## 2 Related Work
### System Modelling
#### 3.2.2 Adapted Sine Cosine Optimizer (SCO)
Consider the position update equation (Equation (17)) of the adapted SCO; this position update equation is applied in enhancing the position, speed, and convergence accuracy of the alpha (\(\propto\)) grey wolves of the adapted SCO. This step is taken for maintaining an effective balance between the phases of exploration and exploitation. Further, this step also helps in extending the convergence performance of the adapted grey wolf optimizer framework. The following equations are developed for updating the positions of the alpha (\(\propto\)) grey wolves. \[\overset{\rightarrow}{Z}_{\alpha}= \begin{cases}\varphi_{5}*\sin(\varphi_{5})* \left|\overset{\rightarrow}{Y}_{1}*\overset{\rightarrow}{W}_{\infty}- \overset{\rightarrow}{W}\right|,\ \varphi_{5}<0.5\\ \varphi_{5}*\cos(\varphi_{5})*\left|\overset{\rightarrow}{Y}_{1}*\overset{ \rightarrow}{W}_{\infty}-\overset{\rightarrow}{W}\right|,\ \varphi_{5}\geq 0.5\end{cases}  \tag{18}\]  
\[\overset{\rightarrow}{W}_{1}=\overset{\rightarrow}{W}_{\alpha}-\overset{ \rightarrow}{O}_{1}*\left(\overset{\rightarrow}{W}_{\infty}\right) \tag{19}\]Phase 2: Discovering the Most Appropriate and Reliable Route from the k-Node-Disjoint Routes between Each SN to BS Based on the Hybrid Adapted Grey Wolf Whale Optimizer (HA-GWWO) Framework  
A sustainable and energy-efficient wireless system is the need of the hour for next-generation green communication since sensors are mainly suffering from limited energy availability caused by limited battery capacity. Prolonging the network lifetime has been an evergreen research area for researchers from the last few decades, and efforts are still ongoing to design energy-efficient frameworks for routing in wireless systems. Energy harvesting techniques have emerged as a solution for handling energy scarcity issues of sensors. In this technique, energy is harvested from RF, vibration, thermal, and solar, etc., by utilizing an energy-harvesting component. In the energy-harvesting wireless sensor networks (EH-WSNs), the dead nodes become alive and resume their operation with the help of harvested energy; in this way the life of the network can be extended without bound. It is a fact that during real-time applications, many unavoidable incidents may occur due to difficult environmental conditions, which results in the breakdown of communication links, malfunctioning of sensor nodes, and partitioning of the network. Therefore, the network functions can be severely disrupted. In these real-time scenarios, the success of green communications majorly depends on the fault-tolerance feature, which has become  
Figure 2: Phase 1 of the proposed framework consisting of the hybrid adapted grey wolf sine cosine optimizer (HA-GWSCO) framework. a critical issue for next-generation wireless systems. Further, in the energy-harvesting environment, the time-varying, unstable, and random nature of the harvested energy may compel the nodes to fail. Furthermore, due to this random nature of the harvested energy, the nodes' lifecycle frequently switches between alive and dead, which results in dynamic changes in the quality of the routing. Fault-tolerant routing with awareness of the quality of routing is the only solution for the optimal performance of EH-WSN. Towards enabling fault-tolerant routing, the first step is to establish the multi-node/link disjoint routes, comparing these with the previous route as well as all other alternative routes. In this mechanism, the failure in the previous route due to the breakdown of any or all nodes/links has no impact on the alternative routes. In the proposed framework, we are maintaining the \(k\)-node-disjoint routes from each SN to BS by applying the hybrid adapted grey wolf sine cosine optimizer (HA-GWSCO) framework in the first phase of the proposed framework.