IEEE Computational Intelligence Magazine - November 2021 - 31

and MTO-DRA) can generally outperform the base optimizer,
MMDE, in terms of the MSS values and the relative rankings,
which proves the necessity of resource allocation.
However, in some special cases, the resource allocation component
may adversely affect the original MMDE. To elaborate,
Table IV showcases that MTO-DRA is generally worse than
the original MMDE. Specifically, in the CILS problem and the
PIMS problem, the proposed GRA is also worse than the
original MMDE, even though GRA outperforms MMDE in
other benchmark problems. To explain, when encountering
only two tasks, the resource allocation component can merely
decide which task to invest computational resources into.
Generally, the task with better fitness improvement in the past
few generations is chosen to enjoy additional evaluations. In
this approach, it is possible that the problem with higher difficulty
that needs further evaluations to overcome local optima
is ignored. Conversely, the algorithm without resource allocation
can assign more evaluations to the difficult task, and can
effectively avoid local optima.5 In this case, the resource
allocation component such as GRA and MTO-DRA can be
detrimental to the overall performance. As for the comparison
of GRA and MTO-DRA, since GRA can capture a longterm
optimization performance due to the multi-step nonlinear
regression and can employ the transfer information during
evolution, it can generally outperform MTO-DRA in complex
problems in Table V. In Table IV, it seems like GRA is
comparable with MTO-DRA, since in this case the MOO
extension of MTO-DRA is based on our proposed method in
Section III.D, and the fixed allocation intensity, RAI, of MTODRA
is proper when encountering only two tasks. However,
the overall performance across all the problems and overall
rankings of GRA are still better.6
As for
the 50-task problems depicted in Table VI,
GRA can significantly outperform MTO-DRA and
MMDE due to the controllable resource allocation intensity,
RAI. Recall that in MTO-DRA, the value of RAI is
fixed as /,K11+^h which is as small as 0.0196 in 50-task
problems. Due to the fixed small resource allocation intensity
of MTO-DRA, its overall performance is similar to
that of MMDE. Differently, in GRA, users can predefine
the desired resource allocation intensity, and hence the
EMTO algorithm behavior can be controlled even when
encountered the many-task scenarios. Therefore, the superior
performance of GRA in 50-task problems in
Table VI indicates the advantage of the proposed generalized
allocation framework in Algorithm 2 that possesses
the adjustable resource allocation intensity.
3) Comparison with Adaptive Methods
To clarify the effectiveness of the proposevd GRA, two
additional adaptive multitasking MOO algorithms are
5 The preference towards the easy task or the difficult task can be viewed as an exploration-exploitation
trade-off.
6 Note that, the MOO extension of MTO-DRA is still based on the proposed component
in this paper, which is a major contribution.
involved for comparative studies. To be specific, MOMFEA-II
is a multitasking MOO algorithm that adaptively
adjusts the random mating probability matrix on the fly,
and EMTIL is also an adaptive multitasking MOO algorithm
that selects the individuals to transfer by incremental
learning and local search. In the benchmark problems
described in Table VII, the proposed GRA generally can
attain superior optimization performance compared with
the other two. The reason why EMTIL is generally worse
than MOMFEA-II is that in this paper the population size
is set to 65, and the overall performance of EMTIL may be
restricted. Moreover, the key component of EMTIL is a
local search component to better explore the task searching
space, so it cannot outperform GRA considering that
the base optimizer is also equipped with a local search
component as mentioned in Section III.E. However, GRA
TABLE VI Mean standard score comparison with state-ofthe-art
methods on multitasking MOO many-task problems
over 30 independent runs.
PROBLEMS
MATP1
MATP2
MATP3
MATP4
MATP5
MATP6
MATP7
MATP8
MATP9
MATP10
SUM
RANK
GRA
0.0000E+00
5.6507E-02
0.0000E+00
−2.1223E-01
−6.2413E-02
−1.3743E-01
−2.1591E-01
−1.4437E-01
−1.8843E-01
−4.4002E-02
−9.4828E-02
1.2
MTO-DRA
0.0000E+00
−4.6366E-02
0.0000E+00
8.9087E-02
8.9713E-02
2.0120E-01
1.8857E-01
1.7642E-02
2.9164E-02
5.5049E-02
6.2406E-02
2
MMDE
0.0000E+00
−1.0140E-02
0.0000E+00
1.2314E-01
−2.7299E-02
−6.3766E-02
2.7342E-02
1.2673E-01
1.5926E-01
−1.1048E-02
3.2422E-02
2.2
TABLE VII Mean standard score comparison with adaptive
methods on multitasking MOO benchmark problems over
30 independent runs.
PROBLEMS
CIHS
CIMS
CILS
PIHS
PIMS
PILS
NIHS
NIMS
NILS
SUM
RANK
GRA
−7.9929E-01
−1.3855E+00
−7.5674E-01
−7.3931E-01
−1.0265E+00
−7.5066E-01
−8.4271E-01
−6.8711E-01
−7.2152E-01
−7.7093E+00
1
MOMFEA-II
−6.0799E-01
4.8832E-01
−6.5550E-01
−6.7430E-01
−2.8095E-01
−6.6264E-01
−5.5930E-01
4.0459E-01
−6.9257E-01
−3.2403E+00
2.1
EMTIL
1.4073E+00
8.9717E-01
1.4122E+00
1.4136E+00
1.3075E+00
1.4133E+00
1.4020E+00
2.8252E-01
1.4141E+00
1.0950E+01
2.9
NOVEMBER 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 31
IEEE Computational Intelligence Magazine - November 2021

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