the j-th dimension, and Cr i,j is calculated as follows: where ub j and lb j are the upper and lower bounds of the j-th dimension, respectively, and Rand indicates a random number.

2) EFFECT TEMPERATURE ON CRAYFISH INTAKE
Fluctuations in temperature can influence crayfish behavior, prompting transitions between various stages.When the ambient temperature exceeds 30 • C, crayfish exhibit a preference for seeking out cooler environments as a means of engaging in their summer retreat.Crayfish will engage in foraging activity when exposed to suitable temperature conditions.The quantity of food consumed by crayfish is influenced by temperature.The optimal feeding range for crayfish falls from 15 • C to 25 • C, with 30 • C being particularly favorable.Consequently, It is possible to model the feeding quantity of crayfish using a normal distribution., illustrating the impact of temperature on their feeding behavior.Due to the robust foraging behavior exhibited by crayfish within the 20 to 30 • C temperature range, COA defines a temperature range extending from 20 to 35 • C. The equation for temperature is eq.3.The representation of crayfish intake is depicted in eq.4. Figure 2 illustrates the schematic of food intake.
where µ stands for the ideal temperature for crayfish, and σ and W are employed to regulate the amount of crayfish consumed at different temperatures.

FIGURE 2.
The influence of temperature on intake on crayfish [13].

3) PHASE OF SUMMER RESORT (EXPLORATION)
If the temperature is more than 30, it's too hot.At this point, the crayfish decide to spend the summer in the cave.The cave X shade is described as follows: where Cr G denotes the optimal position achieved through the cumulative iterations while Cr L signifies the optimal position within the current population.The phenomenon of crayfish engaging in territorial disputes within caves can be characterized as a stochastic occurrence.When the value of the random variable rand is less than 0.5, it indicates the absence of any rival crawfish for caverns, hence resulting in the direct entry of the crawfish into the cave for the purpose of summer vacation.This process is simulated as follows: In this context, t is the current number of iterations, and t + 1 signifies the iteration number for the next generation.Additionally, S is a decreasing curve, as depicted in the following equation: where T is the maximum iteration number.
During the summer resort phase, crayfish aim to approach the cave, symbolizing the best solution.In this phase, crayfish move closer to the cave, effectively bringing individuals nearer to the best solution.This process strengthens COA's exploitation ability, facilitating faster algorithm convergence.

4) PHASE OF COMPETITION (EXPLOITATION)
When the temperature is above 30 degrees, and the rand is less than 0.5, It's a sign that the cave is appealing to more than just crayfish.Eq. 8 shows the crayfish vying for control of the cave.

Cr t+1
i,j = Cr t i,j − Cr t z,j + Cr shade (8) where z is a randomly selected individual of crayfish.
Crayfish engage in competition with one another, and crayfish Cr i adjust their positions depending on the position Cr z of another crayfish.This positional adjustment expands the COA search range, thereby enhancing the algorithm's exploration capability.

5) PHASE OF FORAGING (EXPLOITATION)
When the temperature is equal to or below 30 • C, it is considered suitable for crayfish feeding.During this period, Crayfish exhibit active locomotion as they approach the food source.After discovering the food, crayfish evaluate the dimensions of the food item.Crayfish use their claws to dismantle big food items, then ingest them by alternating between their second and third ambulatory appendages.
The size of food Q is presented as: where k represents the food factor, signifying the maximum food size with a constant value of 3. fitness i denotes the i-th crayfish fitness value, while fitness food is the fitness value associated with the location of the food.The crayfishs assessment of food size is based on the dimensions of the largest food item.When Q > (k + 1)/2, it indicates that the portion size of the food is excessive.At present, the crayfish engages in the act of tearing its food using its foremost claw appendage.The following equation simulates this process: The equation for foraging, considering the relationship between the food obtained by crayfish and food intake, is as follows: at Q ≤ (k + 1)/2, The crayfish simply needs to approach the meal and consume it directly.The equation can be expressed as: Crayfish employ several feeding methods depending on the size of their food Q, with food Cr food representing the best solution.If the size of the food Q is appropriate for crayfish consumption, the crayfish will approach the food.When the value of Q is excessively large, it signifies the presence of a substantial disparity between the crayfish and the ideal solution.Hence, it is to decrease the prevalence of Cr food and facilitate its proximity to the food.During the foraging step, the COA algorithm will strive to reach the best solution, hence improving its exploitation ability and exhibiting strong convergence capabilities.The flowchart illustrating the process of COA is depicted in Figure 3.

IV. PROPOSED BinCOA
This section thoroughly elucidates the proposed BinCOA, an approach based on wrappers specifically crafted to address the challenge of Feature Selection.The primary steps of the BinCOA algorithm include Initialization using the Refracted Opposition-Based Learning strategy, the transformation function, the Crisscross strategy, and the evaluation.The subsequent subsections will delve into a detailed explanation of each step.

