IEEE Computational Intelligence Magazine - February 2023 - 63

TABLE III The probability that the two output seed sets
obtained by MTEFIM with MCSS and SOSS on four
representative networks are the same over 20 independent
runs.
NETWORKS
Email URIV
K
3
FIGURE 10 An illustration of two individuals p1
andp2 represent the same seed set.
on a small-scale network. Therefore, the seed set obtained by different
methods does not show a clear distinction. Then, in the
large-scale Fb-pages-public-figure network, the performance
gap ofdifferent methods is obvious. The efficiency ofthe knowledge
transfer process in MTEFIM is confirmed since all EMTO
methods have the same basic genetic operations and selecting
output seed set strategy except for knowledge transfer. Because
knowledge transfer in MFEA is purposeless,MFEA cannot adaptively
transfer shared knowledge across transformations. In the
seed set encoding strategy adopted in this article, multiple individuals
may represent the same seed set, as shown in Fig. 10. This
phenomenon may lead to the inefficiency of the knowledge
transfer process in MFEAII, EMEA, and SBGA. Taking the
example ofMFEAII, different individuals representing the same
seed set may affect the accurate representation ofthe probability
distribution of the current task, resulting in the model inaccuracy.
In the knowledge transfer strategy, the degree of overlap
between seed sets is estimated to capture the relationship
between the transformations, thus avoiding this issue.
C.Analysis ofInter-Transformation Relationship Estimation
The inter-transformation relationship R is central to controlling
the degree ofknowledge transfer across transformations in
Hamsterster
12
21
30
3
Ego-facebook
12
21
30
3
Fb-pages-publicfigure
12
21
30
3
12
21
30
PROBABILITY
100%
100%
100%
100%
100%
100%
100%
100%
100%
100%
100%
100%
90%
90%
75%
75%
MTEFIM.
By calculating the degree ofoverlap across populations
online, the knowledge exchange between transformations
is adaptive during the evolutionary process. Fig. 11
shows an illustration ofthe parameter r12 in MTEFIM on four
representative social networks, where k is set to 30. In these
figures, the x-axis represents function evaluations, and the yaxis
refers to the parameter r12.
These curves highlight the synergies between transformation
pairs ofthe EDV and the TIS. As shown in Fig. 11, a high value
of r12 is estimated on all networks, showing high similarities
across the EDV and the TIS. This is consistent with the conclusion
of the similarity analysis between fitness landscapes (see
Fig. 1). Therefore, based on the observations, the inter-transformation
relationship estimation can capture potential synergies
between transformations. In addition, the number oftransferred
individuals is determined by r12. In different stages ofevolution,
the estimated r12 adaptively guides different degrees of knowledge
exchange to accelerate theMTEFIMconvergence.
FIGURE 11 An illustration of the parameter r12 in MTEFIM on four
representative real-world social networks, where k is set to 30. (a)
Email URIV, (b) Hamsterster, (c) Ego-facebook, and (d) Fb-pagespublic-figure.
D.Analysis
of Selecting Output Seed Set
After obtaining the optimal individual of each transformation,
the comprehensive performance of the individuals in all transformations
is considered to select the final output seed set.
Table III lists the probability that the two output seed sets
obtained by MTEFIM with MCSS and SOSS on four representative
networks are the same over 20 independent runs,
where the user's prior preference C is set to 1/S to treat each
transformation equally.
It can be seen from Table III that MCSS and SOSS select
the same output seed set in most cases, which indicates the
FEBRUARY 2023 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 63
IEEE Computational Intelligence Magazine - February 2023

Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - February 2023
