Goal Clustering: VNS based heuristics

Given a set V of n elements on m attributes, we want to find a partition of V on the minimum number of clusters such that the associated R-squared ratio is at least a given threshold. We denote this problem as Goal Clustering (GC). This problem represents a new perspective, characterizing a different methodology within unsupervised non-hierarchical clustering. In effect, while in the k-means we set the number of clusters in advance and then test the associated R-squared ratio; in the GC we set an R-squared threshold lower limit in advance and minimize k. We present two Variable Neighborhood Search (VNS) based heuristics for the GC problem. The two heuristics use different methodologies to start the VNS algorithms. One is based on the Ward's construction and the other one resorts to the k-means method. Computational tests are conducted over a set of large sized instances in order to show the performance of the two proposed heuristics.