## 2 Related Work
### System Modelling
#### 3.2.2 Adapted Sine Cosine Optimizer (SCO)
Furthermore, in the second phase, we have designed the enhanced fitness function, named the best suitable route index (BSRI), to select the most reliable node-disjoint route from each \(SN_{i}\) to BS out of available \(k\)-node-disjoint routes by utilizing the hybrid adapted grey wolf whale optimizer (HA-GWWO) framework. The fitness function consists of various effective objective functions, namely, the first function, representing the remaining available energy of each node in a particular route from \(SN_{i}\) to BS; the second function, representing the distance of the edge between the adjacent nodes; the third function, representing the energy consumption of the edge between the adjacent nodes; the fourth function, representing the delay in communication for the node; the fifth function, representing relay hops for the packet in each route; and, finally, the sixth function, representing the reliability index of the particular route from SN to BS. The route with the higher best suitable route index (BSRI) is selected for routing from each SN to BS out of the available \(k\)-node-disjoint routes utilizing the hybrid adapted grey wolf whale optimizer (HA-GWWO) framework. In the proposed framework, we have estimated the quality of the route by effectively designing the fitness functions, covering the all-important metrics for assessing the route suitability for routing that rarely have been considered in the literature for EH-WSN. Next, we are going to explain the six objective functions one by one, as below. The objective function representing the remaining available energy of each node in the node-disjoint route \(R_{j}(SN_{i},BS)\) from \(SN_{i}\) to BS \(\left(f_{ \begin{subarray}{c}R_{j}(SN_{i},BS)\\ Energy_{(RE_{Ast})}\end{subarray} }\right)\) is represented by \((f_{1})\) in Equation (21). \[f_{ \begin{subarray}{c}R_{j}(SN_{i},BS)\\ Energy_{(RE_{Ast})}^{R_{j}(SN_{i},BS)}\end{subarray} }=\frac{\sum_{SN_{i}\in R_{j }(SN_{i},BS)}Energy_{(RE_{Ast})}^{SN_{i}}}{\sum_{SN\in R_{Ast}(SN_{i},BS)}Energy _{(RE_{Ast})}^{SN}} \tag{20}\]  
Here, \(RE_{Avl}\) shows the remaining available energy, \(R_{j}(SN_{i},BS)\) represents the _jth_ node-disjoint route between the _ith_ source node \(SN_{i}\) and BS, \(R_{set(SN_{i},BS)}\) reflects the set of all the node-disjoint routes between the _ith_ source node \(SN_{i}\) and BS, \(SN_{e}\) is one of the sensor nodes in the _jth_ node-disjoint route \(R_{j}(SN_{i},BS)\), i.e., \(SN_{e}\in R_{j}(SN_{i},BS)\), and \(SN\) is one of the sensor nodes in the set of all the node-disjoint routes between the _ith_ source node \(SN_{i}\) and BS, i.e., \(SN\in R_{set(SN_{i},BS)}\). \(f_{ \begin{subarray}{c}R_{j}(SN_{i},BS)\\ Energy_{(RE_{Ast})}^{R_{j}(SN_{i},BS)}\end{subarray} }\) is the ratio of the remaining available energy \((Energy_{(RE_{Ast})}^{SN_{i}})\) of each node \(SN_{e}\in R_{j}(SN_{i},BS)\) in route \(R_{j}(SN_{i},BS)\) from \(SN_{i}\) to BS to keep the remaining available energy \((Energy_{(RE_{Ast})}^{SN})\) of each node \(SN\in R_{set(SN_{i},BS)}\) in the set of all node-disjoint routes from \(SN_{i}\) to BS. \(f_{ \begin{subarray}{c}R_{j}(SN_{i},BS)\\ Energy_{(RE_{Ast})}\end{subarray} }\) should be maximum for improved life of the wireless system. \(f_{1}=f_{ \begin{subarray}{c}R_{j}(SN_{i},BS)\\ Energy_{(RE_{Ast})}\end{subarray} }\) (21)Next, the second objective function representing the distance of the edge \(distance(l)\) between the adjacent nodes in the node-disjoint route \(R_{j}(SN_{i},BS)\) from \(SN_{i}\) to BS \(\left(f_{distance(l)^{R_{j}(SN_{i},BS)}}\right)\) is represented by \((f_{2})\) in Equation (23). \[f_{distance(l)^{R_{j}(SN_{i},BS)}}=\frac{\sum_{l\in R_{j}(SN_{i},BS)}distance (l)}{\sum_{l\in R_{net(SN_{i},~{}BS)}}distance(l)} \tag{22}\]  
Here, \(l\in R_{j}(SN_{i},BS)\) reflects the edge in the _jth_ node-disjoint route between _ith_ source node \(SN_{i}\) and BS, \(l\in R_{set(SN_{i},~{}BS)}\) represents edge in the set of all the node-disjoint routes between _ith_ source node \(SN_{i}\) and BS, \(distance(l)\) shows the distance of the edge.