## 2 Related Work
### System Modelling
#### 3.2.2 Adapted Sine Cosine Optimizer (SCO)  
The adapted sine cosine optimizer (SCO) is based on sine and cosine functions [47]. This optimizer was originally proposed by [PERSON] [48]. It is basically applied in global optimization functions for phases of exploitation and exploration. Initially, it generates multiple random solutions and these random solutions show fluctuations, either outwards or towards the best possible solution. This complete mechanism utilized the sine and cosine functions-based mathematical model, as shown by Equations (15) and (16). \[\overset{\rightarrow}{W}_{i}(t+1)=\overset{\rightarrow}{W}_{i}(t)+\varphi_{1 }*\sin(\varphi_{2})*\left|\varphi_{3}*l_{i}(t)-\overset{\rightarrow}{W}_{i}(t)\right| \tag{15}\]  
\[\overset{\rightarrow}{W}_{i}(t+1)=\overset{\rightarrow}{W}_{i}(t)+\varphi_{1 }*\cos(\varphi_{2})*\left|\varphi_{3}*l_{i}(t)-\overset{\rightarrow}{W}_{i}(t)\right| \tag{16}\]  
The current position is represented by \(\overset{\rightarrow}{W}_{i}(t)\); \(\varphi_{1},\ \varphi_{2},\text{ and }\varphi_{3}\) are random numbers \(\in[0,1]\), and the targeted global optimal solution is represented by \(l_{i}\). The conditions \(0.5\leq\varphi_{4}<0.5\) are also used in Equations (15) and (16) for representing the phases of exploitation and exploration, respectively. \[\overset{\rightarrow}{W}_{i}(t+1)= \begin{cases}\overset{\rightarrow}{W}_{i}(t)+ \varphi_{1}*\sin(\varphi_{2})*\left|\varphi_{3}*l_{i}(t)-\overset{\rightarrow}{W }_{i}(t)\right|,\ \varphi_{4}<0.5\\ \overset{\rightarrow}{W}_{i}(t)+\varphi_{1}*\cos(\varphi_{2})*\left|\varphi_{3} *l_{i}(t)-\overset{\rightarrow}{W}_{i}(t)\right|,\ \varphi_{4}\geq 0.5\end{cases}  \tag{17}\]  
2.3 Hybrid Adapted Grey Wolf Sine Cosine Optimizer (HA-GWSCO) Framework for Finding the Maximum Node-Disjoint Routes from All SNs in EH-WSN  
The main characteristics of these optimizers, namely, the adapted GWO and SCO, are the efficient accuracy. These optimizers usually show efficient performance in providing solutions to various optimization problems when compared with well-known other swarm intelligence optimization frameworks. Further, various pieces of literature attest to this claim. The only limitations of these optimizers belong to the fact that these are somehow not suitable for handling highly complex functions; also, the second limitation belongs to the phenomenon of getting trapped in local optima. For effectively handling these limitations, a hybrid version [49] is required. The hybrid version enhances the overall searching capability of the framework and consequently can provide the best optimal solutions to complex optimization problems. Now, this hybrid framework is called the hybrid adapted grey wolf sine cosine optimizer (HA-GWSCO). In the hybrid adapted grey wolf sine cosine optimizer (HA-GWSCO) framework, the sine cosine optimizer plays a major role in improving the movement of the alpha (\(\propto\)) wolves of the grey wolf optimizer since for the grey wolves community, these wolves are assumed as the leaders. The beta (\(\beta\)) wolves are designated as the second-level leaders of the grey wolves, while the delta (\(\delta\)) ones are the third-level leaders. Therefore, the hybrid adapted grey wolf sine cosine optimizer (HA-GWSCO) framework has achieved robust search capabilities, and consequently the mechanism behind the global convergence, exploration, and exploitation is enhanced. From the above discussion, it is clear that the ultimate aim of the hybrid adapted grey wolf sine cosine optimizer (HA-GWSCO) framework is to replace the worst results in finding a new population based on an individual approach, since this hybrid framework results in efficient accuracy. There are mainly three procedures (see Equations (18) and (19)) responsible for enhancing the capability of the hybrid adapted grey wolf sine cosine optimizer (HA-GWSCO) framework for finding the efficient solution of maximum node-disjoint routes utilizing the minimum RNs from SNs to BS. Next, Figure 2 illustrates Phase 1 of the proposed framework consisting of HA-GWSCO.