Ramadas, Gisela C. V.Fernandes, Edite M. G. P.Rocha, Ana Maria A. C.2015-01-152015-01-152014978-3-319-09128-0978-3-319-09129-7http://hdl.handle.net/10400.22/5409In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global minimizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several iterations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.engSystem of equationsMultiple rootsPenalty functionRepulsionHarmony searchjournal article10.1007/978-3-319-09129-7_10