Many-Objective Optimization Using Adaptive Differential Evolution with a New Ranking Method
Table 2
IGD, GD, and HV obtained by MODER, MOEA/D, NSGAII, and NSGAII-CE on DTLZ1.
IGD
GD
Mean
Std.
Mean
Std.
DTLZ1-5
MODER
0.0719
0.0067
0.0311
0.0025
MOEA/D
0.0756(+)
0.0074
0.0317(+)
0.0035
NSGAII
23.789(+)
15.261
233.69(+)
20.501
NSGAII-CE
0.2989(+)
0.1023
0.0124(−)
0.0202
DTLZ1-10
MODER
0.0921
0.0146
0.1160
0.0075
MOEA/D
0.1045(+)
0.0081
0.1141(=)
0.0242
NSGAII
25.065(+)
6.9643
343.45(+)
10.444
NSGAII-CE
0.3246(+)
0.0969
0.0055(−)
0.0079
DTLZ1-15
MODER
0.0968
0.0063
0.1925
0.0103
MOEA/D
0.1141(+)
0.0101
0.1340(−)
0.0198
NSGAII
15.866(+)
11.499
222.14(+)
5.2899
NSGAII-CE
0.4152(+)
0.0942
0.5510(+)
0.0457
DTLZ1-20
MODER
0.1523
0.0613
0.2289
0.0056
MOEA/D
0.1162(−)
0.0176
0.1542(−)
0.0133
NSGAII
32.596(−)
13.770
373.34(+)
5.1034
NSGAII-CE
0.4197(−)
0.0604
0.1218(−)
0.1244
DTLZ1-25
MODER
0.2030
0.0585
0.2679
0.0302
MOEA/D
0.1599(−)
0.0881
0.2165(−)
0.1604
NSGAII
37.273(+)
21.605
389.85(+)
6.1814
NSGAII-CE
0.4694(+)
0.0558
0.1237(−)
0.1144
DTLZ1-50
MODER
0.3180
0.0392
0.2865
0.0845
MOEA/D
0.1623(−)
0.0142
0.1570(−)
0.0290
NSGAII
33.276(+)
13.482
364.25(+)
9.7122
NSGAII-CE
1.1990(+)
2.3179
1.5583(+)
3.5537
“+” means that MODER outperforms its competitor algorithm, “−” means that MODER is outperformed by its competitor algorithm, and “=” means that the competitor algorithm has the same performance as MODER.
