Table 7: Comparative results of all the compared algorithms on the UF test problems regarding HV.

ProblemsAlgorithms
MOEA/D-DEMOEA/D-DRAMOEA/D-FRRMABMOEA/D-STMMOEA/D-UCB-TMOEA/D-ARGMOEA/D-LSIAS

UF1
 Mean3.58833.59373.61573.62653.61593.61893.6225
 IQR
 Rank7651432
UF2
 Mean3.60943.61583.63553.62023.63433.62693.6383
 IQR
 Rank7625341
UF3
 Mean3.54573.57533.56713.59663.56883.60073.6043
 IQR
 Rank7463521
UF4
 Mean3.17293.16673.20673.18183.20723.22293.2244
 IQR
 Rank674532≈1
UF5
 Mean2.79222.85372.95873.19192.92283.05373.1661
 IQR
 Rank7641532
UF6
 Mean2.76712.80212.98913.00712.99202.84443.1059
 IQR
 Rank7642351
UF7
 Mean3.41473.42763.43963.45343.43923.46153.4774
 IQR
 Rank7643521
UF8
 Mean6.35766.33276.78286.63256.78136.47926.5927
 IQR
 Rank6713254
UF9
 Mean6.81277.02367.03457.15757.03277.10827.1056
 IQR
 Rank7641523
UF10
 Mean3.64433.74563.71983.62113.72033.81083.8102
 IQR
 Rank6357412

Rank Sum67573931392918

+/−/≈0/10/00/10/01/9/04/6/01/9/02/7/1

“+,” “−,” and “≈,” respectively, indicate the result of the algorithm is better than, worse than, and similar to that of MOEA/D-LSIAS based on the Wilcoxon’s rank sum test with a significance .