## 7 Experimentation and Results
### Analysis of Pareto-Optimal Set of the Four Algorithms
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Objective** \\ **Functions** \\ \end{tabular} } & \multirow{2}{*}{**Algorithm (I)**} & \multirow{2}{*}{**Algorithm (J)**} & \multirow{2}{*}{**Mean Difference**} & \multirow{2}{*}{**Std. Error**} & \multirow{2}{*}{**\(p\)-Value**} & \multicolumn{2}{c}{**95\% Confidence Interval**} \\ \cline{5-8}  & & & & & **Lower Bound** & **Upper Bound** \\ \hline \multirow{3}{*}{\begin{tabular}{c} Energy \\ Efficiency \\ \end{tabular} } & \multirow{3}{*}{MOSFP} & SPEA2 & 0.116 & 0.018 & \(<\)0.001 \({}^{\star}\) & 0.068 & 0.163 \\ \cline{3-6}  & OMOPSO & 0.009 & 0.018 & 0.965 & \(-\)0.039 & 0.056 \\ \cline{3-6}  & NSGA-II & 0.013 & 0.018 & 0.888 & \(-\)0.034 & 0.061 \\ \hline \multirow{3}{*}{\begin{tabular}{c} Packet \\ Throughput \\ \end{tabular} } & SPEA2 & 0.394 & 0.101 & \(<\)0.001 \({}^{\star}\) & 0.133 & 0.655 \\ \cline{3-6}  & OMOPSO & 0.015 & 0.101 & 0.999 & \(-\)0.246 & 0.276 \\ \cline{2-8}  & NSGA-II & 0.066 & 0.101 & 0.916 & \(-\)0.195 & 0.327 \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} End-to-End \\ Delay \\ \end{tabular} } & SPEA2 & \(-\)0.265 & 0.045 & \(<\)0.001 \({}^{\star}\) & \(-\)0.380 & \(-\)0.150 \\ \cline{2-8}  & OMOPSO & \(-\)0.018 & 0.045 & 0.977 & \(-\)0.133 & 0.097 \\ \cline{2-8}  & NSGA-II & \(-\)0.034 & 0.045 & 0.872 & \(-\)0.149 & 0.081 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} End-to-End \\ Latency \\ \end{tabular} } & SPEA2 & \(-\)2.718 & 0.472 & \(<\)0.001 \({}^{\star}\) & \(-\)3.933 & \(-\)1.502 \\ \cline{2-8}  & OMOPSO & \(-\)0.257 & 0.472 & 0.948 & \(-\)1.473 & 0.958 \\ \cline{1-1} \cline{2-8}  & NSGA-II & \(-\)0.306 & 0.472 & 0.917 & \(-\)1.521 & 0.910 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Analysis of one-way ANOVA (Tukey’s test) between SPEA2, MOSFP, OMOPSO and NSGA-II for four objective functions. 1. The Marginal concept of optimality: the optimal value based on this concept can be illustrated by the intersection points between a set of objective functions, which some of them minimization and the others are maximization [74]. Figure 9 presents the optimum value based on the intersection between two objective functions [75]. 2. The knee point: is a point on the Pareto front curve, which is referred to the most preferred solution. Knee point can be estimated by determining the greatest reflex angle that bends of the front from its left to its right or vice-versa. Based on Figure 10 [76], three points called A, B, and C are used to illustrate the knee point concept. The B point is considered as the knee point, which makes the greatest reflex angle between C point on the right side of the front and the A point on the left side of the front. Figures 11-14 show a sample of optimizing the four objective functions denoted by maximizing both energy efficiency and packet throughput and also minimizing both end-to-end delay and end-to-end latency using four algorithms. These algorithms are MOSFP, OMOPSO, NSGA-II, and SPEA2. From the results, the value of end-to-end latency decreases sharply and end-to-end delay decreases slightly until the value of packet payload size reaches 45 bytes, after that, both of them stabilize below 2 when the packet payload size is beyond 45 bytes. On the other hand, the packet throughput increases slightly until the value of packet payload size reaches 45 bytes, after that, it increases dramatically until the value of packet payload size reaches 114 bytes. Furthermore, the energy efficiency increases slightly until the value of packet payload size reaches 45 bytes, after that, it stabilizes above the 0.5 when the packet payload size increases more than 45 bytes. From the figures, we can notice that the optimum points are represented by different colors (i.e., green, red, yellow and blue), which are the intersection points of all the objective functions. These points are created when the packet payload size equal to 45 bytes. Figure 10: The knee point concept [76]. Figure 9: The optimum value based on the intersection between two objective functions [75].