Differential evolution and particle swarm optimisation in partitional clustering

In recent years, many partitional clustering algorithms based on genetic algorithms (GA) have been proposed to tackle the problem of finding the optimal partition of a data set. Surprisingly, very few studies considered alternative stochastic search heuristics other than GAs or simulated annealing. Two promising algorithms for numerical optimization, which are hardly known outside the heuristic search field, are particle swarm optimisation (PSO) and differential evolution (DE). In this study, we compared the performance of GAs with PSO and DE for a medoid evolution approach to clustering, which Paterlini and Minerva (2003) introduced in a previous paper. Moreover, we compared these results with the nominal classification, k-means and random search (RS) as a lower bound. Our results show that DE is clearly and consistently superior compared to GAs and PSO for hard clustering problems, both in respect to precision as well as robustness (reproducibility) of the results. Only for simple data sets, the GA and PSO can obtain the same quality of results in contrast to k-means and RS, and, as expected, for trivial problems all algorithms can obtain comparable results. Apart from superior performance, DE is very easy to implement and requires hardly any parameter tuning compared to substantial tuning for GAs and PSOs. Our study shows that DE rather than GAs should receive primary attention in partitional cluster algorithms. Key-words: Cluster analysis, partitional clustering, differential evolution, particle swarm optimization, genetic algorithms.