IEEE Computational Intelligence Magazine - May 2023 - 56

comparison with other state-of-the-art algorithms. Moreover, in
large-scale synthetic networks (i.e., Syn2 and Syn3), MOEA-CPI
still maintains outstanding accuracy due to the combination of
prior information guidance and the self-adjustment ability and
dynamic adaptability ofthe weighting strategy.
The experimental results prove the superiority of our proposed
MOEA-CPI algorithm. There are three main reasons for
this finding. 1) The MOEA-CPI algorithm extracts graph-level
information based on Node2vec and the density-based aggregation
strategy and guides the topological structure reconstruction
and initialization processes according to this graph-level information.
Therefore, the prior layer and initial population can guide
the algorithm from a global perspective. 2) Considering that the
mutation strategy is essentially a node-to-node operation,
MOEA-CPI extracts node-level information based on Jaccard
similarity and appliesthisinformation to guide the mutation strategy.
Since the node-level information is compatible with the
mutation strategy, MOEA-CPI can make the most of the
extracted node-level information. 3) Most existing algorithms do
not distinguish the weight of each network layer. Based on the
modularity obtained by the fast clustering method, the MOEACPI
algorithm can dynamically set the weights of the objective
functions for each layer, which can help the algorithmbetter adapt
to the specific structures ofmultilayer networks.
2) Robustness Experiment
As mentioned above, the proposed MOEA-CPI algorithm
makes full use of both kinds of prior information (i.e., graphlevel
information and node-level information) to guide the
algorithm to distribute similar nodes into the same community,
so that the accuracy and robustness of MOEA-CPI can
be further improved. To evaluate the robustness of the proposed
method, 30 synthetic networks with various structures
and layers (described in Section IV-A2) and three state-of-theart
comparison algorithms are selected for the experiment.
Figure 7 shows that our proposed algorithm performs better
than three classic methods on networks with different
structures and numbers of layers. As shown in Figure 7(a),
although SC-ML and S2-jNMF perform well, the proposed
MOEA-CPI approach exhibits more stable accuracy because
MOEA-CPI also captures prior information, which can guide
the algorithm to find high-quality solutions, especially for networks
with disordered community structures. As Mp becomes
closer to 0.5 in Figure 7(b), the community structures ofmultilayer
networks become more complicated. NMI decreases
are observed for all four algorithms. Notably, SC-ML and
MOEA-CPI still maintain high accuracy. However, when
Dc=0.4, the NMI ofSC-ML shows a larger decline. Although
the structure of the network is complicated (i.e., Mp=0.5 and
Dc=0.2) and leads to a performance decline, our proposed
MOEA-CPI approach achieves good accuracy under the guidance
of prior information. In Figure 7(c) and (d), the performance
of MOEA-CPI is analyzed on networks with various
numbers of layers. Similarly, MOEA-CPI still performs best
56 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2023
FIGURE 7. The experimental robustness analysis results. (a) and (b)
describe the experiments conducted on the networkwith different Mp
and Dc values, where the Mp values in (a) and (b) are 0.4 and 0.5,
respectively. (c) and (d) demonstrate the analyses performed on
networks with different numbers of layers, where the Mp and Dc values of
the networks in (c) are 0.5 and 0.4, and their values in (d) are 0.5 and 0.6.
due to the effect of the prior information. In conclusion, our
proposed MOEA-CPI method can maintain satisfactory
robustness and accuracy due to the synergy of its different
components, that is, the guidance ofthe prior information, the
optimization capability ofthe MOEA, and the adaptive capacity
ofthe weighting strategy for various networks.
D. Discussion
1)Ablation Analysis
The overwhelming performance superiority of MOEA-CPI
has been proven through the overall experimental results in
the above section. To further evaluate the effect ofeach module,
this paper designs an ablation analysis, as shown in
Table III. More specifically, four algorithms are developed to
apply different combinations ofmodules.
Basic applies the original MOEA method, which utilizes
random initialization and traditional genetic operations. In
addition, this algorithm performs community partitioning
depending only on the given topological structure.
Basic+weighted adds the weighting strategy to the
objective function based on the Basic method.
Basic+weighted+Jaccard applies the Jaccard similarity as
the prior information (node-level information) to guide the
mutation operation based on the aforementioned method.
MOEA-CPI is our proposed algorithm, which applies all the
modules proposed in this paper and contains both the weighting
strategy and the prior information-based components (i.e., initialization,
network reconstruction andmutation).
Three phenomena are indicated in Table III. 1) The original
MOEA (the Basic method) cannot address the MCD problem
very well, which leads to unsatisfactory results. After
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