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An Improved Deep Convolutional Neural Network by Using Hybrid Optimization Algorithms to Detect and Classify Brain Tumor Using Augmented MRI Images

Automated brain tumor detection is becoming a highly considerable medical diagnosis research. In recent medical diagnoses, detection and classification are highly considered to employ machine learning and deep learning techniques. Nevertheless, the accuracy and performance of current models need to be improved for suitable treatments. In this paper, an improvement in deep convolutional learning is ensured by adopting enhanced optimization algorithms, Thus, Deep Convolutional Neural Network (DCNN) based on improved Harris Hawks Optimization (HHO), called G-HHO has been considered. This hybridization features Grey Wolf Optimization (GWO) and HHO to give better results, limiting the convergence rate and enhancing performance. Moreover, Otsu thresholding is adopted to segment the tumor portion that emphasizes brain tumor detection. Experimental studies are conducted to validate the performance of the suggested method on a total number of 2073 augmented MRI images. The technique's performance was ensured by comparing it with the nine existing algorithms on huge augmented MRI images in terms of accuracy, precision, recall, f-measure, execution time, and memory usage. The performance comparison shows that the DCNN-G-HHO is much more successful than existing methods, especially on a scoring accuracy of 97%. Additionally, the statistical performance analysis indicates that the suggested approach is faster and utilizes less memory at identifying and categorizing brain tumor cancers on the MR images. The implementation of this validation is conducted on the Python platform. The relevant codes for the proposed approach are available at: https://github.com/bryarahassan/DCNN-G-HHO.

the tumor accurately. Different kinds of machine learning approaches have been utilized for identifying the tumor through the MRI along with the k-means, thresholding, Fuzzy C-means (FCM), level set approaches, and kernel extreme learning machine (KELM) [10,11]. Even though machine learning techniques have some issues, such as interpretation of results, high error susceptibility [12]. To overcome the issues, deep learning-based approaches are creating more attention. Deep learning methods are preferred for the segmentation process, particularly CNN is best for recognizing patterns [13]. Moreover, these approaches absorb the features in terms of hierarchy while comparing with the other statistical methods, including support vector machine (SVM); these depend on the hand-crafted features [14]. Deep CNN approaches are successfully implemented for analyzing the clinical images with the retrieval, segmentation, and classification [15].
Based on the previous works presented above, the following are the difficulties of brain tumor detection encountered by current methodologies: • The first disadvantage of the current models is their binary categorization of tumors, creating further ambiguity for the radiologist. Additionally, a lack of data hinders the researcher's inability to get reliable results [16].
• Tumor categorization using brain imaging is a challenging task for two reasons. The first reason is that brain tumors exhibit a great degree of variability in size, severity, and form.
The second reason is that tumors come in various pathological varieties, showing the same symptoms [17].
• In [18], a method called Adaptive Convex Region Contour (ACRC) was developed for segmenting brain tumors using magnetic resonance imaging. The SVM was used to categorize the slice to determine whether it was expected or pathological. Furthermore, the technique demonstrated enhanced performance and resolved high dimension, short sample size, and nonlinearity problems. However, this method required tremendous feature values, introducing noise into the classification results.
• In [19], a convolutional neural network-based deep learning model was developed to identify different brain tumors. While deep learning methods improve tumor classification, they need a large amount of training data for analysis. Moreover, the computational cost and training time associated with brain tumor classification are substantial.
• Segmentation and identification of tumorous areas from brain MRIs are complicated and take much time for analysis. In addition, the method's accuracy is significantly impacted when identifying brain tumors [20].
The images used to identify brain tumors are important since brain tumors are considered the most severe illness. Accurate diagnosis of a brain tumor may enable the tumor's precise location in the brain to be determined. As a result, the mortality rate will decrease. Thus, it is critical to detect hidden patterns to improve images and the diagnostic process. However, obtaining an appropriate diagnosis for the different lesion types becomes difficult, regarded as the primary issue. To address this issue, traditional methods are employed, including presenting a DCNN based on the enhanced HHO methodology. This study aims to provide a method for detecting brain tumors that incorporate a DCNN presentation based on the improved HHO. The proposed approach automatically detects brain cancers in magnetic resonance images, with feature extraction doing the classification. To begin, magnetic resonance images of the brain are regarded as input for preprocessing to create images suitable for subsequent processing. The pre-processed images are then subjected to the segmentation process using the Otsu thresholding method. Once the segmentation procedure is complete, extracting the texture and statistical characteristics from each segment could be carried out. The characteristics include the tumor's size, variance, and mean. Moreover, these retrieved features are formulated in the feature vector. Finally, the detection of brain tumors is carried out using DCNN and the feature vector, where the Deep CNN method is trained using improved HHO. The suggested approach enhanced HHO combines the standard GWO and HHO optimizations to benefit practical classifier training.
This research is distinguished from earlier ones by the following significant contributions: • G-HHO improves DCNN to detect and classify brain tumors from augmented MRI images effectively; • The G-HHO has the features of GWO and HHO; • Otsu thresholding is used to segment the tumor part, emphasizing the identification of brain tumors; • Experiments are conducted by the Python platform on vast augmented MRI image datasets; • The performance of the suggested DCNN-G-HHO is improved and enabled better detection and classification results.
The remainder of this research paper is ordered as follows: Section 2 describes the traditional brain tumor detection methods used in the literature and the difficulties encountered, which served as the motivation for creating the suggested approach. Section 3 describes the recommended technique for detecting brain tumors using DCNN based on improved HHO. Section 4 proposes G-HHO to improve DCNN to classify brain tumors. Experimental results are also discussed in Section 5. Section 6 compares the suggested approach to alternative ways, and Section 7 concludes remarks of this work.

