IEEE Computational Intelligence Magazine - November 2021 - 28

E. Implementation Details of GRA
The proposed framework is implemented based on MMDE
[31], wherein each task is resolved by a JADE [32] optimizer
with an additional adaptive local search component. Within the
local search component, the local search radius r ,ij
in decision
space for each dimension j of each individual i is reserved, and
these local search radius will also undergo variation operators
in JADE as normal decision parameters do. Moreover, an adaptive
update mechanism is employed for the local search radius
so that a successful local search can be rewarded by a reward
rate m and an unsuccessful local search can be punished by the
same reward rate. For more details of MMDE, one can refer to
the original work [31].
When computing the normalized attainment function of
given MOO solution sets as indicated in equation (13), GRA
normalizes the solutions into [, ]01 n
by the corresponding
largest solution in the last M time steps as indicated in equation
(15). However, in some complex scenarios where different
objective values can decrease in different degrees of
magnitude, the normalized attainment function cannot illustrate
the MOO performance of the solution set well. To remedy
such cases, the integral domain of
is set to [, ]eps 1 n
[, ]xxr
-
instead of [, ]01 n
05 05
in equation (13)
, where eps is set to -0.5 in
this paper. This means the coverage we aim to compute is
fixed at origin [. ,. ]
in Fig.3.
-- instead of [, ]00 , as depicted
IV. Experimental Analysis
In this section, comparative studies are conducted to justify
the functionality and analyze the behavior of the devised generalized
resource allocation mechanism. To be specific, MOMFEA
[43] and MFEARR [35] serve as the baseline
methods for illustrating the superiority of GRA. Moreover,
f1
1
S1
S2
S3
B. Performance Metrics
Since when considering resource allocation, it is expected that
the overall optimization performance of all the tasks can be
improved, herein we compare different algorithms in an integrated
way. First, to evaluate the MOO searching performance
for each task, the inverted generational distance (IGD) [45] is
applied, which can be defined as equation (16):
1
f2
IGD =
where A, P ,)
(-0.5, -0.5)
FIGURE 3 Illustration of the revised attainment function for a given set
{ ,,}
SS S123 in the objective space. Points in the grey area can dominate at
least one element in the given set. The origin point is set as (−0.5, −0.5)
instead of (0,0).
4 http://www.bdsc.site/websites/MTO/index.html
1
|| pP)
P
)
!
dist(p, a), |*| stand for the MOO solution set of
our algorithm, the reference solution sets representing the optimal
solution set, the distance between solution a and reference
/ aA
!
min dist pa
2(, )
(16)
MTO-DRA [40] and MMDE [31] are employed for clarifying
the effectiveness of GRA. Besides, the resource allocation
details and parameter sensitivities are also explored for better
analyzing the algorithmic behavior. To comprehensively evaluate
the proposed algorithm, the algorithm with different
implementations and the real-world application studies are
also covered in this section.
A. Test Problems
For a more comprehensive comparative analysis, the comparison
experiments are conducted on three sorts of problems:
benchmark problems, complex problems, and many-task problems
of multitasking MOO.
Among them, benchmark problems involve nine multitasking
MOO optimization problems, and each problem contains
two tasks with certain associations that cover different degrees
of fitness landscape similarity and different degrees of optima
intersection between two tasks. The intersection degrees
encompass complete intersection (CI), partial intersection (PI),
and no intersection (NI). The similarity degrees encompass
high similarity (HS), medium similarity (MS), and low similarity
(LS). By these different problem attributes, nine sets of problems
can be constructed including CIHS, CIMS, CILS, PIHS,
PIMS, PILS, NIHS, NIMS, and NILS. For more details of
benchmark multitasking MOO problems, one can refer to the
original work [44].
The complex problem set, CPLX, involves 10 multitasking
MOO problems among which each contains two optimization
tasks. Moreover, the many-task problems, MATP,
includes 10 multitasking MOO problems among which
each contains 50 optimization tasks. For both CPLX and
MATP, every single one of the optimization tasks is exactly
a multi-objective problem. Notably, CPLX and MATP are
both the test problems utilized in the Competition on Evolutionary
Multi-Task Optimization of WCCI-2020. For
more details of the two problems, one can refer to the official
website4.
28 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2021
http://www.bdsc.site/websites/MTO/index.html
IEEE Computational Intelligence Magazine - November 2021

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