Evolutionary Algorithm Reinforce with Linear Projection and Clustering

From the view point of practical applications and the theory of evolutionary algorithms, an important problem is the location of many local extrema showing at the same time the position of a global extremum. To accomplish this task, a new space exploration procedure is proposed by applying a so-called "linear projection". Additionally, a clustering technique is introduced to the selection procedure. Operation of the method is illustrated by searching the function of two and ten variables with extrema with a box-type limitation. Each time, irrespective of the number of clusters, calculations enabled location of many extrema.