Literature review
Brain tumors are a particularly aggressive kind of cancer that may result in significant problems in the human body. Thus, early, and accurate identification of a brain tumor may significantly improve the chance of survival. However, proper identification of various tumor types is a difficult problem. Thus, developing an efficient tumor representation via an optimization algorithm is critical toward successful brain tumor identification. Ten current methods for detecting brain tumors are examined in this research work, and the shortcomings of each approach serve as inspiration for developing a new brain tumor detection strategy. Thaha MM et al. [21] have presented the enhanced convolutional neural network for the computerized segmentation process using the BAT algorithm. Furtherly, they have used skull stripping and image enhancement algorithms for the pre-processing. Chen S et al. [22] have presented the segmentation models, such as multi-level deep medic, dual force training scheme, auxiliary classifier, and multi-layer perceptron-based post-processing approach to improving the standard of the hierarchical features for detecting brain tumors. Nonetheless, they failed to provide enhanced segmentation capability for the deep architecture to avoid the individual post-processing steps. Anaraki AK., Ayati M., and Kazemi F., [23] have presented the hybrid method based on the Genetic Algorithm (GA) and convolutional neural network (CNN) to categorize the various category of glioma by MRI.
Furtherly, an ensemble algorithm was used to reduce the prediction error variance. Talo M et al. [24] have presented pre-trained models for automatically classifying MR images, such as AlexNet, egg-16, ResNet -18, ResNet-34, and ResNet-50. The images are categorized into normal, cerebrovascular, neoplastic, degenerative, and inflammatory diseases classes. Toğaçar M et al. [25] have presented the convolutional neural network model called BrainMRNet based on the attention modules using the augmentation and hyper column approaches. Where Accessible magnetic resonance images were utilized to identify the brain tumor along with the brainMRNet model. Özyurt F et al. [26] have presented the hybrid method of Super-resolution fuzzy-c-means CNN (SR-FCM-CNN) based on the convolutional neural network, and the learning machine algorithm, and fuzzy c-means to identify the brain tumor. Where features are extracted by the squezeeNet architecture from the CNN model. Sharif M et al. [27] have presented the brain surface extraction method to get skull removed images. They have presented particle swarm optimization (PSO) for segmentation purposes. They have used GA for feature selection. Also, artificial neural networks and classifiers were used to categorize the tumor levels. Navid Ghassemi et al. [28] have presented the deep learning technique to classify brain tumors in MRI images. Where deep neural network was pre-trained in a generative adversarial network (GAN) to separate the features and analyze the structure of MR image within its convolutional layer. Zeineldin RA et al. [29] have presented the Deepseg technique from the genetic deep learning architecture to provide computerized identification and segmentation of tumors through the FLAIR MRI data. For the extraction process, they were used CNN. The CNN models, such as dense convolutional network (DenseNet), NASNet, and residual neural network (ResNet) were used based on the improved architecture of U-Net. Vijh S et al. [30] have presented the particle swarm optimization with the Otsu algorithm for automatically diagnosing the brain tumor. An anisotropic diffusion filter was used to eliminate the noise, and a convolutional neural network was used for the classification process. Finally, the most recent research work has presented an optimization-based approach, called Whale Harris Hawks optimization (WHHO), for brain tumor diagnosis utilizing magnetic resonance imaging (MR) images [20]. Segmentation was carried out utilizing cellular automata and rough set theory, and several parameters were retrieved from the segments. Furthermore, brain tumor diagnosis was accomplished via DCNN, which was trained using the proposed WHHO. The  Based on the above-presented table, current methods' difficulties are (i) Insufficient precision in identifying brain tumors. (ii) Inaccurate classification of brain tumors. (iii) Lack of using large MRI image datasets as input data. Therefore, this paper provides the following contributions for mitigating the limitations of the current algorithms: • G-HHO enhances DCNN to identify and classify brain malignancies from enhanced magnetic resonance imaging pictures more efficiently.
• G-HHO provides all the good characteristics of both GWO and HHO.
• Otsu thresholding is used to segment the tumor portion, emphasizing the detection of brain tumors.
Additionally, Table (2) indicates the primary questions of this work and how we have addressed them.

