Data mining is the fastest-expanding domain of information technology, owing to the vast amounts of data gathered every day and the need to translate this data into meaningful information [1]. The pre-processing steps for data mining include knowledge presentation, pattern assessment, and other pre-processing steps (integration, filtering, transformation, reduction, etc.). The selection of features is one of the primary pre-processing stages that seeks to remove irrelevant and redundant features from a particular dataset [2]. In general, there are two categories into which feature selection (FS) algorithms may be divided: filters and wrapper methods [3]. The filter class contains techniques that operate directly on the dataset without using classifiers [4]. Classifiers are used in wrapper feature selection techniques to look for variable interactions [5]. Wrapper-based approaches are superior to filter-based approaches for the classification algorithm [6]. In the wrapper-based method, three essential components are often required to be specified: classifiers such as Support Vector Machines (SVM), K nearest neighbor (KNN), etc., feature subset assessment criteria, and the search algorithm to find a subset containing the best features. Finding the optimal collection of features is difficult and costly. Recently, it seems that metaheuristics are trustworthy and efficient techniques to address various optimization issues, such as feature selection [7]. Metaheuristics perform better than precise search mechanisms because they do not need to explore the entire search space, as opposed to exact search methods. In reality, they are not an exhaustive search algorithm. Exploration of the search space and the exploration of finding optimum solutions are two opposing aspects to consider when using or modeling a metaheuristic (MA). Performing a good balance of exploration and exploitation (E&E) will increase the performance of the search algorithm [8]. To achieve a healthy balance, one alternative is to use a hybrid technique in which two or more algorithms are integrated to increase the performance of each algorithm; this hybrid approach is known as a memetic method.

This work presents a binary variant of the hybrid TLBO-CO and uses CO as a wrapper feature selection technique. The growing complexity and high dimensionality of medical datasets necessitate effective feature selection methods to enhance classification performance while reducing computational costs. Traditional feature selection approaches, particularly wrapper-based methods, provide superior results but are often computationally intensive due to their exhaustive nature. To address this, metaheuristic algorithms have emerged as powerful alternatives for identifying optimal feature subsets efficiently. However, achieving a balance between exploration and exploitation remains a critical challenge in metaheuristic design. The motivation behind this study is to enhance the capability of existing approaches by developing a robust and efficient hybrid approach. The objective is to propose a Binary variant of the Teaching-Learning-Based Optimization-Cheetah Optimization (BTLBO-CO) that leverages the global search strength of TLBO and the local refinement capability of the CO within a wrapper-based framework for optimal feature selection in high-dimensional cancer datasets.

The rest of the sections of the paper are organized as follows. Modern techniques are introduced in Section 2. Section 3 introduces the materials and methods. Section 4 provides a detailed explanation of the suggested model and result analysis. Conclusion and future scope of the study are detailed in Section 5.

