Clustering is one of the most successful techniques for data mining, statistics, neuronal network, territorial design and others. In this kind of grouping, the parameters are usually optimized by means of a single objective.In particular, the partitioning is a clustering problem in the combinatorial optimization area and it has been well discussed and analyzed. However, real applications are far to be solved without the application of Multiobjective approaches. In this research paper we present a bi-objective partitioning proposal to solve the problem that involves census-based variables and geographical data for a territorial design problem.This is known to be a high complex computational problem and we it named Multiobjetive Clustering (MC).Two quality measures for clustering are chosen, which are simultaneously optimized in the partitioning process using Variable Neighborhood Search (VNS) for the optimization phase. The first quality measure obeys a geometrical concept of distances, whereas the second measure focuses in the calculus of the balance for a descriptive variable. In the multiobjetive clustering algorithm proposed(classification by partitioning), ithighlights a clear advantage with respect to the classical clustering algorithms such asK-meansand K-medoids which is the addition of another cost function which performs over variables vectors. The obtained results are shown in the Pareto frontier constructed with the approximate solutions generated by VNS, which are non-dominated and non-comparable with a similar mechanism on which the minimals of a Hasse Diagram and the Maxima Set are reached.