The proposed methodology
During brain tumor detection, the accuracy level of the images is considered an essential one because brain tumors are considered the most critical disease. Accurate diagnosing of a brain tumor may identify the exact affected portion of the brain. Thus, it will reduce the death rate. Therefore, it is essential to identify the hidden patterns to enhance the quality of images and enhance the diagnosis process. But attaining accurate diagnosis for the various lesion cases becomes a complex one, considered the main problem. To overcome this problem, conventional techniques are used, such as a DCNN based on the improved HHO technique, are presented. The presented model automatically identifies brain tumors from the MR images, where feature extraction executes the classification. Firstly, MR images of the brain are considered input for pre-processing to make the images for further processing. After that, the pre-processed images are induced to the process of segmentation through the Otsu thresholding technique. Once the segmentation process is Here, denotes the ℎ image and denote the MRI image's total count in the Database.
In the following sub-sections, three components (Pre-processing, Segmentation using Otsu threshold, and feature extraction) of the proposed DCNN-G-HHO are detailed.
The proposed method consisted of the following stages:

Pre-processing
The primary usage of pre-processing is providing a further smooth process of the input image. The pre-processing step is more required to make the images appropriate for the identification process for processing the image. Furtherly, the pre-processing is executed to remove the artifacts and noises presented in the extracted images. Thus, the pre-processing step performs image enhancement to improve the contrast of the images to detect the brain tumor. Then, for the segmentation process, the pre-processed images are given for fetching the essential features which are more suitable for identifying the tumor.

Segmentation
Using the cellular automata model, the pre-processed images are given to the segmentation module to produce segments. The pre-processed images contain various elements, and every segment denotes the separate regions. In brain tumor identification, Otsu thresholding is employed to discover the cancerous portions by each component.
Otsu algorithm can be distinguished among the foreground and background of the images by setting the image above the calculated value of grayscale. Before executing the segmentation algorithm, the Otsu algorithm needs to calculate the image's grey level histogram. The primary purpose of the Otsu technique is to discover the threshold that reduces the intra-class variance, and it can be described as the two-class weighted sum of variances as shown in Equation (2) [31].
Where, 0 and 1 represent the weights that are the possibilities of the classes, and by the threshold value t, these weights are separated. 0 2 and 0 2 represent the variances of two classes.
After that, the images are binarized more than the threshold value, and covering the holes presented in the segmented image can be made by executing the morphological operations. Furtherly the segmented images are masked upon the original images; thus, the segmented tumor is attained.

