IEEE Computational Intelligence Magazine - November 2021 - 30

TABLE I Mean standard score comparison with baseline
methods on multitasking MOO benchmark problems over
30 independent runs.
other two in 19 of 20 problems, which indicates the superiority
of the proposed algorithm.
PROBLEMS
CIHS
CIMS
CILS
PIHS
PIMS
PILS
NIHS
NIMS
NILS
SUM
RANK
GRA
−1.4142E+00
−1.3449E+00
−1.4142E+00
−1.4083E+00
−1.3783E+00
−1.1253E+00
−1.3398E+00
−1.2498E+00
−1.1473E+00
−1.1822E+01
1
MOMFEA
7.0711E-01
5.7344E-01
7.0711E-01
7.5655E-01
4.5814E-01
−3.0862E-03
2.9116E-01
3.9576E-01
1.0442E+00
4.9304E+00
2.2
MFEARR
7.0711E-01
7.7147E-01
7.0711E-01
6.5179E-01
9.2018E-01
1.1284E+00
1.0486E+00
8.5407E-01
1.0314E-01
6.8919E+00
2.6
TABLE II Mean standard score comparison with baseline
methods on multitasking MOO complex problems over 30
independent runs.
PROBLEMS
CPLX1
CPLX2
CPLX3
CPLX4
CPLX5
CPLX6
CPLX7
CPLX8
CPLX9
CPLX10
SUM
RANK
GRA
−3.4888E-01
−1.3990E+00
−1.1388E+00
−1.3563E+00
−1.3830E+00
−1.3980E+00
−1.3914E+00
−1.3262E+00
−1.3901E+00
−7.0704E-01
−1.1839E+01
1.1
MOMFEA
−5.7392E-01
6.7136E-01
8.5738E-02
7.1928E-01
5.5175E-01
6.9712E-01
7.5790E-01
5.6511E-01
8.3786E-01
3.4535E-01
4.6575E+00
2.2
MFEARR
9.2281E-01
7.2764E-01
1.0530E+00
6.3705E-01
8.3127E-01
7.0087E-01
6.3347E-01
7.6105E-01
5.5228E-01
3.6170E-01
7.1811E+00
2.7
TABLE III Mean standard score comparison with baseline
methods on multitasking many-task benchmark problems
over 30 independent runs.
PROBLEMS
MATP1
MATP2
MATP3
MATP4
MATP5
MATP6
MATP7
MATP8
MATP9
MATP10
SUM
RANK
GRA
−1.3425E+00
−1.3730E+00
−1.3726E+00
−1.3578E+00
−1.3657E+00
−1.3773E+00
−1.3403E+00
−1.3231E+00
−1.3338E+00
−1.3227E+00
−1.3509E+01
1
MOMFEA
3.0013E-01
4.1219E-01
4.0229E-01
3.9274E-01
4.0490E-01
4.3719E-01
3.0109E-01
2.6753E-01
3.1417E-01
2.7190E-01
3.5041E+00
2
MFEARR
1.0424E+00
9.6078E-01
9.7026E-01
9.6510E-01
9.6082E-01
9.4010E-01
1.0392E+00
1.0556E+00
1.0197E+00
1.0508E+00
1.0005E+01
3
2) Comparison with State-of-the-art Methods
To verify that the proposed resource allocation component
can further enhance the overall performance of the existing
state-of-the-art EMTO algorithms, we implement GRA based
on the well-known MMDE [31] method. Besides, the stateof-the-art
resource allocation method MTO-DRA is also
implemented based on MMDE, and MTO-DRA is extended
to MOO problems as described in Remark 3. Therefore, in
this subsection, two questions can be answered: a) whether the
proposed GRA can improve the base optimizer, and b)
whether the proposed GRA is better than its basic counterpart
MTO-DRA. To be specific, for complex problems depicted
in Table V, algorithms with resource allocation (i.e., GRA
TABLE IV Mean standard score comparison with state-ofthe-art
methods on multitasking MOO benchmark problems
over 30 independent runs.
PROBLEMS
CIHS
CIMS
CILS
PIHS
PIMS
PILS
NIHS
NIMS
NILS
SUM
RANK
GRA
−1.0690E+00
−6.1563E-01
2.1983E-01
−1.3353E+00
−2.7167E-01
−9.5101E-02
−4.3203E-01
−7.2102E-01
−4.1779E-01
−4.7378E+00
1.3
MTO-DRA
5.3452E-01
5.1526E-01
6.2052E-02
5.7140E-01
9.4840E-01
6.5294E-02
−1.7869E-02
6.0921E-01
−1.7149E-01
3.1168E+00
2.6
MMDE
5.3452E-01
1.0038E-01
−2.8188E-01
7.6389E-01
−6.7673E-01
2.9807E-02
4.4990E-01
1.1181E-01
5.8928E-01
1.6210E+00
2.1
TABLE V Mean standard score comparison with state-ofthe-art
methods on multitasking MOO complex problems
over 30 independent runs.
PROBLEMS
CPLX1
CPLX2
CPLX3
CPLX4
CPLX5
CPLX6
CPLX7
CPLX8
CPLX9
CPLX10
SUM
RANK
GRA
−2.9987E-01
1.0022E+00
−7.3725E-01
3.9292E-01
2.2346E-01
−2.5872E-01
−1.1805E+00
−1.2565E+00
−3.4173E-03
−6.9444E-01
−2.8120E+00
1.5
MTO-DRA
4.1514E-01
−6.0979E-01
−4.7486E-01
−1.3674E+00
−6.9272E-01
9.6603E-01
7.5577E-02
1.1790E+00
2.7906E-03
2.3182E-01
−2.7437E-01
2.1
MMDE
−1.1527E-01
−3.9246E-01
1.2121E+00
9.7449E-01
4.6926E-01
−7.0731E-01
1.1049E+00
7.7405E-02
6.2665E-04
4.6262E-01
3.0864E+00
2.4
30 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2021
IEEE Computational Intelligence Magazine - November 2021

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