Many-Objective Optimization Using Adaptive Differential Evolution with a New Ranking Method
Table 3
IGD, GD, and HV obtained by MODER, MOEA/D, NSGAII, and NSGAII-CE on DTLZ3.
IGD
GD
Mean
Std.
Mean
Std.
DTLZ3-5
MODER
0.231
0.0168
0.0837
0.0040
MOEA/D
0.2499(+)
0.0667
0.0869(+)
00071
NSGAII
0.6093(+)
0.1186
0.8738(+)
0.1039
NSGAII-CE
1.0903(+)
02406
0.0913(+)
0.0914
DTLZ3-10
MODER
0.4099
0.0171
0.3130
0.0126
MOEA/D
0.4264(+)
0.0585
0.3219(+)
0.0182
NSGAII
65.508(+)
14.659
812.75(+)
23.198
NSGAII-CE
1.0413(+)
0.3021
152.583(+)
234.71
DTLZ3-15
MODER
0.4723
0.0106
0.5662
0.0436
MOEA/D
0.6953(+)
0.0585
0.7038(+)
0.0703
NSGAII
85.563(+)
18.166
937.31(+)
22.914
NSGAII-CE
1.1584(+)
0.3419
20.217(+)
53.426
DTLZ3-20
MODER
0.5642
0.1296
0.8176
0.0746
MOEA/D
0.7542(+)
0.0233
1.0025(+)
0.0512
NSGAII
36.307(+)
17.207
573.32(+)
11.818
NSGAII-CE
1.2466(+)
0.3100
0.9260(+)
0.5774
DTLZ3-25
MODER
0.5292
0.0340
0.9388
0.0508
MOEA/D
0.7894(+)
0.1075
1.1898(+)
0.0433
NSGAII
90.042(+)
111.47
931.18(+)
14.475
NSGAII-CE
1.4141(+)
0.0002
6.7310(+)
15.187
DTLZ3-50
MODER
0.7507
0.0337
0.5076
0.0048
MOEA/D
0.9589(+)
0.2665
1.1179(+)
0.4531
NSGAII
71.523(+)
31.877
703.20(+)
284.21
NSGAII-CE
0.9211(+)
0.4885
1.9211(+)
0.4885
“+” 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.
