# Elite Multi-Criteria Decision Making--Pareto Front Optimization in Multi-Objective Optimization
## 5 Discussion
In addition, eMPF had better performance than all other optimizers in the generational distance (\(GD\)) except for the N4 test function. **Osyczka and Kundu Function:** All of the optimization techniques had nearly the same optimal value in terms of minimum values for each objective function. However, the eMPF optimizer was able to find a more diverse set of solutions compared with the other optimization techniques. Moreover, it was able to generate good solutions with greater consistency. In addition, eMPF had the better generational distance (\(GD\)) than NSGA-II. **Constr-Ex Function:** The eMPF optimizer was able to achieve the lowest minimum values out of all of the optimizers. However, the average values were slightly higher than other optimization techniques, making it somewhat skewed. This skew can be clearly seen in Figure 4. The generational distance (\(GD\)) does concur with the results due to its higher value for the eMPF. The spread (\(\Delta\)), on the other hand, showed good diversification of the solutions generated by eMPF. **VR-UC Test Functions:** In the VR-UC test function 1, eMPF had the better average and the highest standard deviation compared with other optimizers. However, eMPF had a higher generational distance (\(GD\)) than the other optimizers. Despite the higher generational distance, the spread of solutions is better for the eMPF optimizer. In the  
Figure 3: Pareto front generated for the Chancing and Haimes function using NSGA-II, NSGA-III, M-PF, and eMPF optimizers  
**MSGA Test Function:** eMPF outperformed all other optimizers in exploring the lowest fitness values of both objectives and was able to produce reliable solutions. This can be established with the lower mean and the higher standard deviations of the eMPF optimizer when compared to other optimizers. In addition, eMPF had a better generational distance (\(GD\)) and spread (\(\Delta\)) than NSGA-III and the M-PF optimizer. **Viennet Function:** As mentioned in Appendix A, this was a three-dimensional minimization multi-objective optimization problem. The average fitness values of the eMPF optimizer were better than other optimizers in all of the three objective functions. The eMPF optimizer had better generational distance (\(GD\)) than that of the M-PF optimizer, and it also had the highest spread (\(\Delta\)) values over other optimizers. **MHHM Functions:** These test functions also had three objective functions as mentioned in Appendix A. In both of the test functions, eMPF had the lowest average fitness, lowest generational distance (\(GD\)), and highest spread (\(\Delta\)) values over the other optimizers. This demonstrates eMPF's dominance in generating better and more diverse solutions when compared to other optimizers on these test functions. The Pareto front plot confirms eMPF's dominance, as shown in Figure 5.  
Overall, eMPF was able to find diverse solutions in all test scenarios while maintaining consistency in the solution set. Moreover, it was able to find better solutions than existing optimization techniques. In challenging problems such as Zitzler-Deb-Thiele's functions, it was able to generate better solutions than NSGA-II and NSGA-III. Reliability was also demonstrated with lower standard deviations for Schaffer functions and Poloni's two objective functions. The learning curves generated from the fitness values showed a higher learning rate in most test scenarios than the other optimizers. Moreover, when the objective functions were increased from two to three, the eMPF optimizer was able to perform better than the other optimizers demonstrated using the Viennet and MHHM test functions. However, the optimizer was not able to outperform other optimizers in all the test functions. The reliability and diversification of the solutions obtained using eMPF were not always better than other optimizer solutions. Additionally, when the true Pareto front was a straight line, such as in the Chankong Haimes function, the solutions from eMPF were not as reliable.