  A variety of clustering criteria has been applied as an objective function in
Evolutionary Multi-Objective Clustering approaches (EMOCs). However, most EMOCs
do not provide detailed analysis regarding the choice and usage of the
objective functions. Aiming to support a better choice and definition of the
objectives in the EMOCs, this paper proposes an analysis of the admissibility
of the clustering criteria in evolutionary optimization by examining the search
direction and its potential in finding optimal results. As a result, we
demonstrate how the admissibility of the objective functions can influence the
optimization. Furthermore, we provide insights regarding the combinations and
usage of the clustering criteria in the EMOCs.
