IEEE Computational Intelligence Magazine - November 2021 - 25

Task Pool
Task K
Task 1
Task 2
Task 1 Task 2 Task 3
Allocating Resources
POP 1
POP 2
POP K
Resource
Pool
Control Parameter
Softmax Normalization
Evolve
Transfer Information
Cross-Population
Mutation/Crossover
Performance
Measure
Task 1 Task 2 Task 3
Performance
Improvement
FIGURE 1 Illustration of the proposed GRA framework and the general idea of resource allocation. The left section depicts the multi-population
framework, the cross-population evolution, and the resource allocation components. The right section depicts our general algorithmic idea,
which is to allocate more resources for more promising tasks.
the population performance on the multi-objective problems,
and the transfer information that is introduced in subsection C
can be captured. In the resource allocation process, the performance
measurement and the transfer information obtained in
the evolution process can be utilized to compute the resource
allocation vector IoI, with controllable allocation parameter that
is introduced in subsection B.
B. Controllable Allocation Intensity
Similar with MTO-DRA, the multi-population framework is
also adopted in which each sub-population is evolved for handling
a distinct optimization task, as shown in line 2 to line 6 in
Algorithm 2. Unlike allocating extra algorithm generations in
Algorithm 1, GRA conducts resource allocation in an embedded
approach by a control parameter RAP, as shown in line 9 to
line 17. Through this approach, the resource allocation intensity
can be explicitly controlled by the algorithmic users. To be
specific, as indicated in equation (8), the resource allocation
intensity (RAI) in MTO-DRA will decrease with increasing
task amounts and conversely in GRA the value of RAI is exactly
the same as RAP, which is convenient for interactive control.
C. Incorporation of the Knowledge Transfer Information
The proposed GRA incorporates the knowledge transfer information
during the evolution process and the resource allocation
process. To be specific, herein the knowledge transfer refers to
enabling the individual interaction between populations for different
tasks. Moreover, to control the individual interaction frequencies
between population i and population j, a random
mating parameter rmp ,ij is maintained, and this parameter matrix
can be considered as the knowledge transfer information.
The knowledge transfer information is gathered by adaptive
control in the evolution process. In Algorithm 2, in line 19,
the selected sub-population is evolved for one more generation
to solve the corresponding task. During the evolution
process, as depicted in Algorithm 3, a random mating
Algorithm 3 Evolution Process of Sub-Population i.
Data: Random mating parameter matrix rmp, Population set Pop,
Knowledge transfer rate
kt [, ]
r 01!
Result: New sub-population Newpop
1 Pop ! Q
2 if
3
4
5
6
7
8
9
10
11
12
13 else
14
15
16
17 end
rand (, ) rmpii,
01 1
then
/*Conduct cross-population evolution*/
j ! Roulette-Wheel Selection on
[,..., ,,...,
,
!
rmprmp rmprmp ]
PopPop Popij
iiiiiiK11 1-+,, ,,
Newpop ! optimizer(Pop) on task i
/*Incorporate transfer information*/
if sub-population i is improved then
rmprmp /ktr ,,
ij =
else
rmprmp ktr,,
ij =
end
/*Conduct normal evolution*/
PopPopi
!
Newpop ! optimizer(Pop) on task i
ij *
ij
NOVEMBER 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 25
Re-Evaluation of IoI Vector
Allocation

IEEE Computational Intelligence Magazine - November 2021

Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - November 2021