Abstract: Various methods have been proposed to utilize Genetic Algorithms (GA) in handling the clustering problem. GA work on encoded strings, namely chromosomes, and the representation of different clusters as a linear structure is an important issue about the usage of GA in this domain. In this paper, we present a novel encoding scheme that uses links to identify clusters in a partition. Particularly, we restrict the links so that objects to be clustered form a linear pseudo-graph. A one-to-one mapping is thus achieved between the genotype and phenotype spaces. The other feature of the proposed approach is the use of multiple objectives in the process. One of the two objectives we use is to minimize the Total Within Cluster Variation (TWCV), identical to the one used by other k-means clustering approaches. However, unlike other k-means methods, number of clusters is not required specified in advance. Combined with a second objective, minimizing the number of clusters in a partition, our approach obtains the optimal partitions for all the possible numbers of clusters in the Pareto Optimal set returned by a single GA run. The performance of the proposed approach has been tested using two well-known data sets, namely Iris Data and Ruspini Data. The obtained results are compared with the output of the classical Group Number Encoding and it has been observed that a clear improvement has been achieved with the new representation.
