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Calibration of parameters in Dynamic Energy Budget models using Direct-Search methods

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Abstract

Dynamic Energy Budget (DEB) theory aims to capture the quantitative aspects of metabolism at the individual level, for all species. The parametrization of a DEB model is based on information obtained through the observation of natural populations and experimental research. Currently the DEB toolbox estimates these parameters using the Nelder–Mead Simplex method, a derivative-free direct-search method. However, this procedure presents some limitations regarding convergence and how to address constraints. Framed in the calibration of parameters in DEB theory, this work presents a numerical comparison between the Nelder–Mead Simplex method and the SID-PSM algorithm, a Directional Direct-Search method for which convergence can be established both for unconstrained and constrained problems. A hybrid version of the two methods, named as Simplex Directional Direct-Search, provides a robust and efficient algorithm, able to solve the constrained optimization problems resulting from the parametrization of the biological models.

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Authors and Affiliations

  1. MARETEC - Marine, Environment and Technology Center, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

    J. V. Morais & G. M. Marques

  2. Department of Mathematics, FCT-UNL-CMA, Campus da Caparica, 2829-516, Caparica, Portugal

    A. L. Custódio

Authors
  1. J. V. Morais
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  2. A. L. Custódio
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  3. G. M. Marques
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Corresponding author

Correspondence to J. V. Morais.

Additional information

Support for J. V. Morais was provided by FCT/MCTES (PIDDAC) through Project UID/EEA/50009/2013. Support for A. L. Custódio was provided by Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) under the Project UID/MAT/00297/2013 (CMA).

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Morais, J.V., Custódio, A.L. & Marques, G.M. Calibration of parameters in Dynamic Energy Budget models using Direct-Search methods. J. Math. Biol. 78, 1439–1458 (2019). https://doi.org/10.1007/s00285-018-1315-x

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  • DOI: https://doi.org/10.1007/s00285-018-1315-x

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