When trying to find the optimal value in a high-dimensional space, the single metaheuristic method always has disadvantages, including low accuracy, poor generalization performance, and poor local optima avoidance ability. Using the differences between the two optimization approaches, the hybrid method combines their advantages and balances their shortcomings to improve general performance in addressing challenging optimization tasks. Pashaei and Pashaei [9] presented an ML model to choose biomarkers. For the selection of stable informative genes, the Binary COOT algorithm is combined with simulated annealing (SA) to improve the local exploitation capacities of the algorithm. Furthermore, used as a pre-filtering technique to minimize duplicated genes, known as minimum redundancy maximum relevance (mRMR). A wrapper-based FS method is built using an enhanced hybrid metaheuristic methodology derived from Grey Wolf Optimization (GWO) and Whale Optimization Algorithm (WOA). The main goal of the proposed approach is to reduce the shortcomings of both approaches, including early convergence and stagnation of local optima. Enhanced mechanisms for both algorithms [10] help them hybridize. In this study, a two-stage model called Mine Blast Algorithm (MBA)-Simulated Annealing (SA) is suggested to improve the feature selection process. Here, SA is a local search to improve the solutions discovered by MBA [11] in the exploitation phase. Based on the Mayfly Algorithm and the Harmony Search metaheuristics put forth by [12], Mayfly Harmony Search (MA-HS) is a new feature selection tool. By better use of the search space, combining harmony search with the Mayfly Algorithm increases the performance of the Mayfly Harmony Search (MA-HS) method. This work offers a novel wrapper-based feature selection method intended to address feature selection problems based on biogeography-based optimization (BBO) hybridization and the sine-cosine algorithm (SCA). The BBO algorithm integrates the location update mechanism of the SCA algorithm to enhance habitat variety [13]. In this work, a hybrid Sine Cosine Ant Lion Optimizer (SCALO) is developed that combines the Sine Cosine Algorithm (SCA) with the Ant Lion Optimizer (ALO). The proposed method is carried out on the basis of transfer functions. In this work, a hybrid Sine Cosine Ant Lion Optimizer (SCALO) is presented and assigned to its binary counterparts using the concept of transfer functions [14]. In [15], a hybrid algorithm with integration of Sine Cosine and Cuckoo Search Algorithm was proposed to handle the high-dimensional cancer datasets. Similarly, SCHO-GO [16] is a novel hybrid model with a combination of a genetic operator with Sinh Cosh Optimizer to prevent the limitation of falling into local optima. The performance of the proposed model is tested with eight gene expression microarray datasets. To balance the gap between exploration and exploitation, a hybrid model, based on Grey Wolf Optimizer(GWO) and Harris Hawks Optimizer (HHO), is proposed to handle cancer datasets [17]. For an accurate prediction of diabetes cases, the authors in [18] presented a unique machine learning model with the integration of the Al-Biruni earth radius and the dipper-throated optimization. To enhance the effectiveness of performance, the authors presented a PSO-based multi-objective feature selection method to deal with a high-dimensional dataset [19]. To deal with the curse of dimensionality issue, the authors presented a multiobjective cuckoo search feature selection model. In this approach, an S-shaped transfer function is used to convert from continuous to binary search space [20]. In [21], the authors proposed a problem-specific non-dominated sorting GA algorithm to select the best optimal feature subset. A mutation-retry operator and a combination operator were adopted in this study to enhance the efficiency of the model. In [22], a novel hybrid model named iBABC-CGO is proposed with a combination of the island model of the artificial bee colony algorithm and the chaos game optimization algorithm with an SVM classifier to enhance the classification accuracy.

Many of the widely used optimization techniques in machine learning applications involve several tuning values that have to be optimized for the best efficiency. One challenging aspect of the feature selection process is the tuning of these parameter values. TLBO is a simple metaheuristic algorithm that needs two parameters, such as population size and termination criteria. TLBO is implemented in various areas such as FS, text classification, machine design, robotics, etc. Using a fuzzy adaptive mutant PSO coupled with the TLBO algorithm, Shahbeig et al. [23] identified a subset of related genes from the breast cancer microarray data set and evaluated performance using SVM classification. A novel hybrid TLBO method that solves classification problems with University of California, Irvine (UCI) data using extreme learning machines (ELM) [24]. To avoid early convergence of TLBO and also improve the performance of the proposed model, Rezaei & Fard proposed a hybrid model combining a marine predator algorithm with a teaching-learning-based optimization algorithm [25]. To improve the classification performance of bioinformatics data [26], a two-stage hybrid TLBO method (TS-TLBO) is proposed. In this study, the concept of opposition-based learning is used to improve the quality of solutions. Pan et al. [27] proposed a modified version of TLBO using the hierarchical learning scheme. In this study, 25 different UCI datasets are used to evaluate the performance of the proposed model. A hybrid TLBO with the Salp swarm algorithm (SSA) is combined to select the optimal features of the digital mammography data set. In this model, an artificial neural network (ANN) is implemented as a fitness evaluator [28]. To avoid limitations such as the slow convergence speed of the salp swarm algorithm(SSA), a hybrid model with a combination of TLBO and SSA was designed, and the efficacy of the model was tested with various benchmark datasets. In [29], the authors presented a survey about the application of various machine learning models for the accurate detection of Alzheimer’s disease. Similarly, in [30], the authors presented a deep study about how explainable AI (XAI) plays an important role in easy and accurate prediction of neurodegenerative disorders. A lung cancer predictive model is proposed by integrating the K-means algorithm with different metaheuristic algorithms [31]. Similarly, Das et al. in [32] developed a deep learning enriched marine predictor algorithm for leukemia cancer prediction using cancer image datasets. To solve complex engineering problems, a novel model is presented by hybridizing the artificial rabbit algorithm with a chaotic local search model [33]. Similarly, a novel TLBO-Elephant Herding Optimization (EHO) hybrid model is proposed by [34] to identify the malignant features from breast cancer datasets. Authors in [35] proposed a Probabilistic Bi-Level TLBO model to select the significant features from cancer image datasets. In [36], a deep learning model with various pretrained models is implemented for the accurate selection of biomarkers from a cancer dataset. A hybrid model called TLBO + MPA ([37]) and TLBO + Jaya ([38]) was proposed to deal with various complex problems and NSL-KDD datasets. The importance of TLBO encouraged the development of a new hybrid model to deal with microarray cancer datasets.

