## 3 Materials and Methods
### AOp Prediction Model Development
#### 3.1.2 Optimization of ANN Model
The pseudocode for SMA model implementation is available in [PERSON] et al. [44]. The MVO, as introduced by [PERSON] et al. [45], is a nature-based optimization algorithm, like the SMA, but it differs from the SMA in that it is based on the multi-verse theory in physics. The optimizer consists of three distinct phases, exploration, exploitation, and local search, based on the main concepts and mathematical structures of black, white, and wormholes (Figure 6a) [46]. Similar to other population-based metaheuristic algorithms, the search process is divided into exploration and exploitation. The ideas and theories of white and black holes are employed to explore search spaces, whereas wormholes help the optimizer in search space exploitation [46]. In the MVO algorithm, universes are considered solutions and are expressed by the size of their populations. In addition, each object in the universe is specified as a parameter in the search area of the universe. The inflation rate is used to appraise the fitness of each solution while the objects move in the search area (Figure 6b). Figure 6: \(Cont.\)  
The optimizer applies this set of guidelines during the optimization process:  
1. There is a higher positive proportionality between the inflation rate and white holes. 2. There is a lower negative proportionality between the inflation rate and black holes. 3. Universes with higher inflation rates are liable to transmit objects with the assistance of white holes. 4. Universes with lower inflation rates are liable to accept multiple objects with the assistance of black holes. 5. The objects in the universes may experience periodic motion towards the solution space through wormholes, irrespective of the rate of inflation. During the exploration stage, a roulette wheel mechanism was chosen to simulate the white- and black-hole tunnels computationally and exchange the objects of the solutions. The solutions were then sorted based on their inflation rates at each iteration, and a solution was selected using a roulette wheel to obtain a white hole. Taking \(G\) as the entire universe (solution), as in Equations (9) and (10), respectively:  
\[G= \begin{pmatrix}y_{1}^{1}&y_{1}{}^{2}\cdots&y_{1}{}^{d}\\ \vdots&\ddots&\vdots\\ y_{n}{}^{1}&y^{2}{}_{n}\cdots&y^{d}{}_{n}\end{pmatrix}  \tag{9}\]  
\[y_{i}^{i}=\left\{ \begin{array}{ll}y_{k}^{i}r1<NI(Gi)\\ y_{i}^{i}r1\geq NI(Gi)\end{array} \right. \tag{10}\]  
where \(d\) is the number of parameters, \(n\) denotes the number of solutions (universe), \(yi\) denotes the \(j\)th parameter of the \(i\)th solution (universe), \(Gi\) denotes the \(i\)th solution (universe), \(NI\) (\(Gi\)) denotes the \(i\)th universe's normalized inflation rate, \(r1\) is a uniformly distributed random number in the range \((0,1)\), and \(yi\) denotes the \(j\)th parameter of the \(k\)th universe as chosen by the roulette wheel method. In the exploitation phase, wormhole tunnels are created using a solution (a universe), and the optimal solution formed thus far ensures local changes for each solution and has  
Figure 6: (**a**) Representation of white, black, and wormholes in a solution space; (**b**) the principle of the multi-verse optimizer (adapted from [45]). a greater tendency to enhance the rate of inflation through wormholes. This method is described by Equations (11) and (13), as follows:  
\[y_{i}^{j}=\left\{ \begin{array}{l}y_{j}+TDR\times((gb_{j}-lb_{j}) \times r4+lb_{j})r3<0.5\\ y_{j}-TDR\times((gb_{j}-lb_{j})\times r4+lb_{j})r3\geq 0.5\end{array} r2<WEP\\ r2\geq WEP\end{array}\right. \tag{11}\]  
where \(y_{j}\) is the \(j\)th variable of the optimal solution formed thus far; \(lb_{j}\) is the \(j\)th variable's minimum value; \(ubj\) is the maximum value of the \(j\)th variable; \(xii\) is the \(j\)th variable of the ith solution; and \(r2,r3\), and \(r4\) are randomly distributed random numbers in the range \((0,1)\). The wormhole existence probability (WEP) determines the likelihood of finding a wormhole in a solution.