## 3 The Proposed Model
### Image Classification
Moreover, all the objects are considered as density \((D_{i})\), volume \((V_{i})\), and acceleration \((\Gamma_{i})\) that are randomly determined by the subsequent equation:  
\[O_{i}=O_{i}^{\text{Min}}\,+r1\times\Big{(}O_{i}^{\text{Max}}\,-O_{i}^{\text{Min }}\,\Big{)};i=1,2,\ldots,N \tag{1}\]  
\[D_{i}=r_{2} \tag{2}\]  
\[r_{t}=\sigma(W_{r}x_{t}+U_{r}h_{t-1}+b_{r})\]0  
\[r_{t}=\sigma(W_{r}x_{t}+U_{r}h_{t-1}+b_{r})\]1  
Let \(O_{i}\) be the \(i\)th object, and \(O_{i}^{\text{Min}}\) and \(O_{i}^{\text{Max}}\) refers to the maximum and minimum bounds of the searching space, correspondingly. \(r_{1},r_{2},r_{3}\), and \(r_{4}\) denotes random vector lies between \([0,\,1]^{Dim}\). In the updating of volume and density, the values of density and volume for every object were upgraded by the control of the optimal density and volume as follows:  
\[r_{t}=\sigma(W_{r}x_{t}+U_{r}h_{t-1}+b_{r})\]2  
\[r_{t}=\sigma(W_{r}x_{t}+U_{r}h_{t-1}+b_{r})\]3  
From the equation, \(s_{1}\), \(s_{2}\) refers to numbers lying within zero and one. Next, the collision between objects happened till attaining the equilibrium state. The key role of the transfer function \((T_{c})\) is to shift from exploration to exploitation modes, determined as follows:  
\[r_{t}=\sigma(W_{r}x_{t}+U_{r}h_{t-1}+b_{r})\]4  
The \(T_{c}\) exponentially increases over time until obtaining 1. \(t\) refers to the existing iteration, whereas \(T\) represents the maximal iteration count. Similarly, the reduction of the density scalar \(d_{s}\) in AOA permits to discover an optimum solution [22]:  
\[r_{t}=\sigma(W_{r}x_{t}+U_{r}h_{t-1}+b_{r})\]5  
In the exploration phase, the collision between agents is appeared by randomly selecting material \((Mr)\). Therefore, the update of the acceleration object is employed if the transfer function value was lesser or equivalent to 0.5. \[r_{t}=\sigma(W_{r}x_{t}+U_{r}h_{t-1}+b_{r})\]6  
In the exploitation, the collision between agents was not realized. Therefore, the update of the acceleration object can be employed if the transfer coefficient values are higher than 0.5. \[r_{t}=\sigma(W_{r}x_{t}+U_{r}h_{t-1}+b_{r})\]7  
In Equation (10), \(\Gamma_{Best}\) represents the acceleration of the optimum object \(O_{Best}\). During normalization, we normalize the acceleration to define the rate of change as follows:  
\[r_{t}=\sigma(W_{r}x_{t}+U_{r}h_{t-1}+b_{r})\]8  
In Equation (11), \(\alpha\) and \(\beta\) are set as 0.9 and 0.1, correspondingly. \(\Gamma_{i-norm}^{t+1}\) illustrates the proportion of steps adapted by every agent. A low acceleration value specifies that the object was working under the exploitation mode; or else, the object was working under an exploration mode. For the exploration stage \((T_{c}\leq 0.5)\), the location of the \(i^{th}\) object in the \(t+1\) iteration is adapted using the following equation, where the object location is upgraded in the exploitation stage (\(T_{c}>0.5\)). \[r_{t}=\sigma(W_{r}x_{t}+U_{r}h_{t-1}+b_{r})\]9  
where \(c1\) is set as 2. \[\overline{h}=\sigma(W_{h}x_{t}+U_{h}(r_{t}E\odot h_{t-1})+b_{h})\]0  
where \(c2\) is set as 6. \(F\) is applied for flagging which controls search direction:  
\[F=\left\{ \begin{array}{l}+1\;if\;\zeta\leq 0.5\\ -1\;if\;\zeta>0.5\end{array} \right. \tag{14}\]  
where \(\zeta=2\times rand-0.5\). Lastly, the novel population is estimated via score index \(Sc\) to define the best object \(O_{Best}\) and the best additive data involving \(D_{Best}\), \(V_{Best}\), and \(\Gamma_{Best}\). The AOA method makes a derivation of a fitness function for attaining advanced classifier performances. It sets a positive numeral for indicating the superior performance of the candidate solutions. In this article, the reduction of the classifier error rate can be assumed as the fitness function, as presented below in Equation (15). \[fitness(x_{i})=ClassifierErrorRate(x_{i})=\frac{number\;of\; misclassified\;samples}{Total\;number\;of\;samples}*100 \tag{15}\]