Clustering methods aim to categorize the elements of a dataset into groups according to
the similarities and dissimilarities of the elements. This paper proposes the Multi-objective
Clustering Algorithm (MCA), which combines clustering methods with the Nondominated
Sorting Genetic Algorithm II. In this way, the proposed algorithm can automatically define
the optimal number of clusters and partition the elements based on clustering measures. For
this, 6 intra-clustering and 7 inter-clustering measures are explored, combining them 2-to-2,
to define the most appropriate pair of measures to be used in a bi-objective approach. Out
of the 42 possible combinations, 6 of them were considered the most appropriate, since they
showed an explicitly conflicting behavior among the measures. The results of these 6 Pareto
fronts were combined into two Pareto fronts, according to the measure of intra-clustering
that the combination has in common. The elements of these Pareto fronts were analyzed
in terms of dominance, so the nondominanted ones were kept, generating a hybrid Pareto
front composed of solutions provided by different combinations of measures. The presented
approach was validated on three benchmark datasets and also on a real dataset. The results
were satisfactory since the proposed algorithm could estimate the optimal number of clusters
and suitable dataset partitions. The obtained results were compared with the classical kmeans
and DBSCAN algorithms, and also two hybrid approaches, the Clustering Differential
Evolution, and the Game-Based k-means algorithms. The MCA results demonstrated that
they are competitive, mainly for the advancement of providing a set of optimum solutions
for the decision-maker.