A. INITIALIZATION WITH THE REFRACTED OPPOSITION-BASED LEARNING STRATEGY
Efficient utilization of the local space plays a crucial role in pursuing an optimal solution, significantly impacting the obtained optimal solution quality.Our proposed algorithm, BinCOA, incorporates the Refracted Opposition-Based Learning strategy [42] to enhance the population's initialization.The solution space is expanded by the acquisition of an opposition-based solution derived from the existing solution, hence facilitating the identification of a more optimal alternative solution to address a given problem.The integration of the metaheuristic with opposition-based learning has been established to demonstrate the effective enhancement of algorithmic solution accuracy.In the initialization phase of BinCOA, refracted opposition-based learning is employed to adjust the positions of crayfish within the search space.The concept of refracted opposition-based learning is illustrated in Figure 4.
The search interval for solutions on the x-axis extends within the range [lb, ub]; the origin O is situated at the midpoint of the interval [lb, ub].Here, α and β are assigned as the angle of incidence and the angle of refraction, respectively.Additionally, m and m * denote the lengths corresponding to the incident and refracted rays, respectively.The refracted formula can be expressed as follows: Put σ = m * m and n=1 in Eq.15, and COA is extended to a high-dimensional space, resulting in the solution for the refracted direction Cr * i,j , as follows: 28626 VOLUME 12, 2024 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.where Cr i,j is the i-th crayfish position at j-th dimensions, Cr * i,j is the refracted inverse solution of Cr i,j , and lb j and ub j are the lower and upper bounds of the dynamic boundary.

B. TRANSFORMATION FUNCTION
The Feature Selection process has traditionally been conceptualized as a binary problem.However, the positions of particles generated by the original Crayfish Optimization Algorithm (COA) are characterized by continuous values.Consequently, to convert the continuous space of the original COA into a binary search space, introducing a transformation function becomes imperative.In the context of feature subset selection challenges, the concentrations of particles are constrained to binary values of 0 or 1. Figure 5 depicts the binary representation of a COA solution designed for a dataset comprising D features.The values of 1 and 0 signify the selected or unselected of the corresponding feature.The proposed binary COA algorithm employs a binarization technique to transform each solution into its corresponding binary representation.The sigmoid function stands out as one of the most frequently utilized transformation functions within the S-shaped family [43].The sigmoidal function can be classified as a member of the S-shaped family of transfer functions, described as follows: where Cr d i (t) the i-th crayfish position.In order to obtain the binary value, the concentration of i-th crayfish is updated according to the following procedure: The variable rand represents a randomly generated value inside the interval [0,1].

C. APPLYING CRISSCROSS STRATEGY TO BinCOA
In this section Crisscross Strategy is described in detaels to enhances the solution accuracy of the BinCOA algorithm by applingHorizontal crossover and vertical crossover.

1) HORIZONTAL CROSSOVER
The arithmetic crossover applied across all dimensions between two agents is referred to as horizontal crossover [44].Suppose the i-th crayfish.Cr i and the k-th crayfish Cr k are employed to execute the horizontal crossover operation at the j-th dimension.This can be formulated as: where Cr ′ i,j and Cr ′ k,j represent the moderation solutions generated as offspring from Cr i,j and Cr k,j , respectively.r 1 and r 2 are randomly selected from the range [0,1], while c 1 and c 2 are randomly chosen from the interval [−1,1].To maintain superior crayfish, comparing the solutions generated by the horizontal crossover operation with the pre-crossover solutions is essential.

2) VERTICAL CROSSOVER
Vertical crossover involves applying an arithmetic crossover to all agents between two dimensions [44].Suppose the i 1 -th and the j 2 -th dimensions of the crayfish Cr i , they are employed for conducting the vertical crossover operation.
where Cr ′ i,j is the offspring of Cr i,j1 and Cr i,j2 , r are randomly selected from the range [1,0].The solutions produced through the vertical crossover operation must be compared with the pre-crossover solutions to preserve crayfish better.

