Interval oriented multi-section techniques for global optimization

Authors:
S. Karmakar;S. K. Mahato;A. K. Bhunia
Affiliations:
Department of Mathematics, The University of Burdwan, Burdwan-713104, India;Darjeeling Govt. College, Darjeeling-734101, India;Department of Mathematics, The University of Burdwan, Burdwan-713104, India
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

This paper deals with two different optimization techniques to solve the bound-constrained nonlinear optimization problems based on division criteria of a prescribed search region, finite interval arithmetic and interval ranking in the context of a decision maker's point of view. In the proposed techniques, two different division criteria are introduced where the accepted region is divided into several distinct subregions and in each subregion, the objective function is computed in the form of an interval using interval arithmetic and the subregion containing the best objective value is found by interval ranking. The process is continued until the interval width for each variable in the accepted subregion is negligible. In this way, the global optimal or close to global optimal values of decision variables and the objective function can easily be obtained in the form of an interval with negligible widths. Both the techniques are applied on several benchmark functions and are compared with the existing analytical and heuristic methods.