Feature extraction
By now, numerous research on deep feature extraction approaches has been conducted, with promising results for image classification. One of the feature extraction models was proposed by [32] to combine both approaches into a unified framework and to develop an unsupervised linear feature selective projection (FSP) with low-rank embedding and dual Laplacian regularization exploit the intrinsic relationship between data and suppress the impact of noise. The proposed approach outperformed existing state-of-the-art algorithms for feature extraction in the presence of different types of noise. Another study conducted by [33] for feature extraction, took into consideration both the minimizing of reconstruction error and the maximizing of variance in a unified framework. The experimental findings from multiple databases demonstrated the model's efficacy. However, it was expected to explore a more straightforward but efficient method for its selection. Last but not least, unsupervised multi-view feature selection using cross-view local structure-maintained diversity and consensus representation learning was suggested by [34].
Projecting each original data view onto a shared label space with a consensus component and a diversity part captures shared and distinct knowledge across images. Numerous pre-defined viewspecific similarity graphs are employed to train a shared similarity network across views. Despite its shortcomings, the suggested method's effectiveness is shown by a parameter sensitivity analysis on real-world Multiview datasets.
To address the limitation of the above studies, the feature is obtained from the MRI input images to create a feature vector. When attaining the segments, the features are extracted, and it carries out the pre-processed images for every segment. The feature extraction assures the effectual identification of brain tumors because it involves texture and statistical features. For extracting the features, every segment considers it for attaining better accuracy in detecting brain tumors. As earlier discussed, from each segment the feature extraction proceeds in terms of tumor size, mean, variance. This can be described below:

Mean
The mean value can be computed by summarizing the entire numbers presented in the dataset and dividing it by the total count of the number presented in the dataset. The mean value is considered the vital parameter for the image segmentation process. A two-layer feed-forward neural network can forecast the growth of the tumor within the 16% MSE. The mean can be computed by calculating the pixel's average presented in the image, and it can be mathematically expressed as formulated in Equation (3).
Here, n represents the total segments, ( ) denotes the every segments pixel values and | ( )| represents the total pixel of the segment.

Variance
Measuring the spread among the numbers of a dataset is known as a variance. This variability implies measuring the distance between each number from another number in a dataset. Variance can find the reasons for the deviation in the brain, and it helps recognize the tumor cells in the brain. The variance features are computed and mathematically expressed in Equation (4) according to the mean value.

Tumor Size
From the Brain MR images, tumor size extracts the features to detect the brain tumor. Tumor segmentation process from the brain MRI contains various covering pathology such as MRI material science, perception of radiologist and analysis of the image. A brain tumor can be of any size; it has different shapes and may locate on any portion and may show deviation in the image intensities.
The variable Q indicates the tumor affected boundary, the derivation of the area of feature vector from the tumor-dominated portion. Q is mathematically represented in Equation (5).
Where L represents the length of the tumor size, W denotes the width of the tumor size.

Formation of the feature vector
The below expression describes the set of texture and statistical features. Therefore, the extracted features of every segment are represented as shown in Equation (6).
Where J represents the extracted feature vector by each segment such as , , , denotes the mean. denotes the variances. , indicate the tumor size. After that, the extracted feature vector is fed to the DCNN, which categorizes the images based on the given features, and forms the class label. The classifiers are used to formulate the class label and segregate the cancerous and noncancerous cells concerning the input image.
This section, presents the proposed G-HHO technique to detect the brain tumor where the detection process is executed with the consideration of a feature vector. Moreover, the extracted features are further processed for classification by DCNN trained with enhanced HHO to classify the tumor.
In the improved HHO, the parameters of GWO are utilized; therefore, the performance of HHO can be improved. Based on the social behavior of the GWO is developed. The GWO algorithm is more suitable to get optimum global results because it gives a better convergence rate [35].
Moreover, GWO can resolve real-time problems and complicated search spaces. Also, HHO is adopted from Harris's hawks' helping and chasing behavior. This approach is more effective for witnessing optimization problems and providing optimum results. Even though the HHO technique has some issues in the search space, such as multi-modality, deceptive optima, and optimal local solution, the proposed work that combines the GWO with HHO (G-HHO) will give better results it limits the convergences rate and enhancing the performance. = { 1 , 2 , … . , ℎ , … . } Here, l denotes the total count of the convolutional layer of the Deep CNN model and ℎ ℎ a convolutional layer of the Deep CNN can be represented by the ℎ . Using the units (p,w), the output can be derived and expressed in Equation (8).
Where the conv operator can be denoted as * and is used for permitting the extraction process of pattern from the results taken out from the adjacent convolutional layer, feature maps can be represented as | ( −1 ) + , + | . total count of feature maps can be denoted by The following three sub-sections are given below for the proposed algorithm (G-HHO).

