IEEE Computational Intelligence Magazine - February 2023 - 53

Each transformation is assigned an evolutionary solver. Three
major components of MTEFIM are conducted via: 1)
estimating the potential relationship across transformations
based on the degree of overlap across individuals of different
populations, 2) transferring individuals across populations
adaptively according to the inter-transformation relationship,
and 3) selecting the final output seed set containing all the
transformation's knowledge. The effectiveness ofMTEFIM is
validated on both benchmarks and real-world social networks.
The experimental results show that MTEFIM can efficiently
utilize the potentially transferable knowledge across multiple
transformations to achieve highly competitive performance
compared to several popular IM-specific methods. The
implementation of MTEFIM can be accessed through the
external link in the footnote.1
I. Introduction
S
ocial networks are employed to describe the communication
in convention and connection between people
in a word-of-mouth manner [1]. With the rapid
increase in the number ofusers, new online social network
sites or apps such as Twitter, MicroBlog, TikTok, and
Instagram have become the mainstream networking platforms
for people to share and exchange ideas, providing great convenience
for marketers to target prospective customers [2], [3].
In recent years, the rise of these websites or apps has
boosted a complete industrial chain in social media marketing,
including influencers and marketing agencies [4]. Influencers,
such as Charli D' Amelio and Addison Rae, have tens of millions
of followers on TikTok. Usually, these influencer marketing
agencies promote their products by collaborating with
initial influencers (such as actors and celebrities), which is
proven effective and successful by the market. Finding influencers
who can help engage new consumers exponentially is
essential to the success ofinfluencer marketing [5]. Coincidentally,
this issue also appears in a series of practical applications
in political campaigns [6] and epidemic analyses [7], which is at
the core ofthe influence maximization (IM) problem.
The above IM problem intends to select a group of users
from social networks, called a seed set, to maximize the spread
of influence under an information diffusion process [8]. Some
popular models have been proposed to study the diffusion process,
such as the independent cascade (IC) [9], weighted cascade
(WC) [10], and linear threshold (LT) [11], which
simulate the independent or collective behavior of the seed
set. Since information production is interfered by a variety of
social or biological factors in different problems, existing works
tend to employ network structure information to find those
influencers under these models [12]. Domingos et al. [8] first
formalized IM as an NP-hard combinatorial optimization
problem, which shows that only the optimal set with a certain
1[Online]. Available: https://github.com/xiaofangxd/MTEFIM
degree of approximation could be found. Domingos et al. [8]
further proposed a series ofgreedy-based IM algorithms. Theoretical
results show that under the IC model, the greedy
method can produce an optimal solution with an accuracy of
no less than 11/e. Then, several algorithms are developed to
address the inefficiency and insufficient scalability of the
greedy method. Leskovec et al. [13] proposed an improved
greedy algorithm with a " Cost-Efficient Lazy Forward
(CELF) " strategy, which is reported to be 700 times faster than
the greedy method. Goyal et al. [14] further extended
CELFþþ by considering the submodularity property of IM.
In addition, Chen et al. [10] proposed a new greedy algorithm
to conduct the diffusion process on a network after pruning.
However, these simulation-based greedy methods require
thousands of Monte Carlo simulations to evaluate influence
spread, which is unattainable in practice.
To overcome the limitations ofsimulation-based methods,
several heuristic methods have been presented to handle largescale
networks. A simple ranking idea can be employed to select
the seed set, such as using degree, PageRank [15], and distance
centrality [16]. Chen et al. [10] designed a degree discount heuristic
method, which assumes that the influence spread increases
with the user's degree. Wang et al. [17] further extended to a
generalized degree discount heuristic. However, these approximation
methods may be quite different from the influence diffusion
process (see the experimental analysis in [9], [10]).
In the last decade, a series ofmeta-heuristic algorithms have
been proposed to solve IM problems due to their superiority in
solving NP-hard problems, such as the simulated annealing (SA)
and the evolutionary algorithm (EA). These methods have
excellent performance on many real-world networks. Jiang et al.
[18] proposed a cheap approximate model, named the expected
diffusion value (EDV), to replace the diffusion process and optimize
the objective by the SA algorithm. Lee et al. [19] introduced
an approximation model for the diffusion process by
limiting the spread on users with two hops ofthe seed set. Gong
et al. [20] reduced the search space for IM problems by using
community information in a social network, and proposed a
memetic algorithm to optimize the two-hop influence spread,
called TIS in this article. In addition, Gong et al. [21] proposed a
discrete particle swarm optimization algorithm to optimize the
local influence estimation (LIE) that approximates the 2-hop
influence spread. Wang et al. [22] presented a new influence estimation
model by considering the estimate and variance ofusers
in a 2-hop neighborhood, called IEEV in this article. Singh et al.
[23] introduced a learning-based particle swarm optimization for
IM and extended the EDV to approximate two-desired areas. In
addition, an ant colony algorithm [24] is proposed to optimize
the local influence evaluation. Li et al. [25] presented a discrete
crow search algorithm based on the network topology structure.
Ma et al. [26] proposed a novel evolutionary deep reinforcement
learning algorithm for IM problems in complex networks, where
the IM problem is transformed into a continuous weight optimization
problem ofdeep Q-networks. Furthermore, many methods
combining reinforcement learning and network embedding
FEBRUARY 2023 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 53
https://github.com/xiaofangxd/MTEFIM
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