A clustering method for global optimization based on the k-th nearest neighbour

In this paper we describe a stochastic method for global optimization based on a uniform sampling in the search domain. After a reduction of the sample, computing the distance between the remaining points and using the distribution of the k-th nearest neighbor enables clusters of points to be built up, hopefully fitting the regions of attraction of significant local optima; from each of these a local search is started. The properties of the method are analyzed, and detailed computational results on standard test functions are provided.