Rectified linear unit and pooling layer
Rectified linear unit and pooling layer (ReLU) is considered an activation function because its contribution is highly significant in simplicity and efficiency. Moreover, ReLu in Deep CNN provides speed processing with large networks. The output obtained through the ReLu layer is given based on providing feature maps in Equation (9).
Where represents the input and −1 represents the output and () represents the ℎ layer activation function.

Fully connected layers
To initialize the classification process of objects, the patterns of the convolutional and pooling layers are provided as an input to the completely connected layers. The output of the completely corresponding layer can be mathematically expressed in Equation (10).
where, , , , represents the weights (m,n), which is connected with the − 1 layer's ℎ feature map and u layer's ℎ unit. By the proposed G-HHO approach, these weights are optimally tuned.

The network architecture of the proposed DCNN model
The proposed work has six architecture layers that incorporate three convolutional layers, two fully connected layers, and the last layer, one classification layer. These convolutional layers are connected by three rectified linear operator (Relu) layers and max-pooling layers. The initial convolutional layer has a total number of fifty-two filters with a size value of 7 × 7 pixels, a stride of 2 pixels, and no padding is coming after ReLu. A max-pooling layer has a value of 3 × 3 region Hawks Optimization is considered to enhance the performance. The following section illustrates the GWO and HHO in detail.

HHO
HHO technique is considered to enhance the performance of the deep learning technique [38].
HHO is mainly relying on two stages exploration and exploitation. As represented in Figure (2), the following section provides the step-by-step procedure of HHO.

exploration
The first stage is the exploration stage, where the entire Harris Haws represent the candidate solution. Here, fitness value is based on targeted prey that may change every iteration. Equation (11) represents the exploration performance [38].
Where: can be explored, and the random scaled feature enables the diversification technique. Equation (12) represents the average solution position [38]. Where: ( ) => Coordinate average of solutions which is presented in the current iteration,

=>
Whole possible results, The Hawk's prey catching process is based on a random solution that can be achieved through Equation (10 (i)). The entire hawks show the best solution can be done through Equation (10 (ii))

Transition from exploration to exploitation
Based on the rabbit's energy (E), the movement of Harris hawk's optimization from exploration to exploitation is described in this stage.
In this algorithm, the prey (Eng) energy is significant to execute the optimization through the exploration and exploitation shown in the following Equation (13) [38]. The preys escaping pattern will be reduced due to the action of HHO. The energy reduction is indicated from [1, -1] is indicated as 0 . Where: => Overall iterations, => Current iteration.

exploitation
At the time of hunting, the prey takes maximum effort to escape from being attacked. Therefore, HHO executes four different techniques to confuse its prey in the exploitation stage, where the position is highly significant. These techniques are soft besiege, soft besiege with progressive rapid dives, hard besiege, and hard besiege with advanced quick dives.
Based on variables such as and | |. That is escaping probability and prey's energy level, respectively. These two variables are essential in the HHO strategy. The condition applied is r < 0.5, which shows the higher possibility for prey escaping. The ≥ 0.5 condition indicates chances of running are reduced. The following sections provide brief illustrations about each tactic.

a) Soft besiege
Rabbit is the usual prey of Hawks which has adequate energy level to escape from being attacked that can be illustrated by | | ≥ 0.5 and ≥ 0.5. On the other hand, Hawks executes its tactics to minimize its prey energy level by encircling it by soft besieges. This strategy is done before running the surprise pounce of the Hawk. The mathematical derivation is shown in Equation (14) below [38].

=>
c) Soft besiege with rapid dives In this stage, the prey still has some energy for escape with the variable's value of | | ≥ 0.5 and < 0.5. Therefore, the Hawk is smartly encircling the rabbit, and before the performance of surprise pounce, it patiently dives. Here, two steps are utilized to update the hawks' position, and the event of dive is known as intelligent soft besiege. The Hawk moves forward to the rabbit with the help of the prey's next move. Equation (16) [38] is derived from the action above. Hence, the position of the Harris hawks is updated with the progressive rapid dives calculated using Equation (19) [38]. Where:

=> Next location of the new iteration .
This new iteration is performed by utilizing the equations (18) and (19).

