  In this paper, we first propose a graph neural network encoding method for
multiobjective evolutionary algorithm to handle the community detection problem
in complex attribute networks. In the graph neural network encoding method,
each edge in an attribute network is associated with a continuous variable.
Through non-linear transformation, a continuous valued vector (i.e. a
concatenation of the continuous variables associated with the edges) is
transferred to a discrete valued community grouping solution. Further, two
objective functions for single- and multi-attribute network are proposed to
evaluate the attribute homogeneity of the nodes in communities, respectively.
Based on the new encoding method and the two objectives, a multiobjective
evolutionary algorithm (MOEA) based upon NSGA-II, termed as continuous encoding
MOEA, is developed for the transformed community detection problem with
continuous decision variables. Experimental results on single- and
multi-attribute networks with different types show that the developed algorithm
performs significantly better than some well-known evolutionary and
non-evolutionary based algorithms. The fitness landscape analysis verifies that
the transformed community detection problems have smoother landscapes than
those of the original problems, which justifies the effectiveness of the
proposed graph neural network encoding method.
