A Decomposition-Based Multiobjective Evolutionary Algorithm with Adaptive Weight Adjustment
Table 5
HV, GD, and IGD obtained by MOEA/D with three the initialization methods.
Problems
HV
IGD
Mean
Std
Mean
Std
UF8
MOEA/D1
0.6094(+)
0.0426
0.1246(+)
0.0395
MOEA/D2
0.6388(+)
0.0153
0.1319(+)
0.0262
MOEA/D3
0.6421
0.0315
0.1165
0.0241
UF9
MOEA/D1
0.8036(+)
0.0954
0.1549(+)
0.1036
MOEA/D2
0.8996(=)
0.0765
0.1082(=)
0.0537
MOEA/D3
0.9064
0.0961
0.1127
0.0886
UF10
MOEA/D1
0.3716(+)
0.1214
0.3145(+)
0.0614
MOEA/D2
0.3718(+)
0.0962
0.2245(+)
0.0443
MOEA/D3
0.4881
0.0634
0.1665
0.0476
DTLZ1
MOEA/D1
0.0904(+)
0.0004
0.0260(+)
0.0005
MOEA/D2
0.0934(=)
0.0003
0.0244(+)
0.0002
MOEA/D3
0.0950
0.0009
0.0201
0.0004
DTLZ2
MOEA/D1
0.6716(+)
0.0031
0.0680(+)
0.0004
MOEA/D2
0.6989(+)
0.0023
0.0632(+)
0.0006
MOEA/D3
0.7041
0.0061
0.0612
0.0009
DTLZ3
MOEA/D1
0.6813(+)
0.0046
0.0624(+)
0.0009
MOEA/D2
0.6983(+)
0.0032
0.0633(+)
0.0004
MOEA/D3
0.7105
0.0068
0.0580
0.0008
DTLZ4
MOEA/D1
0.6954(+)
0.0058
0.0651(+)
0.0008
MOEA/D2
0.6997(=)
0.0038
0.0632(+)
0.0005
MOEA/D3
0.7012
0.0045
0.0604
0.0012
DTLZ5
MOEA/D1
0.4214(+)
0.0003
0.0091(+)
0.0002
MOEA/D2
0.4366(=)
0.0001
0.0071(=)
0.0002
MOEA/D3
0.4374
0.0003
0.0061
0.0004
DTLZ6
MOEA/D1
0.3410(+)
0.0001
0.0830(+)
0.0001
MOEA/D2
0.3461(+)
0.0300
0.0820(+)
0.0289
MOEA/D3
0.3815
0.0020
0.0101
0.0042
DTLZ7
MOEA/D1
1.4263(+)
0.0716
0.1925(+)
0.0861
MOEA/D2
1.5107(+)
0.0617
0.1790(+)
0.1156
MOEA/D3
1.5846
0.0604
0.0912
0.0754
“+” means that MOEA/D3 outperforms its competitor algorithm, “−” means that MOEA/D3 is worse than its competitor algorithm, and “=” means that the competitor algorithm has the same performance as MOEA/D3.