d) Hard besiege with progressive rapid dives
Here, the values of variables are | | < 0.5 and < 0.5. In this situation, hawks try to reach the rabbit by rapid dives because it has no more energy to escape. This action is performed before the surprise pounce to catch the rabbit. In this Equation, is updated by utilizing Equation (20), and is accomplished by using Equation (20) [38].
The ( ) is obtained by utilizing Equation (12), the four strategies are helping hawks catch their prey.
With the help of exploration and exploitation techniques of Harris Hawks Optimization, the weightage of the classification technique's parameters is enhanced in the proposed work.
By utilizing the presented enhanced HHO algorithm, the DCNN training process can find the optimum weights for tuning the DCNN classifier. The hyperparameters tuning is done by adopting GWO [39] and HHO. The HHO is improved by utilizing the technique GWO; therefore, the performance of the deep learning technique can be significantly enhanced on performance level.
The proposed work has implemented the HHO strategy to select the optimization problem in choosing the hyper-parameters. This algorithm enables a better searching strategy; therefore, the performance and results can be most effective. As discussed in the previous section, DCNN performance is improved by tuning the parameters of CNN with the G-HHO strategy. The parameters utilized for this work are three convolutional Layers, two fully connected layers, and finally, one classification layer. Each convolutional layer is connected by three ReLu layers and a max-pooling layer. The pseudocode of the proposed method is presented in Algorithm (1)

Experimental setup
This section integrated with the proposed brain tumor detection outcome through an experimental analysis-based Deep CNN model. The proposed model is analyzed and validated with the existing techniques. To prove the performance of the proposed DCNN-G-HHO is highly effective than existing. Therefore, the performance analysis parameters such as accuracy, recall, precision, f1measure are considered. Furthermore, the datasets are initially divided into training and testing, where 70% of datasets are utilized for training, and the remaining 30% are being used for testing.
The implementation of the suggested DCNN-G-HHO is done through the Python platform. The Python source code of DCNN-G-HHO can be accessible in [40].
The following sub-sections are explanations on data description, Implementation components, and performance evaluation.

Dataset description
The brain MRI images are obtained from the open-source datasets from the internet Kaggle [41].
In this work, the MRI scanned image-based datasets are downloaded and utilized. The obtained datasets are fed into Deep CNN-IWOA. That mainly focuses on detecting brain tumor detection and classification by using the deep learning technique. Therefore, MRI-based brain tumor classification can be obtained from massive datasets. The total number of input images is utilized before augmentation is 248, and once after augmentation is completed, the input images are turned into 2073. The sample input images of the proposed work are given in Figure (3). Also, Figure (4) shows the brain tumor image. The following Figure (4) shows the sample images of brain tumor affected MRI images. In each MRI brain image, a strange shape contaminated is a brain tumor. Figure (5) shows the augmentation samples of the proposed work.

Figure (5): Augmented images
The other section describes the implementation requirements of the proposed model.

Implementation components
In this part, the experimental results are discussed and clarified. By using the python software, the implementation process is executed. The performance analysis is conducted to evaluate the proposed approach with the existing precision, F-measure, accuracy, and recall methods. For the training process, 70% of the dataset is used, and for the testing process, 30% of the data set is used for executing the process. The execution process is performed on Windows 10 operating system with 16 GB RAM. The epoch values are taken from 0 to 500. According to [42], the best accuracy is achieved by the 1024 batch size. The author states that based on their results, the higher the batch size, the higher the accuracy, meaning that the batch size has a massive impact on the CNN performance. The batch size is set to 1024 for each epoch on this premise. Also, the kernel size is considered at 5 X 5. Additionally, our proposed classifier is evaluated against the state-of-the-art algorithms regarding execution time and memory usage on the MRI dataset.

Evaluation and result analysis
This section is divided into three sub-sections: performance evaluation, comparative performance analysis, and statistical performance analysis.

Performance evaluation
The presented approach can be estimated by some statistical measurements, such as true negative (TN), true positive (TP), False Negative (FN), and False positive (FP) [43]. These values are represented as a confusion matrix in Table (3).  The F-measure value for the proposed approach is 0.97.   (7) shows that the x-axis represents the epoch value, and the y-axis represents the loss value.
The blue color represents the training process, and the orange color represents the testing process.
The epoch values are taken from 0 to 500.

