## 5 Experimental Results and Analysis
### Experimental Results and Discussion on Algorithms Comparison
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **Best** & **Worst** & **Median** & **Average** & **StdDev** \\ \hline NSGAII & \(4.57\times 10^{1}\) & \(1.15\times 10^{3}\) & \(1.17\times 10^{2}\) & \(2.12\times 10^{2}\) & \(2.84\times 10^{2}\) \\ MOPSO & \(1.33\times 10^{3}\) & \(5.82\times 10^{3}\) & \(2.44\times 10^{3}\) & \(2.87\times 10^{3}\) & \(1.32\times 10^{3}\) \\ MOAO & \(1.14\times 10^{3}\) & \(4.52\times 10^{3}\) & \(2.26\times 10^{3}\) & \(2.56\times 10^{3}\) & \(1.01\times 10^{3}\) \\ MOHBA & \(1.30\times 10^{3}\) & \(3.75\times 10^{3}\) & \(2.17\times 10^{3}\) & \(2.22\times 10^{3}\) & \(6.87\times 10^{2}\) \\ MOWOA & \(9.95\times 10^{2}\) & \(6.85\times 10^{3}\) & \(3.05\times 10^{3}\) & \(3.67\times 10^{3}\) & \(1.85\times 10^{3}\) \\ MOGWO & \(1.01\times 10^{3}\) & \(2.90\times 10^{3}\) & \(1.78\times 10^{3}\) & \(1.85\times 10^{3}\) & \(5.62\times 10^{2}\) \\ MOFECO & \(4.12\times 10^{2}\) & \(7.87\times 10^{3}\) & \(1.25\times 10^{3}\) & \(1.77\times 10^{3}\) & \(1.84\times 10^{3}\) \\ LSMOFECO & \(2.77\times 10^{1}\) & \(1.35\times 10^{3}\) & \(1.51\times 10^{2}\) & \(2.39\times 10^{2}\) & \(3.33\times 10^{2}\) \\ MOFECO-MS & \(3.99\times 10^{1}\) & \(1.59\times 10^{2}\) & \(5.91\times 10^{1}\) & \(8.07\times 10^{1}\) & \(4.29\times 10^{1}\) \\ \hline \end{tabular}
\end{table} 
Table 39: Statistical results of SP indicator of the eight comparison algorithms for \(a280\_n2790\). Based on the experimental results presented in Figures 8-16 and the detailed metrics analysis, we can derive key insights into the performance of the MOFECO-MS algorithm compared to other competing algorithms across the various BITTP instances:  
* Overall summary:
* MOFECO-MS demonstrated outstanding performance across multiple instances, particularly in the HV (Hypervolume) and SP (Spread) indicators, proving its overall advantage in multi-objective optimization problems. * While MOFECO-MS did not achieve the highest PD (Pure Diversity) values in every instance, its performance remained stable and close to optimal. * The comparison charts show that MOFECO-MS consistently outperformed other algorithms in terms of solution distribution and quality across different instances, highlighting its ability to generate diverse and stable solutions. * Specific instance analysis:
* HV Indicator: MOFECO-MS achieved the best HV values across all statistical measures in 15 runs, demonstrating strong overall performance. The only exception was its variance, which was not the best, but its overall performance remained excellent. * SP Indicator: MOFECO-MS had convergence results slightly behind LSMOFECO, but the performance was very close, showing excellent capability in maintaining solution concentration and convergence. * PD Indicator: Although not the highest, MOFECO-MS still performed well, indicating strong competitiveness in diversity. * HV and SP Indicators: MOFECO-MS excelled in these key indicators, showing outstanding performance in both overall quality and convergence. * PD Indicator: Second to MOFECO but still ranked highly, indicating strong diversity performance. Figure 16: Plots of the non-dominated solutions in the objective space of _a280\(n\)2790 obtained by nine algorithms in 15 independent runs (solutions obtained in each run are denoted by each color). _eil_51\(n\)500:
* HV Indicator: MOFECO-MS achieved the best HV values, confirming its overall performance advantage. * SP Indicator: It performed closely with LSMOFECO, showing good convergence. * PD Indicator: Second to MOFECO, but still ranked highly. * \(ch150\_n149\):
* HV and SP Indicators: MOFECO-MS achieved the best performance in both indicators, showing strong performance in medium-scale instances. * PD Indicator: While not the highest, it remained at a high level. * \(ch150\_n1395\), \(ch150\_n1490\):
* HV and SP Indicators: MOFECO-MS continues to perform best in these two indicators, showing excellent performance in more complex instances. * PD Indicator: Slightly behind MOFECO but still close to optimal, indicating a good balance in diversity.