Computational Intelligence - February 2017 - 39
It is clear that the proposed algorithm is not very sensitive
to the setting of maximum number of generations since its
HV-metric is very stable after 300 generations of evolution.
Figs. 8-10 plot the distributions of the solutions with the
median HV-metric obtained by M2M versus MOEA/D (not
using the M2M decomposition strategy) for the three networks.
From these figures, we can compare the convergence and diversity of the solutions obtained by M2M and MOEA/D in an intuitive way. Obviously, M2M using the population decomposition
strategy outperforms MOEA/D both in convergence and diversity. It is because of the M2M population strategy that the information of infeasible solutions can be fully utilized to guide the
population search. Since the TA planning problem has a lot of
complex constraints, some infeasible solutions can be very crucial
during the evolutionary process. In the M2M framework, the
selection operator is conduced independently in each subpopulation, and those infeasible but crucial solutions are more likely to
survive. The algorithm without the M2M population strategy
TABle 5 The Location Update Cost (LUC), Paging Cost (PC) and Weight Sum Cost (WSC) of network 2 for 10 groups of test parameters.
NeTwOrk 2
MulTi-OBjecTive MOdel
SiNgle-OBjecTive MOdel
grOuP
luc
Pc
wSc
luc
Pc
wSc
1
5994
26235
86175
5994
26235
86175
2
6372
21159
84879
7648
18019
94499
3
6258
24310
86890
9086
17267
108127
4
6576
24512
90272
7566
19440
95100
5
6816
23519
91679
6928
23736
93016
6
6410
23014
87114
6992
25375
95295
7
7212
21704
93824
6934
21210
90550
8
5762
26430
84050
7868
18321
97001
9
7090
21038
91938
8338
21322
104702
10
7346
21217
94677
10080
15132
115932
TABle 6 The Location Update Cost (LUC), Paging Cost (PC) and Weight Sum Cost (WSC) of network 3 for 10 groups of test parameters.
NeTwOrk 3
MulTi-OBjecTive MOdel
SiNgle-OBjecTive MOdel
grOuP
luc
Pc
wSc
luc
Pc
wSc
1
16148
70297
231777
18210
57814
239914
2
15274
50119
202859
18738
55787
243167
3
14238
54597
196977
17596
54089
230049
4
14490
60501
205401
19330
60836
254136
5
15114
54757
205897
18288
60033
242913
6
13762
50298
187918
18576
60557
246317
7
13872
57336
196056
18572
54191
239911
8
15274
50119
202859
18378
60369
244149
9
14238
54597
196977
17776
61728
239488
10
14490
60501
205401
17446
63466
237926
TABle 7 Best, worst, median, mean, and standard deviation of HV-metric values obtained by M2M and MOEA/D
in 15 independent runs for each network.
neTwOrk
AlgOrIThM
BeST
wOrST
MedIAn
MeAn
STd
1
M2M
22.0228
21.3033
21.69178
21.68115
0.194377
MOeA/d
21.6442
21.0631
21.33346
21.33535
0.210806
M2M
21.6862
21.1803
21.41088
21.39275
0.188406
MOeA/d
21.3409
20.5926
20.93512
20.9217
0.272798
M2M
18.4156
17.7834
18.10996
18.14175
0.194861
MOeA/d
17.6228
17.0018
17.32225
17.3455
0.204509
2
3
FEbruary 2017 | IEEE ComputatIonal IntEllIgEnCE magazInE
39
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