# Coverage Optimization of WSNs Based on Enhanced Multi-Objective Salp Swarm Algorithm
## 5 Results and Discussion
### Performance Analysis of the Proposed Algorithm  
To validate the effectiveness of the EMSSA algorithm, four challenging multi-objective test functions were selected for benchmarking. Due to the complexity of these multi-objective test functions, a larger number of search agents (60) and a higher maximum iteration limit (1000) were employed. It is worth noting that the maximum archive size for both MSSA and EMSSA was set to 100 in Table 1, and the parameter settings for the test functions are shown in Table 2. After running the algorithm for 30 iterations, quantitative results were calculated using the IGD measure, as shown in Table 3. The obtained Pareto-optimal fronts are illustrated in Figures 3-6. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Parameters** \\ \hline NSGA-II & \(pc=0.9\), \(pm=1/n\), \(\eta c=\eta m=20\) \\ MSSA & \(c_{2}\in[0,1]\), \(c_{3}\in[0,1]\), \(repository=100\) \\ EMSSA & \(c_{2}\in[0,1]\), \(c_{3}\in[0,1]\), \(repository=100\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter Setting. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & \multicolumn{3}{c}{**ZDT1**} \\ \cline{2-4}  & **Ave** & **Std.** & **Best** & **Worst** \\ \hline NSGA-II & \(6.25\times 10^{-3}\) & \(5.21\times 10^{-3}\) & \(6.05\times 10^{-4}\) & \(2.16\times 10^{-2}\) \\ MSSA & \(3.15\times 10^{-3}\) & \(8.99\times 10^{-4}\) & \(2.19\times 10^{-3}\) & \(6.28\times 10^{-3}\) \\ EMSSA & \(1.06\times 10^{-4}\) & \(9.69\times 10^{-5}\) & \(5.51\times 10^{-4}\) & \(7.21\times 10^{-4}\) \\ \hline \hline \multicolumn{4}{c}{**ZDT2**} \\ \cline{2-4}  & **Ave** & **Std.** & **Best** & **Worst** \\ \hline NSGA-II & \(1.35\times 10^{-2}\) & \(1.22\times 10^{-2}\) & \(6.15\times 10^{-4}\) & \(4.29\times 10^{-2}\) \\ MSSA & \(3.58\times 10^{-3}\) & \(1.66\times 10^{-3}\) & \(2.08\times 10^{-3}\) & \(9.51\times 10^{-3}\) \\ EMSSA & \(6.01\times 10^{-4}\) & \(7.81\times 10^{-5}\) & \(4.58\times 10^{-4}\) & \(8.46\times 10^{-4}\) \\ \hline \hline \multicolumn{4}{c}{**ZDT3**} \\ \cline{2-4}  & **Ave** & **Std.** & **Best** & **Worst** \\ \hline NSGA-II & \(9.52\times 10^{-3}\) & \(7.03\times 10^{-3}\) & \(8.32\times 10^{-4}\) & \(2.25\times 10^{-2}\) \\ MSSA & \(6.67\times 10^{-3}\) & \(2.78\times 10^{-3}\) & \(3.92\times 10^{-3}\) & \(1.75\times 10^{-2}\) \\ EMSSA & \(1.02\times 10^{-3}\) & \(1.60\times 10^{-4}\) & \(7.70\times 10^{-4}\) & \(1.61\times 10^{-3}\) \\ \hline \hline \multicolumn{4}{c}{**DTLZ7**} \\ \cline{2-4}  & **Ave** & **Std.** & **Best** & **Worst** \\ \hline NSGA-II & \(2.12\times 10^{-3}\) & \(1.56\times 10^{-3}\) & \(1.14\times 10^{-3}\) & \(7.75\times 10^{-3}\) \\ MSSA & \(2.25\times 10^{-3}\) & \(9.51\times 10^{-4}\) & \(4.23\times 10^{-3}\) & \(9.62\times 10^{-4}\) \\ EMSSA & \(1.34\times 10^{-3}\) & \(1.57\times 10^{-4}\) & \(1.07\times 10^{-3}\) & \(2.05\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test Function Parameter Settings. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Function** & \multicolumn{2}{c}{**Dimension**} & **Pareto Front** \\ \cline{2-4}  & **Variables** & **Objectives** & **Number of Samples** \\ \hline ZDT1 & 30 & 2 & 1000 \\ ZDT2 & 30 & 2 & 1000 \\ ZDT3 & 30 & 2 & 536 \\ DTLZ7 & 22 & 3 & 4700 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the three algorithms (using IGD) on the test functions employed. The Pareto-optimal solutions obtained from Figure 4 reveal that NSGA-II exhibits low coverage and performs worse than the EMSSA and MSSA algorithms. The Pareto front obtained by the MSSA algorithm also exhibits a gap. ZDT3 exhibits a Pareto front with common region separations often seen in practical problems. As shown in Figure 5, EMSSA outperforms MSSA and NSGA-II in both convergence and coverage. The results indicate that EMSSA is effective in locating all the separate regions of the Pareto front with higher distribution on each region. Figure 4: Best Pareto front determined by NSGA-II, MSSA, and EMSSA on ZDT2. Figure 5: Best Pareto front determined by NSGA-II, MSSA, and EMSSA on ZDT3.