IEEE Computational Intelligence Magazine - November 2021 - 34

generation 880 to generation 1000, which results in the stable
decrease of IGD value of task 1. In the later optimization
process, the allocation component of GRA tends to
allocate resources in an average and a fair way, and to some
extent still prefers task 1 for its stable IGD decreasing trend.
The detailed analysis in turn justifies that the proposed
attainment function can capture the performance of the
MOO solver.
For CPLX10, due to the powerful base optimizer MMDE,
all the algorithms can immediately attain the best solution sets
in task 2. Under the circumstance, the proposed GRA can
effectively allocate more resources for task 1, thereby leading to
CPLX8-Task 1
CPLX10-Task 1
0.0065
0.0060
0.0055
0.0050
0.0045
50
60
70
80
MTO-DRA
MMDE
GRA
0.008
0.007
0.006
0.005
0.004
Total Computational Budget (%)
90 100
(a)
CPLX8-Task 2
0.009
0.008
0.007
0.006
0.005
50
60
70
80
MTO-DRA
MMDE
GRA
0.0000010
0.0000008
0.0000006
0.0000005
0.0000004
0.0000000
Total Computational Budget (%)
90
(b)
Resource Allocation Details for CPLX8
350
300
250
200
150
100
50
Task 1
Task 2
500
400
300
200
100
700 800 900 1,000
Generation
1,100 1,200 1,300
(c)
100
50
60
70
80
MTO-DRA
MMDE
GRA
Total Computational Budget (%)
90
(d)
CPLX10-Task 2
MTO-DRA
MMDE
GRA
100
0204060
Total Computational Budget (%)
(e)
Task 1
Task 2
80 100
Resource Allocation Details for CPLX10
400 600 800
1,000 1,200 1,400
Generation
(f)
FIGURE 5 Convergence traces of GRA, MTO-DRA, MMDE, and corresponding resource allocation details of GRA on representative problem sets,
CPLX8 and CPLX10.
34 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2021
Accumulated Resources
Average IGD Value
Average IGD Value
Average IGD Value
Accumulated Resources
Average IGD Value

IEEE Computational Intelligence Magazine - November 2021

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