# Elite Multi-Criteria Decision Making--Pareto Front Optimization in Multi-Objective Optimization
## 5 Discussion  
In this section, the performance of the eMPF optimizer is compared with the other tested optimization techniques. The performance is evaluated with the test functions mentioned in Appendix A. The objective and search space of all of the test functions used are plotted and provided in the linked GitHub repository found at the end of this paper. **Binh and Korn Function:** eMPF achieved a low standard deviation, demonstrating its performance in obtaining quality solutions across all test runs. Moreover, it had the lowest average of fitness compared with other optimizers in the first objective function. When the spread (\(\Delta\)) was considered, eMPF had the highest spread value over the other optimization techniques with a larger set of solutions generated over the Pareto front. The eMPF optimizer had 50% better performance than the M-PF optimizer when compared using the generational distance (\(GD\)). **Chancing and Haimes Function:** For this test function, the minimum optimal solution obtained for each objective function was the lowest with NSGA-III and M-PF and had a difference of around 0.1 units higher than NSGA-II. However, eMPF showed a more centered distribution of solutions along with consistently more reliable solutions. When the spread (\(\Delta\)) was considered, eMPF generated a diverse set of solutions, and NSGA-III offered the widest coverage of the Pareto front for this specific function. The generational distance (\(GD\)) of eMPF was higher than that of the rest of the optimizers due to the extreme solutions carried forward to the next generations. Figure 3 demonstrates the extreme solutions generated by the eMPF optimizer. Holding on to these extreme solutions will be beneficial when the complexity of the search space increases. **Fonseca-Fleming Function:** eMPF demonstrated good performance, closely competing with NSGA-II in finding the optimal solutions while surpassing it in average performance and consistency. With the highest spread value, eMPF outperformed all other methods in terms of diversity, indicating its superior capability to explore and cover a wider range of the Pareto front. **Test Function 4:** All the four optimization techniques had similar lowest, average, and standard deviation values. However, eMPF surpassed the other techniques in the spread (\(\Delta\)), showing its diverse set of solution generation capability. **Kursawe Function:** M-PF surpassed all other optimization techniques in spread (\(\Delta\)), proving its diverse solution set. In addition, M-PF outperformed all other optimization techniques even in obtaining minimum values, average, and standard deviation. However,eMPF had more than 25% better performance in the generational distance (\(GD\)) than that of M-PF. **Schaffer Function N1 and N2:** eMPF was able to reach better results than other optimization techniques with respect to the minimum values, mean, and standard deviations. It also had higher spread (\(\Delta\)) values than other optimizers. NSGA-II and NSGA-III, while offering competitive performances, were not able to match eMPF's precision, consistency, and diversity. eMPF outperformed the other optimizers by obtaining accuracy (minimum values), consistency (low mean and standard deviation), and diversity (high spread). **[PERSON]'s Two Objectives:** NSGA-II and eMPF optimization techniques had nearly the same minimum value; however, eMPF had a better mean and standard deviation. NSGA-III and M-PF optimizer had a better spread (\(\Delta\)) value than eMPF. **Zitzler-Deb-Thiele's from N1, N2, N3, N4, and N6:** All of the optimization techniques had nearly the same performance in this set of functions, and there were negligible value variances. For example, in Zitzler-Deb-Thiele's N2, the difference between minimum function 1 values between all optimizers was 0.000001 while considering the precision value of 6. All optimization techniques performed equally well in all of these test functions.