Figure (8): Accuracy for the proposed model
In Figure (8), the x-axis represents the epoch, and the y-axis represents the accuracy. The epoch values are taken from 0 to 500. The blue color represents the training process, and the orange color represents the testing process.

Comparative performance analysis
In this part, the comparative analysis is described for the presented approach and the existing  Table (4). accuracy, precision, recall, and F-measure from this comparative analysis than the existing approaches. The comparative analysis graph is represented in the bar diagram shown in Figure (9).

Figure (9): Bar diagram for the comparative analysis
The x-axis represents brain tumor detection performance metrics in the above Figure,  brown, dark blue, green, light blue, yellow, light gray, and orange. This coloring clearly shows that the presented approach is performed efficiently in accuracy, precision, recall, and f-measure compared with the existing algorithms. Thus, the proposed method is most preferred for detecting brain tumors.

Statistical performance analysis
This section analyses the overall performance benchmarking of the algorithms (execution time/memory consumption) based on the augmented MRI image dataset.

Conclusion
The main intention of the proposed DCNN-G-HHO was to provide an automated detection model for brain tumors. Therefore, a deep learning-based CNN was considered and enhanced by adopting a hybrid optimization algorithm with a combination of GWO and HHO techniques. Moreover, segmentation plays a significant role in detecting tumors. Accordingly, an Otsu thresholding technique is utilized. As a result, effective segmentation and classification were achieved better results.
The technique's performance was ensured by comparing it with the existing technique on huge augmented MRI images in terms of accuracy, precision, recall, f-measure, execution time, and memory consumption. At first glance, the performance comparison proved that the suggested DCNN-G-HHO was highly effective than current techniques. With 0.97 accuracies for brain tumor diagnosis, the recommended DCNN-G-HHO method outperformed current approaches. This demonstrates the approach's accuracy and effectiveness. The proposed approach has a recall of 0.95, whereas the existing methods had lower recollections than our method. Finally, the Fmeasure for the proposed technique is 0.96. Therefore, the proposed methodology is more efficient than the current methods regarding accuracy, precision, recall, and F-measure. Additionally, the overall performance of our proposed approach was benchmarked in terms of execution time and memory use on the enhanced MRI image dataset. The suggested DCNN-G-HHO was faster at identifying and categorizing brain tumor cancers on the MR images. Similarly, our solution used less RAM than its competing methods. Surprisingly, KNN took longer than the other methods, but SVM consumed the most memory. The DCNN-G-HHO approach was quicker and used less memory than the different classifiers.
The main contributions of the newly introduced DCNN-G-HHO were: • High accuracy and precision of detecting and classifying brain tumors due to the use of G-HHO and Otsu thresholding combined with DCNN; • Massive augmented MRI image datasets were used to provide reliable results; • The performance of the suggested DCNN-G-HHO is improved and enabled better detection and classification results.
Thus, we have designed DCNN-G-HHO as a combination of DCNN and G-HHO with few exploratory and exploitative mechanisms. It is also viable to use other evolutionary strategies such as mutation and crossover, multi-swarm and multi-leader structures, evolutionary updating structures, and chaos-based phases. These operators and concepts are advantageous for future works. Binary and multi-objective variants of G-HHO may be developed in future developments.
Additionally, it may be used to address a variety of issues in engineering and other industries.
Another intriguing avenue is to examine various ways of coping with constraints in real-world restricted scenarios.
Because of its high accuracy, DCNN-G-HHO could be deployed on different applications.
Besides, the modifications, as well as hybridizations of the algorithm, have been a hot spot for scholars. But still, there is room for others to work in improving our introduced algorithm as it can be hybridized with most recent swarm algorithms, such as backtracking search optimization algorithm [44,45], the variants of evolutionary clustering algorithm star [46][47][48][49], chaotic sine cosine firefly algorithm [50], and hybrid artificial intelligence algorithms [51]. Furthermore, DCNN-G-HHO can be applied to more complex and real-world applications to explore more deeply the advantages and drawbacks of the algorithm or improve its efficiencies, such as engineering application problems [50], laboratory management [52], e-organization and egovernment services [53], online analytical processing [54], web science [55], the Semantic Web ontology learning [56], cloud computing paradigms [57][58][59] [60], and evolutionary machine learning techniques [49,61,62].