IEEE Computational Intelligence Magazine - February 2023 - 61

TABLE I The basic characteristics of five real-world networks
used in this article.
TABLE II Comparison of the statistical results of the
influence spread (Average Standard) obtained by MTEFIM
and MTEFIM-NK over 20 independent runs.
NETWORKS
Email URIV
Hamsterster
Ego-facebook
Fb-pages-public-figure
NetHEPT
1.1K
2.4K
4.0K
j VjjE j
5.5K
11.6K
15.2K
16.6K
88K
67K
58.9K
AC
0.220
0.538
0.605
0.179
0.346
P
0.05
0.03
0.02
0.04
0.05
A. Experiment Setting
1) Datasets
The performance ofMTEFIM is validated on a well-known synthetic
network and five real-world networks [54], [55], [56], [57],
including GN-Network, Email URIV, Hamsterster, Ego-facebook,
Fb-pages-public-figure, and NetHEPT2. The GN networks
are employed to represent modular networks with four
communities and 128 nodes, where each node has the same
degree of16. The parameter m is used to control the number of
links between communities. All baselines are tested on a GN
benchmark network with m¼ 1 in this article. Email URIV is the
category ofemail networks. The Hamsterster network represents
the friendships and family connections between members of the
website http://www.hamsterster.com. The Ego-facebook network
consists of friends lists from survey participants using Facebook.
The large-scale Fb-pages-public-figure network describes
Facebook page networks of different categories. The large-scale
NetHEPT is a collaborative network of paper co-authors. The
basic characteristics ofthese networks are shown in Table I, where
jVj and j Ej denote the number of nodes and edges, respectively.
ACis the average clustering coefficient. The ICmodel, as a
widely popular influence spread model, is employed in this article.
According to j Vj and AC,the configuration of the activation
probability p in the ICmodel is listed in Table I. In addition, EDV
and TIS, two popular proxy models, are selected as alternative
transformations ofIMproblems.
2)Methods
To demonstrate the effectiveness of knowledge transfer in
MTEFIM, MTEFIM-NK, a variant version of MTEFIM, is
constructed by removing the knowledge transfer process
(Lines 10
13 in Algorithm 1). In addition, four popular
EMTO methods are regarded as comparison algorithms to
illustrate the effectiveness of the proposed knowledge transfer
strategy, including MFEA [33], MFEAII [36], EMEA [34],
and SBEA [35]. MFEA, the first one tailored for the MTO
problem, has been applied to many practical problems [58],
[59], [60], [61]. MFEAII tries to minimize the negative transfer
tendency across tasks, to improve knowledge utilization in
MFEA. EMEA, an explicit EMTO algorithm, performs individual
transfers across tasks using a denoising autoencoder.
SBEA is a novel many-task optimization algorithm inspired by
2[Online]. Available: https://networkrepository.com
NETWORKS
GN-Network
K
3
MTEFIM
MTEFIM-NK
10.3960.044 9.2240.206(-)
Email URIV
12 34.2090.105 32.0430.117(-)
21 50.9950.193 48.6580.286(-)
30 63.5960.161 61.8430.572(-)
46.9630.373 45.4760.452(-)
94.7140.683()
3
12 94.7140.000
Hamsterster
21 124.070.810 122.7691.242(-)
30 146.7760.574 145.3410.729(-)
202.3820.021 202.3360.025()
231.6530.000()
12 231.6530.000
Ego-facebook
21 255.1631.043 252.6191.143(-)
30 270.0740.962 267.9611.549(-)
868.3030.000()
3
868.3030.000
Fb-pages-public-figure 3
12 923.1778.409 889.9766.652(-)
21 932.3734.190 923.0040.179(-)
30 949.30910.298 924.2213.575(-)
1168.3770.906 1165.7271.112(-)
NetHEPT
12 1183.9863.894 1170.8901.143(-)
21 1203.1104.854 1178.0630.863(-)
30 1225.2327.250 1181.3784.460(-)
45.4110.001 40.0061.402(-)
3
-//þ
12 116.4930.144 102.9090.250(-)
21 158.6830.944 154.8921.833(-)
30 194.2120.862 187.4532.202(-)
0/4/20
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the symbiosis in biocoenosis. All methods use the same genetic
operators and SOSS proposed in this article for a fair comparison.
The population size in MFEA and MFEAII is 200, and
the population size of each transformation in the other methods
is set to 100. The probabilities of crossover and mutation
are accordingly set to 1.0 and 1/k. The maximum number of
function evaluations in all methods is set to 5000S, where S
is the number oftransformations.
Eight popular methods for the IM problem are selected as
baselines to verify the performance of MTEFIM, including
Degree [62],PageRank[63],SDD [10],CELFþþ [14], EDVEA
[18],TISEA [19],MA-IM [20],and EDRL-LM[26].Degree,
PageRank, and SDD are three popular heuristic methods. These
methods sort nodes according to different indicators and then
select the top k nodes as the seed set. CELFþþ is an improved
greedy algorithm that exploits the sub-modularity ofthe objective
function. The number ofMonte-Carlo simulations is set to 10000
in this method. Three popular genetic operator-based EAs are
taken as comparison algorithms. The optimization objectives of
EDVEA and TISEA are accordingly EDV and TIS. The same
genetic operators are employed in these methods for a fair comparison.
MA-IM is a popular memetic algorithm for the IM problem
FEBRUARY 2023 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 61
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http://www.hamsterster.com https://networkrepository.com
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