IEEE Computational Intelligence Magazine - February 2023 - 64

TABLE IV Comparison of the statistical results of the influence spread (Average Standard) obtained by different transformations
over 20 independent runs.
NETWORKS
K
EDV
GN-Network 3 9.1620.074
TIS
9.0040.212
PS
EDV&TIS
EDV&PS
TIS&PS
EDV&TIS&PS
9.7420.263 10.3960.044 10.4350.058 10.3960.166 10.2970.141
12 33.0410.065 32.2200.137 32.0560.663 34.2090.105 34.2660.889 34.3130.377 34.1160.139
21 49.6100.125 48.8450.256 47.2661.055 50.9950.193 50.9910.120 50.4400.212 50.9960.399
30 62.1620.135 61.1290.254 60.1020.841 63.5960.161 63.6790.086 63.1400.334 63.4990.151
NetHEPT
3 41.4971.510 40.8721.402 37.5344.511 45.4110.001 45.4980.001 47.3271.214 45.4980.924
12 107.0210.000 102.8785.656 107.3423.042 116.4930.144 116.4684.318 115.8013.932 116.5580.137
21 156.0385.480 154.2251.267 139.7914.677 158.6830.944 159.4040.353 159.9332.316 159.6681.043
30 189.3740.609 187.7141.553 165.2734.759 194.2120.862 194.0430.153 191.9380.923 193.8191.168
effectiveness ofthe proposed output seed set selection strategy.
It is worth noting that in the large-scale Fb-pages-publicfigure
network, the individual with the best overall performance
among all transformations is not necessarily the best in
the Monte Carlo simulation. This may be because there is
some preference knowledge in the search process of different
transformations, resulting in optimal individual deviations.
However, the proposed method provides an efficient output
seed set selection strategy that avoids expensive Monte Carlo
simulations.
E.Analysis ofSelecting Transformations
In this section, the performance of MTEFIM with different
transformations is further demonstrated. In addition to EDV
and TIS, another commonly used transformation, probability
sorting (PS), is considered, which is a typical diffusion model
reduction proxy model [29]. PS computes a simplified representative
instance ofthe studied social network. A single diffusion
simulation is performed on PS to approximate the
diffusion process on the original social network. Table IV lists
the influence spread obtained by different combinations of
transformations on the small-scale GN network and the largescale
NetHEPT network over 20 independent runs, where
the size of the selected seed set k is set to 3, 12, 21, and 30.
Compared to optimizing each transformation independently,
optimizing any combination oftransformations has better performance
in terms of the influence spread, in which useful
knowledge carried by transferred individuals can be efficiently
shared. Furthermore, different combinations of transformations
have a similar performance, which also shows that the
proposed method can cope with scenarios with different proxy
models rather than being tailored for a certain one.
F. Performance Comparison
To further verify MTEFIM's effectiveness, several comparative
experiments are conducted in terms of the influence spread
and computational time. Fig. 12 reports the influence spread
of various methods for IM on both the GN benchmark network
and real-world social networks.
The experimental results in Fig. 12(a) show that MTEFIM
has a better performance than the heuristic methods (Degree,
64 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | FEBRUARY 2023
PageRank, and SDD) in the GN networks, an observation
that is also prevalent in the real-world networks (see Fig. 12
(b)-(f)). As the size of seed set k (search space) increases, the
heuristic method is more likely to be trapped in local optima.
This is because they focus on improving the ability to exploit
the landscape, while ignoring the ability to explore the landscape.
As shown in Fig. 12(b)-(f), different methods for IM
have different performances on real-world networks. In
Fig. 12(b), the differences in the influence spread ofnine algorithms
are not obvious for the email network. With the
increase of k, the influence obtained by all methods has
steadily extended. Compared with the single-transformation
FIGURE 12 Influence spread obtained by different methods for IM on
both the GN benchmark network and real-world social networks. (a)
GN Network, (b) Email URIV, (c) Hamsterster, (d) Ego-facebook, (e) Fbpages-public-figure,
and (f) NetHEPT.

IEEE Computational Intelligence Magazine - February 2023

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