Finding Multiple Roots of Systems of Nonlinear Equations by a Hybrid Harmony Search-Based Multistart Method

Authors

Gisela C. V. Ramadas, Department of Mathematics, School of Engineering, Polytechnic of Porto, 4200-072 Porto, PortugalFollow
Edite M. G. P. Fernandes, Algoritmi Research Centre, University of Minho, 4710-057 Braga, PortugalFollow
Ana Maria A. C. Rocha, Algoritmi Research Centre, University of Minho, 4710-057 Braga, PortugalFollow

Author Country (or Countries)

Portugal

Abstract

A multistart (MS) clustering technique to compute multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function is presented. The search procedure that is invoked to converge to a root, starting from a randomly generated point inside the search space, is a new variant of the harmony search (HS) metaheuristic. The HS draws its inspiration from an artistic process, the improvisation process of musicians seeking a wonderful harmony. The new hybrid HS algorithm is based on an improvisation operator that mimics the best harmony and uses the idea of a differential variation, borrowed from the differential evolution algorithm. Computational experiments involving a benchmark set of small and large dimensional problems with multiple roots are presented. The results show that the proposed hybrid HS-based MS algorithm is effective in locating multiple roots and competitive when compared with other metaheuristics.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/120102

Recommended Citation

C. V. Ramadas, Gisela; M. G. P. Fernandes, Edite; and Maria A. C. Rocha, Ana (2018) "Finding Multiple Roots of Systems of Nonlinear Equations by a Hybrid Harmony Search-Based Multistart Method," Applied Mathematics & Information Sciences: Vol. 12: Iss. 1, Article 2.
DOI: http://dx.doi.org/10.18576/amis/120102
Available at: https://digitalcommons.aaru.edu.jo/amis/vol12/iss1/2