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

Note. “” means that the result is significantly outperformed by iTwoArch.