There has been a remarkable improvement in feature selection algorithms; however, as stated by the No Free Lunch (NFL) theorem in optimization, no single algorithm can address every problem optimally. Even with the progress of wrapper-based methods, there is still room for innovation. The next section will explore a new hybrid wrapper-based feature selection technique.

All microarray data sets used in this study consist solely of continuous gene expression features; therefore, categorical variable encoding was not applicable. The preprocessing steps included handling missing values and normalizing the expression levels to ensure comparability across samples. The current research proposed a feature selection technique integrated with the TLBO and CO feature selection algorithms. Prior to these algorithms, the proposed work also employs three filter-based approaches, including mRMR, ReliefF, and IG, to select the relevant features from the original feature set. To present the most relevant features, the proposed model concatenates the generated features of each filter-based approach with the objective of removing redundant features and maximizing the feature space. Then, TLBO is applied to select the optimal feature set. To initialize the initial population of TLBO-CO, the following is used. For the final classification process, the support vector machine (SVM) is used as the classifier.

The PyCharm Integrated Development Environment (IDE) was used to carry out the experiments. The PC running the algorithms has a 2.67 GHz Intel i5 CPU and 16 GB of RAM. Each algorithm is run ten times in this scenario, and the mean value that is produced is used as the accuracy for evaluation. An SVM classifier is employed to assess the efficacy of the developed model. 10 CV validations are applied to each algorithm. Several performance metrics were used to evaluate the effectiveness of the model, and precision was found to be one of the most important features. Performance is evaluated on several parameters, including accuracy (ACC), precision (PRE), recall (REC), specificity (SPE), F-1 score (F1−S), false negative rate (FNR), false positive rate (FPR), and Mathews correlation coefficient (MCC). These parameters can be defined using Eqs. (21)–(29) with t1, t2 as true positive and true negative, f1, and f2 as false positive and false negative, respectively. To assess the efficacy of the hybrid FS model proposed in this study, different traditional methods, such as the PSO, GA, GWO, FA, and JAYA algorithms, were used. The parameter values adopted for different algorithms are shown in Table 4. The empirical analysis of BTLBO-CO is summarized in Table 5 and Fig. 2.(21)ACC=t1+t2t1+f1+t2+f2 (22)MCR=f1+f2t1+f1+t2+f2 (23)PRE=t1t1+f1 (24)REC=t1t1+f2 (25)F1−S=2⋅t1t1+f1⋅t1t1+f2t1t1+f1+t1t1+f2 (26)SPE=t2t2+f1 (27)FNR=f2t1+f2 (28)FPR=f1f1+t2 (29)MCC=(t1⋅t2)−(f1⋅f2)(t1+f1)(t1+f2)(t2+f1)(t2+f2)

BTLBO-CO obtained an ACC of 93.71% on the 11_tumor dataset, with a REC of 97.97% and F1-S of 96.03%, the model clearly found real positive examples and kept a strong balance between accuracy and recall. On the other hand, a high FPR of 18.00% and a much lower SPE of 82.00% reveal that the model was very prone to misclassifying negative data as positive. The MCC of 83.57% shows a significant connection between predicted and actual class labels, thereby supporting the dependability of the model.

