Accumulated densification and applications to global optimization

Abstract

Purpose -In this article the aim is to propose a new form to densify parallelepipeds of R N by sequences of a-dense curves with accumulated densities. Design/methodology/approach -This will be done by using a basic a-densification technique and adding the new concept of sequence of a-dense curves with accumulated density to improve the resolution of some global optimization problems. Findings -It is found that the new technique based on sequences of a-dense curves with accumulated densities allows to simplify considerably the process consisting on the exploration of the set of optimizer points of an objective function with feasible set a parallelepiped K of R N . Indeed, since the sequence of the images of the curves of a sequence of a-dense curves with accumulated density is expansive, in each new step of the algorithm it is only necessary to explore a residual subset. On the other hand, since the sequence of their densities is decreasing and tends to zero, the convergence of the algorithm is assured. Practical implications -The results of this new technique of densification by sequences of a-dense curves with accumulated densities will be applied to densify the feasible set of an objective function which minimizes the quadratic error produced by the adjustment of a model based on a beta probability density function which is largely used in studies on the transition-time of forest vegetation. Originality/value -A sequence of a-dense curves with accumulated density represents an original concept to be added to the set of techniques to optimize a multivariable function by the reduction to only one variable as a new application of a-dense curves theory to the global optimization.