## 3 Proposed Methodology  
The proposed algorithm depicted in Figure 2 is based on the hyperparameter optimization algorithm Surrogate Model (SM), Acquisition Function (AF), and Tree Parzen Estimator (TPE). When resolving a complicated issue, a penalty-based boundary intersection decomposition strategy is chosen because it gives equally scattered alternatives on the perimeter areas of the Pareto Front and has a limited handful of weight vectors. This is significant in our scenario since training CNN models are strongly non-convex optimization issues, and the AHT-based learning model uses a limited amount of weight matrix to minimize computing complexity. On the other hand, the penalty-based boundary intersection technique, necessitates the determination of a compensation element to optimize the uniformity and variability of the results. On the BraTS MRI and BreakHis dataset, we used the AHT algorithms with 10 lists of hyperparameters with different rangesand with penalty component settings of 0.25, 0.5, 0.75, 1, 3, 5, 7, and 10 for the proposed Deep-Hist neural network. Component 7 was chosen since it gave a varied collection of responses that performed significantly in the optimal solutions. This penalty component has also been utilized in other experiments with positive outcomes. The intensities of the optimization methods can vary in numerous situations. A normalizing procedure is required in these circumstances to approach the optimization method's output to a similar magnitude and reduce biases while choosing non-dominated spots. This normalization is critical in the suggested methodology since the accuracy and F1-Score yield values between [0\(\rightarrow\)1], whereas the range of learnable parameters in a system might easily reach thousands. Adaptive Hyperparameter Tuning (AHT) steps for determining the best Hyper settings are as follows:  
In this approach, to find the optimal hyperparameters of deep learning algorithms that bring back the plausible performance. The representation of hyperparameter optimization is depicted in Equation (3). \[\varkappa^{*}=\arg\min\mathbb{F}(\varkappa) \tag{3}\]  
\(\varkappa^{*}\) depicts the optimized hyperparameters list that predicts the lowest error, \(\mathbb{F}\) which is an objective function to minimize the error (Root Mean Squared Error (RMSE)). In this approach, there is a surrogate function that optimizes the objective function on each iteration and selects the next hyperparameter. The objective function (\(\mathbb{F}(\varkappa)\)) is the main evaluator that finds the optimal set of hyperparameters. Generally, It takes a simple set of hyperparameters and returns a negative score and according to the returned score, the set of hyperparameters will adjust for the next iteration. Using the surrogate function, we can approximate the objective function by proposing parameters to the objective function. A Gaussian Process (GP) depicted in Equation (4) is simply a specific term for a method that takes two values in the input vector, \(\varkappa\) and \(\varkappa^{\prime}\), as an argument and determines how \"related\" they are depending on a certain idea of \"connection.\" Tree Parzen Estimator (TPE - depicted in Equation (5)) and Random Forest Regression (RFR). \[k(x,x^{\prime})=\sigma^{2}\exp\left(-\frac{1}{2\ell^{2}}\|x-x^{\prime}\|^{2}\right) \tag{4}\]  
Figure 2: Proposed a novel Hybrid approach for acquiring intelligently and optimized hyperparameters (AHT): We have passed a sample of the combined dataset to our proposed black box model with lists of hyperparameters to process with both Gaussian Process (GP) and Tree Parzen Estimator (TPE) and then the optimal value will send to Probability Improvement (PI) and Expected Improvement (EI) to obtain the next sample value. where \(\|\varkappa-\varkappa^{{}^{\prime}}\|\to\infty\) then \(k(\varkappa,\varkappa^{{}^{\prime}})\to 0\). The duration of the swivels is determined by the \(\ell\) factor. Usually, it will not be possible to estimate greater than \(\ell\) units from the empirical observations.