## 3 Materials and Methods
### AOp Prediction Model Development
#### 3.1.2 Optimization of ANN Model  
The optimum ANN was optimized to further improve its predictive performance. Optimization algorithms improve the performance of ANNs by solving the problems of local minima and slower convergence speeds. The use of optimization algorithms is also cost-effective, as it prevents the use of many neurons in the hidden layer before achieving an accurate model. In this study, a nature-inspired slime mould algorithm (SMA) and a physics-based nature-inspired multi-verse optimizer (MVO) were employed to tune the optimum ANN structure hyperparameters. The selection of these two algorithms to enhance the predictive performance of the ANN in this study was based on their robustness and the need to appraise their predictive performance in predicting AOp. The processes used to execute the optimized ANN models proposed in this study are discussed below. The SMA is modeled based on the oscillation pattern of a eukaryotic organism known as slime mold (SM) in its natural environment. The algorithm exhibits a unique mathematical model that replicates the foraging behavior of SM when forming a route in search of food and survival in its natural habitat [44]. The model replicates the mode of generation of positive and negative feedback exhibited by the SM during the foraging process (Figure 5). It features a flexible framework that consistently maintains a balance between local and global search drifts. The two phases involved in the SMA's implementation are \"approaching food\" and \"warping food,\" as discussed below. In this initial phase, the SM acquires food based on its odor in the air. The approaching behavior of SM can be described mathematically by Equation (2):  
\[\overrightarrow{M(l+1)}\ =\left\{\overrightarrow{M_{b}(l)}+\overrightarrow{V_{b}}*( \overrightarrow{W}*\overrightarrow{M_{A}(l)}-\overrightarrow{M_{B}(l)},r<p \overrightarrow{V_{c}}*\overrightarrow{M(l)},r\geq p\right. \tag{2}\]  
where \(\overrightarrow{V_{b}}\) is a variable which has values between \(-\)a and a; \(\overrightarrow{V_{c}}\) linearly decreases from 1 to 0. \(l\) represents the current iteration, \(\overrightarrow{M_{b}}\) describes each position with optimum odor concentration, \(\overrightarrow{M}\) describes the location of the SM in nature, \(\overrightarrow{M_{A}}\) and \(\overrightarrow{M_{B}}\) are two members that were randomly picked from the group, and \(\overrightarrow{W}\) denotes the SM's body weight. The parameter '\(p\)' in Equation (2) can be expressed as shown in Equation (3):  
\[p=\tanh\lvert G(i)-HF\rvert \tag{3}\]  
Figure 5: The foraging behavior of slime mold in nature (adapted from [44]). where \(G(i)\) denotes the fitness of \(\overset{\rightarrow}{M}\), \(HF\) is the optimal solution found in all iterations, and \(i\in 1\), 2,... \(n\). The mathematical equations for \(\overset{\rightarrow}{V_{b}}\) and the SM's body weight, \(\overset{\rightarrow}{W}\), are as expressed in Equations (4)-(7):  
\[\overset{\rightarrow}{V_{b}}=[-a,a] \tag{4}\]  
\[a=\arctan h(-\left(\frac{l}{max\_l}\right)+1) \tag{5}\]  
\[\overset{\rightarrow}{W(smellIndex(i))}=\left\{ \begin{array}{l}1+r*\log \left(\frac{bF-G(i)}{bF-wF}+1\right),condition\\ 1-r*\log\left(\frac{bF-G(i)}{bF-wF}+1\right),others\end{array} \right. \tag{6}\]  
\[SmellIndex=sort(G) \tag{7}\]  
b. Warping food  
This second phase depicts the contraction behavior of the intravenous network of slime mould while hunting for food in its natural habitat. This phase can be mathematically expressed as Equation (8):  
\[\overset{\rightarrow}{M^{*}}=\left\{ \begin{array}{l}\frac{rand*(ob-mb)+mb,rand <z}{M_{b}(l)+\overset{\rightarrow}{V_{b}}*(\overset{\rightarrow}{W*}* \overset{\rightarrow}{M_{A}(l)}-\overset{\rightarrow}{M_{B}(l)},r<p\overset{ \rightarrow}{V_{c}}*\overset{\rightarrow}{M(l)},r\geq p}\end{array} \right. \tag{8}\]  
where \(mb\) and \(ob\) describe the lowest and highest limits of the search area, and \(rand\) and \(r\) represent the area estimate or value between 0 and 1.