## 4 Framework
### HPA-C Framework
It provides a detailed analysis of the time complexity of the proposed HPA-C and a comparison with baseline algorithms, including GWO, PSO, GA, and Relieff. HPA-C is primarily based on GWO while incorporating enhancements inspired by the ABC and BA. These modifications improve the exploration and exploitation phases but do not introduce additional iterations, keeping the overall complexity comparable to that of GWO. **Initialization Phase:**

\[O(P\times D)+O(P\times f(D)),\]

where \(P\) is the population size, \(D\) is the feature number, and \(f(D)\) represents complexity of the fitness evaluation. **Iterative Optimization Phase:** The computational steps per iteration are outlined as follows:

* Position updates (based on GWO structure with ABC and BAT modifications): \(O(P\times D)\)
* Binary discretization (constant-time adjustments): \(O(P\times D)\)
* Fitness evaluation and sorting: \(O(P\times f(D))+O(P\log P)\). The total complexity per iteration remains as follows:

\[O(P\times(D+f(D))+P\log P).\]

Since the core framework is GWO, the additional computations from ABC and BAT do not introduce new loops or higher-order terms, preserving the asymptotic complexity. Thus, in theoretical terms, the complexity of HPA-C remains identical to that of GWO. For max_iterations iterations, the overall complexity is expressed as follows:

\[O(\texttt{max\_iterations}\times P\times(D+f(D)+\log P)).\]

Table 3 showcases a comparative analysis of the time complexities of HPA-C and the baseline algorithms. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Algorithm** & **Per-Iteration Complexity** & **Overall Complexity** \\ \hline GWO & \(O(P\times(D+f(D))+P\log P)\) & \(O(\texttt{max\_iterations}\times P\times(D+f(D)+\log P))\) \\ PSO & \(O(P\times D+P\times f(D))\) & \(O(\texttt{max\_iterations}\times P\times(D+f(D)))\) \\ GA & \(O(P\times D+P\times f(D)+P\log P)\) & \(O(\texttt{max\_iterations}\times P\times(D+f(D)+\log P))\) \\ Relieff & \(O(f(D))\) & \(O(f(D))\) \\ HPA-C & \(O(P\times(D+f(D))+P\log P)\) & \(O(\texttt{max\_iterations}\times P\times(D+f(D)+\log P))\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of time complexities of HPA-C and baseline algorithms. The computational complexity of HPA-C remains comparable to that of GWO. The additional computational overhead from ABC and BAT is minimal, since no extra loops or high-order dependencies are introduced, ensuring computational efficiency. ### Proposed CNN Framework

The proposed 17-layer CNN is specifically designed for feature-based classification. It strikes a balance between efficiency and accuracy; the architecture is shown in Figure 2. Compared with traditional CNNs that process raw images, our model has structured feature representations (\(1\times 1\times num\)_Features_) as input, reducing computational overhead. The architecture primarily has three convolutional layers, each followed by batch normalization and ReLU activation. Their combinations are represented as LC1, LC2, and LC3. The first and third convolution layers use \(3\times 3\) kernels to capture local feature patterns, while the middle \(1\times 1\) convolution layer in LC2 acts as a bottleneck to reduce dimensionality and improve computational efficiency. A max-pooling layer (stride = 2) is used to refine feature representations. It is followed by a dropout layer (50%) to enhance generalization. The model transitions into a 128-neuron dense layer with ReLU activation before reaching the final softmax and classification layer. Different alternative architectures and activation functions were considered during the design phase. Deeper networks with additional convolutional layers or larger dense layers (e.g., 256 or 512 neurons) were tested but did not provide significant performance improvements while increasing design complexity. Conventional CNNs designed for raw image processing were unsuitable due to redundant feature learning. Activation functions such as sigmoid and tanh were explored but led to vanishing gradient issues. This slowed down convergence.