Table 6 shows a comparative analysis of the proposed approach with the mentioned traditional feature selection methods. For 11_tumors (T), the proposed BTLBO-CO outperforms the performance of PSO by ∼13.20%, GA by ∼12.40%, GWO by ∼1.37%, FA by ∼3.98%, and JAYA by ∼1.18%. Using Lung Cancer (LUC), the performance of the proposed model outperforms PSO, GA, GWO, FA, and Jaya by ∼36.48%, ∼29.51%, ∼9.94%, ∼7.93%, and ∼8.72%, respectively. While considering the Leukemia (LEU) dataset, the proposed BTLBO-CO outperforms the traditional PSO, GA, GWO, FA, and Jaya by ∼30.41%, ∼22.46%, ∼12.30%, ∼7.09%, and ∼4.44%, respectively. Similarly, for the SRBCT (SR) dataset, the BTLBO-CO outperforms traditional PSO, GA, GWO, FA, and Jaya by ∼15.40%, ∼15.35%, ∼9.64%, ∼2.32%, and ∼8.67%, respectively. Considering the DLBCL (DL) dataset, the BTLBO-CO outperforms PSO, GA, GWO, FA, and Jaya slightly by ∼1.32%, ∼0.20%, ∼0.85%, ∼10.09%, and ∼4.18%, respectively. Using the Prostate Tumor (PT) dataset, the proposed model outperforms the PSO, GA, GWO, FA, and Jaya slightly by ∼3.21%, ∼2.31%, ∼1.44%, ∼6.15%, and ∼6.80%, respectively. Fig. 4 shows the performance comparison of the proposed work with traditional methods.

This paper proposes a hybrid feature selection model named BTLBO-CO. The multifilter method serves as a filtering technique to choose the most significant characteristics from the dataset. The hybrid BTLBO-CO is subsequently employed to identify the most appropriate feature subset from those previously established using the filter approach. This model has been evaluated on six distinct cancer datasets, including 11_tumors (T), Lung Cancer (LUC), Leukemia (LEU), SRBCT (SR), DLBCL (DL), and Prostate Tumor (PT), to demonstrate its efficacy with cancer datasets. The results demonstrate superior classification accuracy across all six datasets, achieving 93.71%, 96.12%, 98.13%, 97.11%, 98.44%, and 98.84%, respectively. The results analysis validates the model’s effectiveness compared to the benchmark model.

The BTLBO-CO algorithm demonstrated notable efficacy despite the several restrictions included in this investigation. The study is confined to a particular group of six high-dimensional cancer datasets, which may not adequately reflect the diversity of real-world medical data. Secondly, computing performance may still be impeded by exceedingly huge datasets. Moreover, reliance on wrapper-based assessment utilising a classifier may elevate computational cost. The work may be expanded to include multi-objective optimization parameters. Although the current study aims at combining the BTLBO with CO to realize functional feature selection in correlation to the traditional classifiers, the proposed methodology is adaptable to encompass the deep learning techniques. Within the frame of such a hybrid environment, the deep learning techniques, including Convolutional Neural Networks (CNNs), Deep Belief Networks (DBNs), or Autoencoders, may be initially used in order to learn higher-order non-linear representations of raw medical data. These deep feature representations could then be used with BTLBOCO to pick a good subset, which might increase the classification accuracy and generalization property that may be degraded by removing the redundant features or noisy features. Such a coupling can be used to complement the power of cancer typologies that are otherwise more powerful, especially in conditions where the raw data are real, not only heterogeneous but also high-dimensional. Nevertheless, deeper learning would necessitate the need for bigger annotated datasets and more computing resources, which cannot always be available in any clinical setting. Investigation into such deep learning hybrid frameworks can therefore form a potential line of future research.