Research Article
A Two-Archive Algorithm with Interactive Mechanism for Many-Objective Optimization
Table 3
Performance comparison on WFG problems with respect to the average HV values.
| Problem | Obj. | iTwoArch | TwoArchA+ | TwoArch2 | MOEAD | MOEADAM2M | NSGAIII |
| WFG1 | 3 | 0.926901 | 0.856271 | 0.867731 | 0.911308 | 0.915450 | 0.819699 | 5 | 0.948594 | 0.737199 | 0.819418 | 0.847980 | 0.902880 | 0.670358 | 8 | 0.816376 | 0.718838 | 0.741628 | 0.686077 | 0.801972 | 0.739105 | 10 | 0.796913 | 0.857521 | 0.777469 | 0.762214 | 0.833262 | 0.742918 | 15 | 0.711188 | 0.820765 | 0.986308 | 0.918149 | 0.914750 | 0.952438 |
| WFG2 | 3 | 0.952058 | 0.934914 | 0.960704 | 0.926123 | 0.948581 | 0.956676 | 5 | 0.994906 | 0.993320 | 0.993009 | 0.957989 | 0.987057 | 0.988425 | 8 | 0.987309 | 0.981483 | 0.994552 | 0.989272 | 0.996225 | 0.979909 | 10 | 0.995084 | 0.990506 | 0.995044 | 0.994259 | 0.997953 | 0.986114 | 15 | 0.994858 | 0.993955 | 0.997924 | 0.993435 | 0.951768 | 0.995440 |
| WFG3 | 3 | 0.695192 | 0.687666 | 0.716139 | 0.705539 | 0.705136 | 0.703835 | 5 | 0.660971 | 0.649774 | 0.658714 | 0.584767 | 0.625069 | 0.673299 | 8 | 0.526521 | 0.490723 | 0.636992 | 0.485826 | 0.580795 | 0.531304 | 10 | 0.505360 | 0.458569 | 0.622333 | 0.425440 | 0.499074 | 0.636623 | 15 | 0.452146 | 0.324792 | 0.604605 | 0.243627 | 0.374232 | 0.605925 |
| WFG4 | 3 | 0.726491 | 0.715394 | 0.737768 | 0.698283 | 0.718604 | 0.729026 | 5 | 0.875610 | 0.867630 | 0.806952 | 0.744254 | 0.819480 | 0.860951 | 8 | 0.917326 | 0.906253 | 0.820707 | 0.822711 | 0.923953 | 0.859924 | 10 | 0.958477 | 0.939936 | 0.800069 | 0.844913 | 0.952985 | 0.896477 | 15 | 0.941565 | 0.966244 | 0.715636 | 0.749120 | 0.735066 | 0.963551 |
| WFG5 | 3 | 0.693701 | 0.686129 | 0.708057 | 0.675991 | 0.695819 | 0.698574 | 5 | 0.833103 | 0.831710 | 0.795315 | 0.712879 | 0.837515 | 0.835516 | 8 | 0.870247 | 0.869837 | 0.799887 | 0.757722 | 0.869645 | 0.858166 | 10 | 0.902923 | 0.899994 | 0.776144 | 0.798187 | 0.889022 | 0.888981 | 15 | 0.894864 | 0.908233 | 0.670493 | 0.783439 | 0.636881 | 0.918765 |
| WFG6 | 3 | 0.700455 | 0.684049 | 0.713969 | 0.672674 | 0.697281 | 0.705634 | 5 | 0.837602 | 0.833408 | 0.787224 | 0.704609 | 0.735872 | 0.830531 | 8 | 0.868866 | 0.860966 | 0.785815 | 0.758439 | 0.872055 | 0.849389 | 10 | 0.901661 | 0.886148 | 0.749615 | 0.772267 | 0.887966 | 0.880136 | 15 | 0.865854 | 0.868941 | 0.657703 | 0.750781 | 0.635003 | 0.896825 |
| WFG7 | 3 | 0.726702 | 0.714129 | 0.739790 | 0.704927 | 0.717896 | 0.730001 | 5 | 0.873202 | 0.868793 | 0.825695 | 0.736929 | 0.810010 | 0.872547 | 8 | 0.921806 | 0.916877 | 0.854173 | 0.811058 | 0.919822 | 0.900116 | 10 | 0.962508 | 0.954990 | 0.827919 | 0.875988 | 0.947103 | 0.939205 | 15 | 0.952157 | 0.969923 | 0.723336 | 0.750785 | 0.693370 | 0.974412 |
| WFG8 | 3 | 0.687804 | 0.671980 | 0.694747 | 0.667656 | 0.677682 | 0.695647 | 5 | 0.818049 | 0.805905 | 0.726794 | 0.664497 | 0.708814 | 0.813213 | 8 | 0.787465 | 0.783934 | 0.685914 | 0.676467 | 0.804487 | 0.778344 | 10 | 0.871625 | 0.828460 | 0.622675 | 0.688680 | 0.788674 | 0.820759 | 15 | 0.839984 | 0.777011 | 0.562198 | 0.385052 | 0.613180 | 0.904617 |
| WFG9 | 3 | 0.706828 | 0.684670 | 0.721881 | 0.675983 | 0.691046 | 0.704539 | 5 | 0.841536 | 0.811042 | 0.790622 | 0.712429 | 0.790458 | 0.820898 | 8 | 0.833432 | 0.813514 | 0.804324 | 0.777175 | 0.872163 | 0.806365 | 10 | 0.835911 | 0.872345 | 0.759983 | 0.730805 | 0.879867 | 0.859226 | 15 | 0.725454 | 0.775216 | 0.604799 | 0.540458 | 0.633879 | 0.882199 |
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Note. ā ā means that the result is significantly outperformed by iTwoArch. |