## 2 Literature Survey
### Performance Metrics  
For evaluating our developed algorithm, we generated two types of metrics: multi-objective optimization (MOO) and application-oriented metrics. For the first type, we calculated the hyper-volume, set coverage, delta, and the number of nondominated solutions. For the second type, we calculated time-series-based metrics for the packet delivery ratio (PDR), end to end delay (E2E-delay), and energy consumption. The equations of the second type are presented in Section 5 while the equations of the first type are presented in this section.  
The effectiveness of search algorithms was assessed using the hyper-volume (\(HV\)) metric in evolutionary and swarm multiobjective optimization. In relation to the poorest solution (the reference point), it calculates the volume of the dominated area of the objective space; this region is the union of the hypercube whose diagonal is the separation between the reference point and a solution \(x\) from the Pareto set (\(Ps\)). More preferable solutions are indicated by higher values of this measure indicator, as shown in Equation (10).  
\[HV=volume(U~{}HyperCube(x)) \tag{10}\]  
The set coverage, or \(C\) metric, which compares the Pareto sets \(Ps1\) and \(Ps2\), is shown in Equation (11).  
\[c(Ps1,Ps2)=\mid\{y\in Ps2|\exists x\in Ps1:x<\
eg y\}\,|\,|Ps2| \tag{11}\]  
\(C\) is equal to the proportion of \(Ps2\)'s nondominated solutions to \(Ps1\)'s nondominated solutions divided by \(Ps2\)'s total number of solutions. Therefore, it is crucial to reduce the value of \(C(X,Ps)\) for all Pareto sets \(X\) while assessing a set of \(Ps\).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{2}{c}{**Solution**} & \multicolumn{1}{c}{**Mobile Sink**} & \multicolumn{1}{c}{**Index of RV**} & \multicolumn{1}{c}{**POS**} & \multicolumn{1}{c}{**Index of nHops**} & \multicolumn{1}{c}{**NHops**} \\ \(sol_{i}\) = \(\{\text{N}ms^{i},N^{i\
eq j}_{\text{R}^{i},N}\text{N}H^{i,j,k},l\left(x_{i,j }\right)\}\) & **mst(\(i\),\(j\))** & **RV(\(i\),\(j\),\(k\))** & **[\(x\),\(y\)]** & **[\(x\),\(y\)]** & **nh(\(i\),\(j\),\(k\))** \\ \hline \multirow{6}{*}{\(sol_{1}=[2,3,2,[150~{}400],[200~{}144],\)\([160~{}350],\)\([549~{}988],\)\([234~{}633],2,3,2,1,3]\)} & \multirow{6}{*}{\(\text{ms}(1,1)\)} & RV(1,1,1) & [150~{}400] & \(\text{nh}(1,1,1)\) & 2 \\ \cline{3-6}  & & RV(1,1,2) & [200~{}144] & \(\text{nh}(1,1,2)\) & 3 \\ \cline{3-6}  & & RV(1,1,3) & [160~{}350] & \(\text{nh}(1,1,3)\) & 2 \\ \cline{3-6}  & & RV(1,2,1) & [549~{}988] & \(\text{nh}(1,2,1)\) & 1 \\ \cline{3-6}  & & RV(1,2,2) & [234~{}633] & \(\text{nh}(1,2,2)\) & 3 \\ \hline \multirow{6}{*}{\(sol_{2}=[3,2,1,3,[237,645],[455,744],\)\([753,433],[543,865],[236,765],[653,778]]\)} & \multirow{6}{*}{\(\text{ms}(2,1)\)} & RV(2,1,1) & [237~{}645] & \(\text{nh}(2,1,1)\) & 3 \\ \cline{3-6}  & & RV(2,1,2) & [455~{}744] & \(\text{nh}(2,1,2)\) & 2 \\ \cline{1-1} \cline{2-6}  & & ms(2,2) & RV(2,2,1) & [753~{}433] & \(\text{nh}(2,2,1)\) & 1 \\ \cline{1-1} \cline{2-6}  & & RV(2,3,1) & [543~{}865] & \(\text{nh}(2,3,1)\) & 2 \\ \cline{1-1} \cline{2-6}  & & RV(2,3,2) & [236~{}765] & \(\text{nh}(2,3,2)\) & 1 \\ \cline{1-1} \cline{2-6}  & & RV(2,3,3) & [653~{}778] & \(\text{nh}(2,3,3)\) & 2 \\ \hline \end{tabular}
\end{table}
Table 6: Two candidate solutions and their corresponding metameric variables.