## 2 Related Work
### System Modelling
#### 3.2.2 Adapted Sine Cosine Optimizer (SCO)
\(f_{distance(l)^{R_{j}(SN_{i},BS)}}\) is the ratio of the distance of the edge \(distance(l)\) between adjacent nodes in the route \(R_{j}(SN_{i},BS)\) from \(SN_{i}\) to BS to the distance of the edge \(distance(l)\) between adjacent nodes in the set of all node-disjoint routes \(R_{set(SN_{i},~{}BS)}\) from \(SN_{i}\) to BS. \(f_{distance(l)^{R_{j}(SN_{i},BS)}}\) should be the minimum for optimal performance of the wireless system. Hence,  
\[f_{2}=\frac{1}{f_{distance(l)^{R_{j}(SN_{i},BS)}}} \tag{23}\]  
Further, the third objective function representing the energy consumption of the edge \(l\) (\(Energy\_Consumption_{l}\)) between adjacent nodes in the node-disjoint route \(R_{j}(SN_{i},BS)\) from \(SN_{i}\) to BS (\(f_{Energy\_Consumption_{l}^{(R_{j}(SN_{i},BS))}}\)) is represented by \((f_{3})\) in Equation (25). \[f_{Energy\_Consumption_{l}^{(R_{j}(SN_{i},BS))}}=\frac{\sum_{l=1}^{ hop(R_{j}(SN_{i},BS))}Energy\_Consumption_{l}}{\sum_{l=1}^{ hop(R_{set(SN_{i},~{}BS))}}Energy\_Consumption_{l}} \tag{24}\]  
Here, \(hop(R_{j}(SN_{i},BS))\) represents the hop counts in the _jth_ node-disjoint route between the _ith_ source node \(SN_{i}\) and BS, and \(hop(R_{set(SN_{i},~{}BS))}\) reflects the hop counts in the set of all the node-disjoint routes between the _ith_ source node \(SN_{i}\) and BS. \(f_{Energy\_Consumption_{l}^{(R_{j}(SN_{i},BS))}}\) is the ratio of the energy consumption of the edge (\(Energy\_Consumption_{l}\)) between adjacent nodes in the node-disjoint route \(R_{j}(SN_{i},BS)\) from \(SN_{i}\) to BS to the energy consumption of the edge (\(Energy\_Consumption_{l}\)) between adjacent nodes in the set of all node-disjoint routes \(R_{set(SN_{i},~{}BS)}\) from \(SN_{i}\) to BS. \(f_{Energy\_Consumption_{l}^{(R_{j}(SN_{i},BS))}}\) should be minimum for optimal performance of the wireless system. Hence,  
\[f_{3}=\frac{1}{f_{Energy\_Consumption_{l}^{(R_{j}(SN_{i},BS))}}} \tag{25}\]  
Furthermore, the fourth objective function representing delay in communication for the node \(SN_{e}\in R_{j}(SN_{i},BS)\) in the route \(R_{j}(SN_{i},BS)\) from \(SN_{i}\) to BS(\(f_{delay_{SN_{e}}^{R_{j}(SN_{i},BS)}}\)) is represented by \((f_{4})\) in Equation (27). \[f_{delay_{SN_{e}}^{R_{j}(SN_{i},BS)}}=\frac{\sum_{SN_{e}\in R_{j}(SN_{i},BS)} delay(SN_{e})}{\sum_{SN\in R_{net(SN_{i},~{}BS)}}delay(SN)} \tag{26}\]  
Here, \(delay(SN_{e})\) represents a delay in communication for the sensor node \(SN_{e}\), \(SN_{e}\in R_{j}(SN_{i},BS)\), since \(SN_{e}\) is the sensor node in the _jth_ node-disjoint route between the _ith_ source node \(SN_{i}\) and BS. Similarly, \(delay(SN)\) reflects a delay in communication for the sensor node \(SN\), \(SN\in R_{set(SN_{i},\ BS)}\), since \(SN\) is the sensor node in the set of all the node-disjoint routes between the _ith_ source node \(SN_{i}\) and BS. \(f_{delay_{S{N_{i}}}}\) is the ratio of delay in communication for the node \(SN_{e}\in R_{j}(SN_{i},BS)\) in the route \(R_{j}(SN_{i},BS)\) from \(SN_{i}\) to BS to the delay in communication for the node \(SN\in R_{set(SN_{i},\ BS)}\) in the set of all node-disjoint routes \(R_{set(SN_{i},\ BS)}\) from \(SN_{i}\) to BS. \(f_{delay_{S{N_{e}}}}\) should be minimum for optimal performance of the wireless system. Hence,  
\[f_{4}=\frac{1}{f_{delay_{S{N_{e}}}^{R_{j}(SN_{i},BS)}}} \tag{27}\]  
Furthermore, the fifth objective function representing relay hops for the packet in the route \(R_{j}(SN_{i},BS)\) from \(SN_{i}\) to BS \(\left(f_{hop^{R_{j}(SN_{i},BS)}}\right)\) is represented by \((f_{5})\) in Equation (29). \[f_{hop^{R_{j}(SN_{i},BS)}}=\frac{hop\big{(}R_{j}(SN_{i},BS)\big{)}}{\sum_{j=1}^ {k}hop\big{(}R_{j}(SN_{i},BS)\big{)}} \tag{28}\]  
\(f_{hop^{R_{j}(SN_{i},BS)}}\) is the ratio of the relay hops for the packet in the route \(R_{j}(SN_{i},BS)\) from \(SN_{i}\) to BS to the hops for the packet in the set of all node-disjoint routes \(R_{set(SN_{i},\ BS)}\) from \(SN_{i}\) to BS. \(f_{hop^{R_{j}(SN_{i},BS)}}\) should be minimum for optimal performance of the wireless system.