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. 2015 Apr 13;10(4):e0121844.
doi: 10.1371/journal.pone.0121844. eCollection 2015.

Testing Nelder-Mead based repulsion algorithms for multiple roots of nonlinear systems via a two-level factorial design of experiments

Gisela C V Ramadas  1 , Ana Maria A C Rocha  2 , Edite M G P Fernandes  2
Affiliations

Testing Nelder-Mead based repulsion algorithms for multiple roots of nonlinear systems via a two-level factorial design of experiments

Gisela C V Ramadas et al. PLoS One. .

Abstract

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. The ‘erf’ penalty for different δ.
Fig 2
Fig 2. Half-normal plot of effects for Y p.
Fig 3
Fig 3. Half-normal plot of effects for Y e.
Fig 4
Fig 4. Half-normal plot of effects for Y t.
See this image and copyright information in PMC

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