IEEE Computational Intelligence Magazine - May 2023 - 47

To tackle this problem, this paper proposes a novel multiobjective
evolutionary algorithm based on consensus prior
information (MOEA-CPI). The proposed algorithm takes full
advantage ofprior informationtoguide the MOEAwithrespect
to topological structures, initializations, and the optimization
process. More specifically, this paper firstextractstwo kindsof
prior information, i.e., graph-level and node-level information,
based on Node2vec andJaccard similarity, respectively. Then, the
prior layer and a high-quality initial population are constructed on
the basis ofthe graph-level information. During the optimization
process, the genetic operator, which integrates the weighting
strategy and node-level information, is applied to guide the
algorithm to distribute similar nodes into the same community.
Extensive experiments are implemented to prove the superior
performance ofMOEA-CPI over the state-of-the-art methods.
networks into account, which may lead to unsatisfactory accuracy
and robustness [1].
To overcome this problem, researchers have proposed a numI.
Introduction
I
n the real world, connections between entities are pluralistic.
However, single-layer networks are unable to effectively
represent the multi-relationships between entities and may
result in network information loss [1].Therefore,multilayer
networks have gradually become a research hotspot due to their
higher effectiveness when addressing complex systems with multirelationships
[2], [3]. A multilayer network (multiplex network or
multi-relationship network) contains a series of single-layer networks
representing several independent relationships. In addition,
the connections in the different layers ofsuch networks are interrelated,
so some complementary information remains between different
layers. Therefore, detecting the community structures of
multilayer networks becomes a research topic that has attracted
much attention [1], [4], [5], [6].
Communitiesare essential attributesofnetworks thatindicate
their potential characteristics [7], [8]. For example, the communities
in protein networks are the protein complexes that regulate
gene expression [1]. Generally, a community is actually a group of
nodes that are closely interconnected [9]. In recent years, community
detection (CD) algorithms for single-layer networks have
made great achievements. However, due to the particularity of
themultilayer networks mentioned above, a nodemay also belong
to different communities in different layers. For example, the
community structures ofmultilayer networks are different in each
layer, resulting in high CD complexity [10], [11].Therefore,itis
worth investigating how to find the most appropriate consensus
community partition by using both the information contained in
each network layer and the complementary information existing
across various layers [1], [4].
Over the last few years, some multilayer network CD (MCD)
algorithms have been proposed [1]. The most intuitive approach is
to use a single-layer network CD algorithm directly via strategies,
such as merging the given multilayer network into a single-layer
network or applying the single-layer networkmethod to each network
layer [12], [13]. However,Ma et al. noted that suchmethods
cannot take the specific structural characteristics of multilayer
ber ofMCD algorithms [1], [4], [14], [15], [16], [17].Byutilizing
different strategies and models to simultaneously consider the
information contained in each network layer, such algorithms can
protect the structural integrity ofmultilayer networks and eventually
extract consensus community partitions. However, one problem
remains: the majority ofthe existing methods only depend on
topological information, leading to unsatisfactory accuracy, especially
when the input network structure is complicated. Yang
et al. indicated that prior information can guide an algorithm to
find the best solution, especially for a network with unclear community
structures [18]. Therefore, how to extract the most out of
the obtained prior information is still a question of great value.
Moreover, the existing methods pay little attention to the structures
ofmultilayer networks. However, the clarity ofthe community
structure in each layer is different, and how to detect these
clarity levels and dynamically adjust the utilized algorithm also
poses a major problem.
To tackle the above problems, this paper proposes a novel
multi-objective evolutionary algorithm based on consensus prior
information (named MOEA-CPI). A comparison between the
traditional algorithm and the proposed MOEA-CPI is described
in Figure 1. To further improve the accuracy and robustness ofthe
traditional algorithm, as shown in Figure 1(b), the main idea of
MOEA-CPI is to combine the consensus prior information and
an MOEA, which can guide the algorithm to find accurate solutions.
More specifically, MOEA-CPI first extracts the prior information,
i.e., graph-level information, through Node2vec and
extracts node-level information via Jaccard similarity. The graphlevel
information is used to generate the prior layer and initial population.
The prior layer can change the topological structure ofthe
network, and a high-quality initialization can help the algorithm
find better solutions. During the optimization process, a mutation
strategy based on the node-level information and a weighting
strategy are proposed to improve the optimization capability of
the algorithm and dynamically adapt to the given multilayer network,
respectively. A series of thorough experiments show that
FIGURE 1. Comparison between the traditional MOEA and our
proposed algorithm.
MAY 2023 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 47
IEEE Computational Intelligence Magazine - May 2023

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