A New Global Optimization Method based on Clustering

The clustering technique and parabolic approximation are used in this method.

This method is basically similar the other evolutionary methods. The initial population, and some of the new generations are created randomly. In each step, the evaluated populations are clustered. The clusters can locate to minima, maxima or between of them. Firstly, undesirable clusters are eliminated. To ensure the local optimum of each cluster, the multidimensional parabola is fitted to each cluster using quadratic least squares estimation (LSE). The usage of parabola fitting brings deterministic properties to the method. By this way, it is quarantined to reach global optimum.