Table 8.
Results of the evaluation metrics for each metaheuristic.
| Test problem | NPS |
MID |
SNS |
HV |
||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| SA | NSGA-II | SEO | AMSEO | SA | NSGA-II | SEO | AMSEO | SA | NSGA-II | SEO | AMSEO | SA | NSGA-II | SEO | AMSEO | |
| SP1 | 5 | 5 | 7 | 7 | 2.7 | 2.3 | 1.45 | 1.6567 | 39053 | 39418.5 | 33613 | 42156 | 2.86E＋09 | 1.58E＋09 | 1.98E＋09 | 2.17E＋09 |
| SP2 | 8 | 10 | 9 | 11 | 1.41 | 1.6 | 3.18 | 1.3832 | 71532 | 78760.5 | 72664 | 84093 | 2.91E＋09 | 5.83E＋09 | 2.85E＋09 | 3.81E＋09 |
| SP3 | 9 | 10 | 11 | 12 | 1.88 | 2.12 | 3.41 | 2.5528 | 103674 | 104004 | 105584 | 104846 | 3.84E＋09 | 4.33E＋09 | 4.81E＋09 | 5.36E＋09 |
| SP4 | 10 | 14 | 12 | 14 | 1.7 | 1.85 | 1.62 | 1.2058 | 116854 | 117621.5 | 113207 | 118923 | 5.18E＋09 | 4.58E＋09 | 3.97E＋09 | 6.48E＋09 |
| MP5 | 11 | 12 | 14 | 12 | 3.53 | 2.85 | 2.19 | 1.1014 | 199064 | 204185.5 | 206584 | 209671 | 4.82E＋09 | 5.00E＋09 | 5.18E＋09 | 8.13E＋09 |
| MP6 | 10 | 12 | 10 | 13 | 2.63 | 1.85 | 2.26 | 1.1175 | 298976 | 283356.5 | 225643 | 268749 | 6.49E＋09 | 9.46E＋09 | 5.92E＋09 | 8.92E＋09 |
| MP7 | 11 | 12 | 13 | 15 | 1.41 | 1.054 | 2.62 | 1.1044 | 289074 | 306566.5 | 319065 | 326843 | 8.18E＋09 | 7.44E＋09 | 7.39E＋09 | 7.49E＋09 |
| MP8 | 10 | 13 | 14 | 13 | 4.23 | 2.67 | 2.66 | 1.3081 | 375463 | 380037.5 | 382970 | 385034 | 9.22E＋09 | 8.63E＋09 | 8.14E＋09 | 9.11E＋09 |
| LP9 | 14 | 12 | 13 | 13 | 1.97 | 1.86 | 3.71 | 2.8128 | 519065 | 546744 | 563271 | 573297 | 8.50E＋09 | 1.13E＋10 | 9.60E＋09 | 1.29E＋10 |
| LP10 | 10 | 13 | 15 | 16 | 1.59 | 1.98 | 1.19 | 2.1869 | 40937 | 43501 | 45748 | 46743 | 2.18E＋10 | 2.34E＋10 | 1.82E＋10 | 2.85E＋10 |
| LP11 | 12 | 13 | 14 | 14 | 1.96 | 1.654 | 1.17 | 1.5879 | 76134 | 72212 | 79267 | 70864 | 1.03E＋10 | 1.41E＋10 | 1.43E＋10 | 1.39E＋10 |
| LP12 | 12 | 14 | 16 | 15 | 3.26 | 2.56 | 2.11 | 2.51 | 100689 | 100466.5 | 106429 | 101948 | 4.81E＋10 | 1.46E＋1 | 12.81E＋10 | 2.64E＋11 |
| Best | 1 | 1 | 4 | 7 | 1 | 2 | 3 | 6 | 1 | 0 | 3 | 8 | 3 | 2 | 1 | 6 |