IEEE Computational Intelligence Magazine - November 2021 - 33

To verify the effectiveness of the proposed GRA, the
comparison results are illustrated in Table XI. In the benchmark
problems, the proposed GRA and MTODRA
can generally outperform MP-MFEA
without resource allocation components, which
justifies the effectiveness of the resource allocation
component. Moreover, the proposed GRA
is slightly better than MTO-DRA. To elaborate,
the key differences between GRA and
MTO-DRA are the time step size and the allocation
intensity. In GRA, when allocating
resources, optimization performance in the last
five steps is involved, and the RAI is 0.40. Conversely,
there are only two steps to consider in
MTO-DRA, and the RAI can be considered as
0.33. For the relatively weak optimizer, MPMFEA,
since the convergence speed is generally
slower, under certain circumstances a lower
resource allocation intensity can guarantee a
proper resource allocation.
MATP10
SUM
RANK
G. Discussions on Resource
Allocation Details
Since the major contribution of this paper is to
propose a resource allocation component, this
subsection is
intended to provide a deeper
insight into the resource allocation behavior of
GRA. In Fig.5, the convergence trends in the
last half of the computational budget for tasks of
representative complex problems, CPLX8 and
CPLX10, have been demonstrated. CPLX8 and
CPLX10 are selected as the representative problems
to illustrate the allocation details for their
special characteristics of convergence. To be
specific, in CPLX8, GRA has the apparent
resource allocation tendency in each convergence
stage, which makes it easy to understand
the allocation strategy. Moreover, in CPLX10,
the optimization difficulties for the two tasks
are rather different, which is easy to verify the
allocation ability for the proposed GRA. Meanwhile,
the corresponding resource allocation
details of GRA are also depicted in Fig.5 and
Fig.6. Fig.5 depicts the convergence traces of
algorithms and the accumulated allocated
resources for different tasks in GRA. Fig.6
depicts the resource allocation details in each
generation, where the point of (x, y) represents
that the computational resources are assigned to
the task y in generation x.
For CPLX8, the performance of GRA is
worse than the other two initially on task 2,
and due to the potential decreasing tendency
of task 2, GRA allocates more resources for
task 2 from generation 700 to generation 880.
Thereafter, GRA's performance on task 2 stagnates and
GRA, in turn, allocates more resources for task 1 from
TABLE IX Mean standard score comparison with adaptive methods on
multitasking MOO many-task problems over 30 independent runs.
PROBLEMS
MATP1
MATP2
MATP3
MATP4
MATP5
MATP6
MATP7
MATP8
MATP9
GRA
−7.0711E-01
−9.6560E-01
−7.0711E-01
−8.0588E-01
−8.2429E-01
−8.0098E-01
−8.1310E-01
−8.2785E-01
−8.1000E-01
−8.1076E-01
−8.0727E+00
1
MOMFEA-II
1.4142E+00
1.3767E+00
1.4142E+00
1.3975E+00
1.3901E+00
1.3993E+00
1.3937E+00
1.3877E+00
1.3970E+00
1.3940E+00
1.3964E+01
3
EMTIL
−7.0711E-01
−4.1115E-01
−7.0711E-01
−5.9159E-01
−5.6585E-01
−5.9832E-01
−5.8059E-01
−5.5990E-01
−5.8700E-01
−5.8323E-01
−5.8918E+00
1.8
TABLE X Comparison of GRA with different RAP.
RAP
CPLX1
CPLX2
CPLX3
CPLX4
CPLX5
CPLX6
CPLX7
CPLX8
CPLX9
CPLX10
SUM
0.35
0.61
0.78
1.31
−3.33
−0.46
−2.16
−0.11
−1.12
2.97
1.09
−0.41
0.4
3.30
−0.75
0.60
1.94
−0.53
0.59
1.24
1.31
−0.16
−0.74
6.80
0.45
−1.71
0.30
−1.81
1.49
0.89
−0.25
−0.47
3.34
−0.98
0.73
1.55
0.5
−0.35
−0.71
−0.25
1.15
1.03
0.05
-2.02
−1.83
1.52
0.55
-0.86
0.55
−0.12
0.75
−0.62
−0.90
−0.43
0.59
−2.36
−0.51
−1.91
−1.17
−6.70
0.6
0.36
2.10
−1.71
0.81
-1.72
−1.09
2.14
−0.08
−1.69
0.98
0.11
0.65
−2.10
−2.47
2.48
−1.16
1.23
2.26
1.57
−1.11
0.24
−1.45
-0.50
TABLE XI Mean standard score comparison on multitasking MOO
benchmark problems over 30 independent runs.
PROBLEMS
CIHS
CIMS
CILS
PIHS
PIMS
PILS
NIHS
NIMS
NILS
SUM
RANK
GRA
−1.3826E+00
1.2683E+00
1.3854E+00
−4.2368E-02
−5.2716E-01
−1.2626E+00
−6.1491E-01
2.5220E-01
−1.1852E+00
−2.1089E+00
1.8
MTO-DRA
9.2793E-01
−7.5211E-01
−8.7079E-01
−3.6719E-01
8.1002E-01
8.3372E-01
−6.4832E-01
−2.8011E-01
1.0934E+00
7.4656E-01
1.9
MP-MFEA
4.5465E-01
−5.1624E-01
−5.1460E-01
4.0955E-01
−2.8286E-01
4.2890E-01
1.2632E+00
2.7910E-02
9.1773E-02
1.3623E+00
2.3
NOVEMBER 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 33
IEEE Computational Intelligence Magazine - November 2021

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