Constrained optimization using a clustering algorithm

In this study, we would like to demonstrate the capabilities of an optimum search clustering algorithm with the approximating solution of some scalar optimization problems with linear and nonlinear constraints. This clustering algorithm, that is, really an evolutionary strategy, determines the local or global minima of the multimodal functions as the center of the clusters. Unlike usual clustering algorithms it approaches the extrema in a single phase, on the basis of the sample points. The handling of the objective function and the constraints are performed separately: the linear and nonlinear constraints are regarded in the form of the measure used with the evolution algorithms, that is, a degree of violation of constraints. The method determines the values and places of the extrema of the usual test examples with an accuracy of about 10^–9.