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 enhances the performance.
Furthermore, our proposed hybrid approach provides better exploration and exploitation than other meta-heuristic algorithms, such as minimal sequential optimization (SMO), BAT, and PSO. The exploration and exploitation of search areas are calibrated to emphasize exploitation as the iteration counter grows. The suggested DCNN-G-HHO model incorporates a trade-off between the exploitation and exploration phases to identify the optimal solutions and converge to the global optimum. Regardless of the common features among the current meta-heuristic algorithms, The DCNN-G-HHO adds a feature of improved searching spaces. The search processes are divided into exploration (diversification) and exploitation (intensification). The algorithm should maximize the use and promotion of its randomized operators throughout the exploration phase to examine different areas and sides of the feature space thoroughly. Thus, the exploratory behaviors of a well-designed optimizer should be sufficiently random to efficiently distribute more randomly produced solutions around the problem topography during the early stages of the search process [36]. Typically, the exploitation step follows the exploration stage. The optimizer concentrates on the neighborhood of higher-quality solutions situated inside the feature space during this phase. It accelerates the search process inside a specific location rather than throughout the terrain. A well-organized optimizer should strike a sensible and delicate balance between exploration and exploitation inclinations. Otherwise, the likelihood of being caught in local optima and suffering from immature convergence downsides grows.
The algorithmic stages of suggested improved HHO and the structure of the Deep CNN model are defined in Eq. (7).
Here, l denotes the total count of the convolutional layer of the Deep CNN model and \({h}^{th}\) a convolutional layer of the Deep CNN can be represented by the \({T}_{h}\). Using the units (p,w), the output can be derived and expressed in Eq. (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 \(\left| {\left({T}_{p}^{u-1}\right)}_{m+z, r+s}\right|\). total count of feature maps can be denoted by \({W}_{1}^{P-1}\) and \({\left({X}_{f,p}^{u}\right)}_{z,s}\) Denotes the weights, where they are trained by the proposed G-HHO.
The following three sub-sections are given below for the proposed algorithm (G-HHO).
4.3. 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 coming after ReLu. A max-pooling layer has a value of 3 × 3 region and 2 pixels for stride. The result obtained through convolutional layer 1 is 52 × 69 × 69; this result is considered an input value for the next layer. The second convolutional layer has filters 256, and the size of them are 5 × 5 pixels, two pixels for stride, and similar to the first convolutional layer, no padding is set after Rectified Linear unit as well as ReLu, and 3 × 3 regions as a value of max pooling and 2 pixels for stride. The resulting outcome for the second convolutional layer has obtained 256 × 15 × 15 pixels as size as the first convolutional layer. This result is taken as an input to the third convolutional layer. The third convolutional layer is set with 156 filters with a 3 × 3 region and 2 pixels for strides. The third layer result goes to the fourth layer as input; this layer is the fully connected layer with neurons 512. This layer comes after the dropout layer with a probability value of 0.5. At last, the classification layer shows the results with two classes. Using appropriate techniques to tune the hyperparameters of DCNN is significant to improve the classification technique [37]; therefore, the combination of Grey Wolf Optimization and Harris Hawks Optimization is considered to enhance the performance. The following section illustrates the GWO and HHO in detail.
4.3.1. 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.
4.3.2. 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. Eq. (11) represents the exploration performance [38].
$$X\left(i+1\right)=\left\{\begin{array}{c}{X}_{rsolu}\left(i\right)-{r}_{1}\left|{X}_{rsolu}\left(i\right)-{2r}_{2}X\left(i\right)\right| q\ge 0.5 rule \left(i\right)\\ \left({X}_{prey}\left(i\right)-{X}_{m}\left(i\right)\right)-{r}_{3}\left(LB+{r}_{4}\left(UB-LB\right)\right) q<0.5 rule \left(ii\right)\end{array}\right.$$
11
Where:
\(X\left(t+1\right)\) => Represents the position of Hawk’s in the next iteration i.,
\(i\) => Iteration,
\({X}_{prey}\) => Prey's position,
\({X}_{rsolu}\left(i\right)\) => Random solution selection process based on current population,
\(X\left(i\right)\) => Represents the position vector of Hawk's based on the current iteration,
\({r}_{1}, {r}_{2},{r}_{3},{r}_{4}, and q\) => Random scaled factor within range of [0, 1] ( updated in every iteration),
\(LB\) => Lower bound of variables,
\(UB\) => Upper bound of variables,
\({X}_{m}\) => Solution's average number.
Based on two rules, the position of hawks is developed by this targeting strategy within \(\left(UB-LB\right)\).
Two strategies are adopted to determine the Hawks' position (UB-LB). The initial rule is Hawks based solutions are generated randomly based on the current population and other hawks. The second rule is a solution prepared based on the Hawk's average position, the prey's location, and the random scaling factor. These steps help to enhance the randomness of the rule. The randomly scaled action in terms of length is fed to the Lower Bound (LB). Therefore, various feature spaces can be explored, and the random scaled feature enables the diversification technique. Eq. (12) represents the average solution position [38].
$${X}_{m}\left(i\right)=\frac{1}{N}\sum _{i=1}^{N}{X}_{i}\left(i\right)$$
12
Where:
\({X}_{m}\left(i\right)\) => Coordinate the average of solutions which is presented in the current iteration,
\(N\) => Whole possible results,
\({X}_{i}\left(i\right)\) => Each result's location in \({i}^{th}\) iteration,
The Hawk's prey catching process is based on a random solution that can be achieved through Eq. (10 (i)). The entire hawks show the best solution can be done through Eq. (10 (ii))
4.3.3. 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 executing the optimization through the exploration and exploitation shown in the following Eq. (13) [38]. The prey escaping pattern will be reduced due to the action of HHO. The energy reduction is indicated from [1, –1] is indicated as \({Eng}_{0}\).
$$Eng={2Eng}_{0}\left(1-\frac{i}{I}\right), {Eng}_{0}\in [-\text{1,1}]$$
13
Where:
\(I\) => Overall iterations,
\(i\) => Current iteration.
