## 3 The Proposed Model
### Hyperparameter Tuning: QWSA Model  
In this study, the QWSA-based hyperparameter tuning process optimally chooses the hyperparameter values of the NASNet model. The WSA has good performance in a majority of the problems; occasionally, it has a chance of becoming trapped in the local optima and early convergence [22]. Here, the concept of quantum computing was taken into account. In quantum space, the location of the male and female WSs is not concurrently defined; therefore, the location of WS must be determined using the wave function \(\psi(X,\ t)\), where \(X\) determines the location of WSs. This implies that the square of mode indicates the likelihood density of WS appearing at the \(X\)-location in space, and it can be expressed as follows [23]:  
\[|\psi|^{2}dxdydz=Qdxdydz \tag{1}\]  
In Equation (1), \(Q\) defines a likelihood density function which fulfills the normalized condition:  
\[\int_{-\infty}^{\infty}|\psi|^{2}dxdydz=\int_{-\infty}^{\infty}Qdxdydz=1 \tag{2}\]  
The location of WS is accomplished using the Monte Carlo method, and its updated formula is provided as follows.  
\[P(t)=\delta\times P_{b}(t)+(1-\delta)\times P_{g}(t) \tag{3}\]  
\[m_{b}(t)=\frac{1}{M}\sum_{i=1}^{M}P_{b_{i}}(t) \tag{4}\]  
\[D(t+1)=2\beta\times|m_{b}(t)-X(t)| \tag{5}\]  
\[\beta=\underline{\beta}-\left(\underline{\beta}-\overline{\beta}\right) \times\left(\frac{t}{G_{\text{max}}}\right) \tag{6}\]  
\[X(t)=P(t)\pm(D/2)\times\text{ ln }(1/\gamma) \tag{7}\]  
From the expression, \(M\) defines the population size; \(\delta\) and \(\gamma\) signify that an arbitrary number lies within [0, 1]; \(P(t)\) determines the local attraction area of the \(t\)-\(th\) iterations of WSs, which define the location of every WSs is an arbitrary location among the global and the individual locations; \(D\) signifies the weighted distance between the candidate and the mean optimum location of population; \(m(t)\) defines the mean value of individual optimum location for the WSs; \(G_{ax}\) determines the iteration count; \(\beta\) denotes the shrinkage-expansion coefficient, i.e., exploited to handle the individual convergence rate lies within \(\underline{\beta}\) to \(\overline{\beta}\). In many instances, \(\left[\frac{\beta}{b},\overline{\beta}\right]=\left[l,0.5\right]\), and \(P_{b}\) and \(P_{g}\) define the candidate and the \(g\), respectively. The flowchart of WSA is shown in Figure 2.  
The updating is implemented in the mating phase of original WSA:  
\[\begin{cases}\chi_{i}^{*}(t)=P(t)\pm\beta\times|m_{b}(t)-x_{i}(t)|\times\text { ln }\left(\frac{1}{1+\gamma}\right)&\text{if mating happens}\\ \chi_{i}^{*}(t)=P(t)\pm\beta\times|m_{b}(t)-x_{i}(t)|\times\text{ ln }\left(\frac{1}{1+\gamma}\right)&\text{or else}\end{cases} \tag{8}\]In these conditions, if \(X_{i}^{*}\) has good outcomes when compared to \(X_{i}(t)\), \(X_{i}(t+1)=X_{i}^{*}(t)\); otherwise, \(X_{i}(t+1)=X_{i}(t)\) as explained in Algorithm 1.  
Figure 2: Flowchart of WSA.  
The QWSA method extracts a fitness function for achieving enhanced classifier performance. It fixes a positive numeral for indicating the superior outcome of a candidate solution. In this article, a classifier error rate reduction was regarded as a fitness function, as provided in Equation (9). The optimum resolution contains a minimal error rate, and the poor resolution achieves a higher error rate.  
\[fitness(x_{i})=ClassifierErrorRate(x_{i})=\frac{number\ of\ misclassified\ samples}{Total\ number\ of\ samples}*100 \tag{9}\]