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Testing Nelder-Mead Based Repulsion Algorithms for Multiple Roots of Nonlinear Systems via a Two-Level Factorial Design of Experiments

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  • Gisela C V Ramadas
  • Ana Maria A C Rocha
  • Edite M G P Fernandes

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.

Suggested Citation

  • Gisela C V Ramadas & Ana Maria A C Rocha & Edite M G P Fernandes, 2015. "Testing Nelder-Mead Based Repulsion Algorithms for Multiple Roots of Nonlinear Systems via a Two-Level Factorial Design of Experiments," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-30, April.
    • Handle: RePEc:plo:pone00:0121844
    DOI: 10.1371/journal.pone.0121844
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    References listed on IDEAS

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    1. Ricardo Silva & Mauricio Resende & Panos Pardalos, 2014. "Finding multiple roots of a box-constrained system of nonlinear equations with a biased random-key genetic algorithm," Journal of Global Optimization, Springer, vol. 60(2), pages 289-306, October.
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