4.3.4. 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 \(r\) and \(\left|Eng\right|\). 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 \(r\ge 0.5\) condition indicates chances of running are reduced. The following sections provide brief illustrations of each tactic.
a) Soft besiege
Rabbit is the usual prey of Hawks which has adequate energy level to escape from being attacked which can be illustrated by \(\left|Eng\right|\ge 0.5\) and \(r\ge 0.5\). On the other hand, Hawks executes its tactics to minimize its prey's energy level by encircling it with soft besieges. This strategy is done before running the surprise pounce of the Hawk. The mathematical derivation is shown in Eq. (14) below [38].
$$\left\{\begin{array}{c}X\left(t+1\right)= \varDelta X\left(t\right)-E\left|{JX}_{rabbit}-X\left(t\right)\right| \\ \varDelta X\left(t\right)={X}_{rabbit}-X\left(t\right)\\ J=2\left(1-{r}_{5}\right), {r}_{5}\in \left[\text{0,1}\right]\end{array}\right.$$
14
Where:
\(J\) => Prey’s jump power,
\({r}_{5}\) => Random variables,
\(X\left(i+1\right)\) => Hawk’s position in the next iteration of i,
\(X\left(i\right)\) => Hawk’s position vector in the current iteration i,
\(Eng\) => Energy of prey,
\(\varDelta X\left(i\right)\) => Variations between the prey's position vector and current location in iteration \(i\).
b) Hard besiege
Here, the rabbit is got tired due to the soft besiege, and its energy is reduced, where the values of the variables are \(\left|E\right|<0.5\) and \(\ge 0.5\).
The soft besiege makes the prey tired (energy level reduced), where the values of variables are \(\left|Eng\right|<0.5\) and \(\ge 0.5\). Then, hawks process the surprise pounce hardly, and encircle the prey. The derivation is shown in Eq. (15) [38].
$$X\left(t+1\right)= {X}_{rabbit}\left(t\right)-E\left|\varDelta X\left(t\right)\right|$$
15
c) Soft besiege with rapid dives
In this stage, the prey still has some energy for escape with the variable's value of \(\left|E\right|\ge 0.5\) and\(r<0.5\). 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. Eq. (16) [38] is derived from the action above.
$$Y={X}_{prey}\left(i\right)-Eng\left|{JX}_{prey}\left(i\right)-X\left(i\right)\right|$$
16
Then, the possible results are compared based on movements executed at earlier dive to decide whether it is a good dive.
The Hawk generates irregular dives when decisions are not taken based on the levy flight (LF) method. This generation is formulated in Eq. (17) [38].
$$Z=Y+S\times LF\left(Dim\right)$$
17
Where:
\(Dim\) => Dimension of solutions,
\(S\) => Random vector of size \(1\times dim\),
\(LF\) => Levy Flight function.
The levy flight function is calculated by using Eq. (18) [38].
$$LF \left(x\right)=0.01\times \frac{u\times \sigma }{{\left|v\right|}^{\frac{1}{\beta }}}, \sigma ={\left(\frac{{\Gamma }(1+\beta )\times \text{s}\text{i}\text{n}\left(\frac{\pi \beta }{2}\right)}{{\Gamma }\left(\frac{1+\beta }{2}\right)\times \beta \times 2\left(\frac{\beta -1}{2}\right)}\right)}^{\frac{1}{\beta }}$$
18
Where:
\(\beta\) => Default constant which is automatically set as 1.5,
\(u,v\) => Random values within [0,1].
Hence, the position of the Harris hawks is updated with the progressive rapid dives calculated using Eq. (19) [38].
$$X\left(t+1\right)=\left\{\begin{array}{c}Y if F\left(Y\right)<F\left(X\right(t\left)\right)\\ Z if F\left(Z\right)<F\left(X\right(t\left)\right)\end{array}\right.$$
19
Where:
\(Y and Z\) => Next location of the new iteration \(t\).
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 \(\left|Eng\right|<0.5\) and \(r<0.5\). 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, \(Z\) is updated by utilizing Eq. (20), and \(Y\) is accomplished by using Eq. (20) [38].
$$Y={X}_{prey}\left(i\right)-E\left|{JX}_{prey}\left(i\right)-{X}_{m}\left(i\right)\right|$$
20
The \({X}_{m}\left(i\right)\) is obtained by utilizing Eq. (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.
4.3.5. The proposed G-HHO for brain tumor detection
By utilizing the presented enhanced HHO algorithm, the DCNN training process can find the optimum weights for tuning the DCNN classifier. The hyperparameter 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):
Algorithm (1): Pseudocode of the Proposed G-HHO
Inputs: N denotes population size, and the maximum number of iterations is i
Outputs: determine the best fitness value, RMSE
then
Initialize new population Wj where J ϵ 1,2,3,.., NP of Grey wolf Optimization
Initialization of a, \(\overrightarrow{C}\), and \(\overrightarrow{A}\),
Compute the fitness value by utilizing every search agent's objective function
Allot
Walpha →
the search agent's best fitness value
Wbeta →
the search agent's second-best fitness value
Wdelta →
the search agent's second-best fitness value
Upgrade the location of Wj (Grey Wolf Optimization) utilizing Harris Hawk
While ( i〈imax) for each search agent
Upgrade the location of the present search agent
End for
Upgrade the value of a, \(\overrightarrow{C}\), and \(\overrightarrow{A}\),
Upgrade the value of Walpha ,Wbeta andWdelta
i = i + 1
end while
Return Walpha