D. THE EVALUATION FUNCTION
Choosing a higher number of features from the data presents a challenge, as the classifier's performance tends to degrade when faced with irrelevant or redundant features.Therefore, it becomes crucial to address this issue by reducing the dimensionality of the data.Feature selection emerges as Algorithm 1 Pseudo-Code of BinCOA 1. Initialization T, Population N, dimension dim 2. Initialize the candidate solutions using Eq. 1 and Eq. 2 3. Apply refracted opposition-based learning using Eq.11 and Eq.12 4. Evaluate the fitness values of the population to get Cr G , Cr L 5. While (t < T) 6. Transform the Crayfish positions into binary space by employing a transfer function using Eq.15 and Eq.16. 7. Evaluate each Crayfish within the population by employing kNN or SVM classifiers.8. Measure the fitness of the entire population of the Crayfish using Eq.20.9. Defining temperature by Eq.3 10. if (temperature > 30) 11.Define cave Cr shade according to Eq.5 12. if (rand < 0.5) 13.Crayfish conducts the summer resort stage according to Eq.6 14. Else 15.Crayfish compute for caves through Eq.8 16.End if 17. Else 18.The food intake P and food size Q are obtained by Eq.4 and Eq.11 19. if Q > 2 20.Crayfish shreds food by Eq.12 21.Crayfish foraging according to Eq.13 22. Else 23.Crayfish foraging according to Eq.14 24.End if 25. Update the position of Crayfish by using the crisscross strategy based on Eq.16 and Eq.18 26.End if 27. Update fitness values, Cr G , Cr L 28. t = t + 1 29.End While a technique aimed at improving the efficiency and effectiveness of a given classifier by eliminating unnecessary or irrelevant features.In evaluating solutions, it is not only the classification accuracy rate that is scrutinized; the number of selected features also plays a significant role.In cases where two solutions demonstrate identical classification accuracy, preference is given to the solution with the fewest selected features.Thus, the objective of the fitness function is to optimize the classification accuracy rate by minimizing the classification error while concurrently reducing the number of selected features.The fitness function provided below serves as the metric for evaluating Bin-COA solutions, striking a balance between these two primary objectives.where ∝∈ [0, 1], γ indicates the classification error rate computed by the kNN or SVM classifier, β = 1− ∝, S represents the selected features, and N is the total features.In the proposed algorithm (BinCOA), kNN or SVM is used as a classifier [7], [45].We use the SVM classifier method when a dataset has two classes.In every other case, the kNN algorithm is used.The procedural steps for the BinCOA are illustrated in Algorithm 1.

V. EXPERRIMENTAL RESUTLS AND ANALYSIS
In this section, we present the outcomes of the suggested methodology and compare them with the latest algorithms.
Both the proposed and recent algorithms underwent testing on a laptop with the following specifications: the Matlab R2016a Software operating on the Windows 8 OS, powered by an Intel Core i7-3630QM processor running at 3.2 GHz, and equipped with 8 GB RAM.

A. DATASETS
We utilized a set of 30 datasets obtained from the UCI data repository to assess and verify the effectiveness of BinCOA in comparison to state-of-the-art algorithms.The selection of these datasets was driven by their diverse range of instances and features, providing a thorough evaluation of BinCOA across various challenges.Table 1 offers a concise overview of the examined datasets, encompassing varied class counts, instance quantities, and attribute variations.

B. CONFIGURATION BinCOA PARAMETER
The performance of BinCOA is compared to several other state-of-the-art feature selection methods.Each algorithm undergoes 20 runs, with a maximum iteration limit of 30 and 10 search agents.The chosen classifiers for this study are kNN and SVM.When datasets comprise more than two classes, the 5-NN classifier takes precedence for generating the optimal subset.Thorough trials and runs on diverse datasets are conducted to determine the optimal K value for kNN.K-fold cross-validation is set at 10 for both kNN and SVM to mitigate overfitting.The parameters for BinCOA are outlined in Table 2.

C. EXPERIMENTAL RESULTS
The experimental process comprises two phases.The initial phase entails a comparison between the proposed BinCOA and the original COA.A comparative analysis is carried out in the subsequent phase between the proposed BinCOA and the latest feature selection algorithms.The experiments in this study are grounded in four primary evaluation measures, as follows: • Classification accuracy: Classification accuracy refers to the classifier's precision in determining the most advantageous subset of features • Average Fitness value: The Average Fitness at each run n can be computed as follows:

Maximum iteration i=1
Fitness i (23) where Fitness i is the Fitness at iteration i.  • No. of selected feature: denotes the minimum number of features obtained in the optimum solution.The present experiments in this section examine the impact of combining the refracted opposition-based learning strategy and the crisscross strategy into the performance of the COA algorithm.Table 3 presents comparative studies between the proposed BinCOA and the original COA regarding average fitness, classification accuracy, and No. of selected features.Concerning average fitness, the table shows that BinCOA consistently outperforms the original COA across all 30 datasets.Table 3 also shows that the BinCOA consistently performs better than the original COA for all 30 datasets in Accuracy classification.The number of selected features for each algorithm is also reported in Table 3. BinCOA achieves the highest ranking in 28 instances out of 30 datasets.Figures 6, 7, and 8 present a comparative analysis between COA and BinCOA, showcasing the overall average fitness value, classification accuracy, and number of selected features across all datasets.In order to investigate the performance of the proposed BinCOA algorithm, a comparison of results with the latest feature selection algorithms was conducted.In the comparative results, we use 7 well-known feature selection algorithms: GWO [46], EO [47], MFO [48], PSO [49], SSA [50], HOA [22], and WOA [51].Tables 4-6 present the numerical outcomes achieved by the proposed BinCOA algorithm in comparison with the latest feature selection algorithms.Table 4 discusses the accuracy of the participants' methodologies and the proposed BinCOA algorithm over 30 iterations on each of the 30 datasets.
Based on the data presented in the table, it can be observed that BinCOA has achieved the highest accuracy value in 96.6% of the instances, namely in 29 out of the total 30 datasets.Subsequently, it has the highest overall average accuracy across all datasets.Figure 9 depicts a bar chart that illustrates a comparison based on the overall average accuracy.According to the presented data, the figure illustrates that the proposed algorithm exhibits the highest ranking in terms of total average accuracy at 96.6%.
The Fitness value of each of BinCOA and the other algorithms for 30 datasets are listed in table 5.According to the results in table 5, the proposed BinCOA algorithm outperforms other algorithms in 28 out of the total 30 datasets.The bar chart in Figure 10 compares the average fitness value for BinCOA and the other algorithms.The IBEVO algorithm has superior performance in achieving the minimal average fitness value (0.1177) across all datasets, and the HOA algorithm comes in second with a value of (0.1245) as shown in figure 10.
In addition to maximizing classification accuracy, minimizing the number of selected features is also considered desirable.The number of selected features for all datasets is reported in table 6.The proposed BinCOA achieves the minimum number of selected features for 30 of the 30 total datasets.The IBEVO demonstrates strong size reduction capabilities, obtaining the smallest average selection size (244.18)across all datasets.The HOA algorithm is ranked second with a value of (272.22), as depicted in Figure 11.The Wilcoxon signed rank-sum test is a statistical technique employed to evaluate the similarity or dissimilarity between two groups.This test analyzes the differences within pairs of groups to determine if they are statistically significantly distinct.In our analysis, the Wilcoxon rank-sum test, conducted at a 5% significance level, compares the results of the BinCOA algorithm to six prominent recent feature selection metaheuristic algorithms across the 30 standard datasets.Table 7 displays the p-values obtained from this test.Upon examination of the data in the table, it becomes evident that all p-values for the compared algorithms fall below the 5% significance level.This result provides compelling evidence to reject the null hypothesis.Consequently, it can be inferred that the binary BinCOA method surpasses all other comparative algorithms.

VI. CONCLUSION
A novel Crayfish Optimization Algorithm (BinCOA) provides for feature selection problems in the present study.The original COA is enhanced by incorporating both the refracted opposition-based learning strategy and the crisscross strategy, leading to improved performance.The k-nearest neighbors (kNN) or support vector machine (SVM) classifier has been found to produce high-quality solutions when used in conjunction with the BinCOA algorithm.Furthermore, these classifiers have proven their ability to learn effectively from the provided training data.The application of k-fold cross-validation is a highly effective approach for addressing the concern of overfitting.In order to promote traversal and variety, the population is initialized using the refracted opposition-based learning technique.It has been discovered that applying the crisscross technique improves optimization accuracy to some extent.It also facilitates a more thorough investigation of possible answers and enhances the algorithm's utilization of the search space.Thirty datasets are used to evaluate the proposed algorithm, and the results are compared with seven well-known feature selection algorithms.The contrasting experiments and the mentioned results demonstrate the superiority of BinCOA over recent feature selection algorithms.Furthermore, the significance of the proposed algorithm is assessed by the utilization of the Wilcoxon rank-sum test.The statistical findings indicate that the proposed algorithm demonstrates superior performance when compared to the most recent feature selection algorithms.

FIGURE 1 .
FIGURE 1.The structure of a crayfish.

TABLE 4 .
The classification accuracy comparison results with other recent algorithms overall dataset.

FIGURE 6 .
FIGURE 6.The average Fitness value of BinCOA compared to COA over all datasets.

FIGURE 7 .
FIGURE 7. Average classification accuracy value of BinCOA compared to COA over all datasets.

FIGURE 9 .
FIGURE 9. Comparison between BinCOA and recent feature selection algorithms in Average Classification accuracy overall datasets.

FIGURE 10 .
FIGURE 10.Comparison between BinCOA and recent feature selection algorithms in Average Fitness over all datasets.

FIGURE 11 .
FIGURE 11.Comparison between BinCOA and recent feature selection algorithms in Average Fitness over all datasets.

TABLE 1 .
Description of the datasets.

TABLE 3 .
Results for BinCOA compared to COA in average Fitness, average accuracy, and average No. of selected feature overall datasets.

TABLE 5 .
Average Fitness comparison results with other recent algorithms overall dataset.

FIGURE 8 .
Average No. of selected feature value of BinCOA compared to COA over all datasets.

TABLE 6 .
No. of selected feature comparison results with other recent algorithms over all datasets.

TABLE 7 .
The Wilcoxon rank sum test results.